Figure 1. Example of the GNSS signal propagation using ray-tracing and a 3D building map.
A particle-filter-based positioning method using a 3D map to rectify the errors created by multipath and non-line-of-sight signals on the positioning result delivered by a low-cost single-frequency GPS receiver takes a multi-GNSS approach, using the combined signals of GPS, GLONASS and QZSS. The method outperforms conventional positioning in availability and positioning accuracy. It will likely be fused with other sensors in a future pedestrian navigation application.
By Li-Ta Hsu, Shunsuke Miura and Shunsuke Kamijo
GPS provides an accurate and reliable positioning/timing service for pedestrian application in open field environments. Unfortunately, its positioning performance in urban areas still has a lot of room for improvement, due to signal blockages and reflections caused by tall buildings. The signal reflections can be divided into multipath and non-line-of-sight (NLOS) effects. Recently, use of 3D building models as aiding information to mitigate or exclude multipath and NLOS effects has become a promising area of study.
At first, researchers used the 3D map model to simulate multipath effects to assess the single-reflection environment of a city. Subsequently, the metric of NLOS signal exclusion using an elevation-enhanced map, extracted from a 3D map, was developed and tested using real vehicular data. An extended idea of identifying NLOS signals using an infrared camera onboard a vehicle has been suggested. The potential of using a dynamic 3D map to design a multipath-exclusion filter for a vehicle-based tightly coupled GPS/INS integration system has also been studied. A forecast satellite visibility based on a 3D urban model to exclude NLOS signals in urban areas was developed.
The research approaches outlined above seek to exclude the NLOS signal; however, the exclusion is very likely to cause a horizontal dilution of precision distortion scenario, due to the blockage of buildings along the two sides of streets. In other words, the lateral (cross direction) positioning error would be much larger than that of the along-track direction.
Therefore, approaches applying multipath and NLOS signals as measurements become essential. One of the most common methods, the shadow-matching method, uses 3D building models to predict satellite visibility and compare it with measured satellite visibility to improve the cross street positioning accuracy. A multipath and NLOS delay estimation based on software-defined radio and a 3D surface model based on a particle filter was proposed and tested in a static experiment in the Shinjuku area of Tokyo.The research team of The University of Tokyo developed a particle-filter-based positioning method using a 3D map to rectify the positioning result of commercial GPS single-frequency receiver for pedestrian applications.
An evaluation of the QZSS L1-submeter-class augmentation with integrity function (L1-SAIF) correction to the proposed pedestrian positioning method was also discussed in an earlier paper by the authors of this article. However, satellite visibility in the urban canyon using only GPS and QZSS would not be enough for this proposed method. The use of emerging multi-GNSS, encompassing GLONASS, Galileo and BeiDou, could furnish a potential solution to the lack of visible satellites for this method. This article assess the performance of the proposed pedestrian positioning method using GPS, GLONASS and QZSS.
Building Models Construction
Our work established a 3D building model by a 2D map that contained building location and height information of buildings from 3D point-clouds data. The Fundamental Geospatial Data (FGD) of Japan, which provided by Japan geospatial information authority, is open to the Japanese public. This FGD data is employed as 2D geographic information system (GIS) data. Thus, the layouts and positions of every building on the map could be obtained from the 2D GIS data. In this article, the 3D digital surface model (DSM) data is provided by Aero Asahi Corporation. Figure 2 shows the process of constructing the 3D building model used here. This process first extracts the coordinates of every building corner from FGD as shown in the left of Figure 2. Then, the 2D map is integrated with the height data from DSM. The right of Figure 2 illustrates an example of a 3D building model established in this way. The 3D building map contains a very small amount of data for each building in comparison to that of the 3D graphic application. For our purposes, the file only contains the frame data of each building instead of the detail polygons data. This basic 3D building map is utilized in the simulation of ray-tracing.
Figure 2. The construction of the 3D building map from a 2D map and DSM.
Our version of the ray-tracing method does not consider diffractions or multiple reflections because these signals occurred under unfavorable conditions. Here, we utilize only the direct path and a single reflected path. The developed ray-tracing simulation can be used to distinguish reflected rays and to estimate the reflection delay distance. Our research work assumes that the surfaces of buildings are reflective smooth planes, that is, mirrors. Therefore, the rays in the simulation obey the laws of reflection. In the real world, the roughness and the absorption of the reflective surface might create a mismatch between the ray-tracing simulation and the real propagation. Here we ignore this effect, as the roughness of the building surface is much smaller than the propagation distance.
The opening figure (Figure 1) shows an example of the GNSS signal propagation using ray-tracing and a 3D building map. Red, green and white lines denote the LOS path, reflected paths and the NLOS paths, respectively. In this environment, a conventional positioning method such as weighted least squares (WLS) usually estimates the position on the wrong side of street as shown in the red balloon. With the aid of 3D building model and ray-tracing, the map-based positioning method is able to provide a result close to the ground truth.
Map-Based Pedestrian Positioning
The flowchart of the 3D city building model-based particle filter is shown in Figure 3. This method first implements a particle filter to distribute position candidates (particles) around the ground-truth position. In Step 2, when a candidate position is given, the method can evaluate whether each satellite is in LOS, multipath or NLOS by applying the ray-tracing procedure with a 3D building model. According to the signal strength, namely carrier-to-noise ratio (C/N0), the satellite could be roughly classified into LOS, NLOS and multipath scenarios. If the type of signal is consistent between C/N0 and ray-tracing classification, the simulated pseudorange of the satellite for the candidate will be calculated. In the LOS case, simulated pseudoranges can be estimated as the distance of the direct path between the satellite and the assumed position. In the multipath and NLOS cases, simulated pseudoranges can be estimated as the distance of the reflected path between the satellite and the candidate position via the building surface.
Figure 3. Flowchart of the particle filter using 3D city building models.
Ideally, if the position of a candidate is located at the true position, the difference between the simulated and measured pseudoranges should be zero. In other words, the simulated and measured pseudoranges should be identical. Therefore, the likelihood of each valid candidate is evaluated based on the pseudorange difference between the pseudorange measurement and simulated pseudorange of the candidate, which is simulated by 3D building models and ray-tracing.
Finally, the expectation of all the candidates is the rectified positioning of the proposed map method. This method can therefore find the optimum position through a dedicated optimization algorithm of these assumptions and evaluations. The positioning principle of the proposed method is very different from the conventional GPS positioning method, that is, WLS. As a result, the calculation of the positioning accuracy of the 3D map method should be also different.
We define two positioning performance measures for the 3D map method: user range accuracy of the 3D map method (URA3Dmap) and positioning accuracy.
The value of URA3Dmap is to indicate its level of positioning service, which is similar to the user range accuracy (URA) of conventional GPS. The URA3Dmap is defined based on the percentage of the valid candidates from all candidates outside the building. The higher percentage of the valid candidate implies a higher confidence of the estimated position. Ideally, if the center of the candidate distribution is not far from the ground truth, the simulated pseudorange of the candidates located at the center of distribution would be very similar to the measurement pseudorange. We define the URA3Dmap as shown in Table 1.
Table 1. The definition of URA and URA3Dmap used in this article.
Experiments and Discussion
We selected the Hitotsubashi and Shinjuku areas in Tokyo to construct a 3D building model because of the density of the tall buildings. In this area, multipath and NLOS effect are frequently observed. We tested pedestrian navigation in a typical path that included walking both sides of street and passing through/waiting at a road intersection. The cut-off angle is 20 degrees. The data were collected in November and December 2014.
We compare here two single point positioning methods: single-point positioning solutions provided by open source RTKLIB software (RTKLIB SPP), and the proposed 3D map method. RAIM FDE of the RTKLIB SPP is used here as a conventional NLOS detection algorithm. The test used a geodetic-grade GNSS receiver and a commercial grade receiver. The geodetic receiver was only used to collect the QZSS L1-SAIF correction signal. The antenna of the commercial receiver was attached in the strap of the backpack as shown in Figure 4. The receiver is connected to a tablet to record the GNSS measurements and is set to output pseudorange measurements and positioning results every second.
Figure 4. Equipment set-up.
We generated a quasi-ground truth using a topographical method.Video cameras were set in the ninth and18th floors of a building near the Hitotsubashi and Shinjuku areas, respectively, to record the traveled path. The video data output by the cameras are used in combination with one purchased high-resolution aerial photo to get the ground truth data. The aerial photo is 25 cm/pixel and therefore the error distance for each estimate can be calculated. The synchronization between video camera and commercial GNSS receiver is difficult to get as accurate as in the topographical method. As a result, we used point to “points” positioning error to evaluate the performance of the dynamic experiment. The synchronization error is limited to 1 second. Hence, for each estimated position x(t), the ground truth points used to calculate the positioning error is xGT (t-1), xGT (t) and xGT (t+1). The point to “points” positioning error is calculated as:
Three performance metrics are used here: mean, standard deviation of the point to points error, and the availability of positioning solution. The availability defined here means the percentage of given solutions in a fixed period. For example, if a method outputs 80 epochs in 100 seconds, the availability of the method is 80 percent.
This research demonstrates two dynamic data. The skyplot of the data are shown in Figure 5. The satellites are tracked by the commercial receiver. The grey areas indicate the obstruction of the surrounding buildings. The two dynamic data are typical signal receptions at Hitotsubashi (middle urban canyon) and Shinjuku (deep urban canyon) areas.
Hitotsubashi Mid-Canyon. To study the benefit of using different GNSS constellations in the 3D map method, Figure 6 shows the trajectory estimated by the proposed method under different satellite constellations. The different colors indicate different values of URA3Dmap of each point. This walking trajectory is divided into five sections (identified as A, B, C, D and E in the right-most of the three plots). In the GPS-only case (left), results in A and B sections have much better performance than sections D and E, because more than half of the GPS satellites are blocked at D and E, as shown in the left of Figure 5.
Figure 5. The left and right are the skyplot of the dynamic experiment at the Hitotsubashi and Shinjuku areas, respectively, in Tokyo.
The middle plot in Figure 6 shows the trajectory using GLONASS. It is obvious that the positioning results located at the right side of street are greatly increased, derived from the greater number of satellites in view. However, the quality of the GLONASS signal is not as good as GPS because multipath has a double effect on GLONASS.
Figure 6. Positioning results of the proposed 3D map method using different combinations of satellite constellations in a middle urban canyon.
In summary, the positioning error of applying GLONASS maintains a similar level, and availability increases about 12 percent compared to using GPS only. The right plot of Figure 6 shows the result after adding QZSS L1 C/A and L1-SAIF. This increases the results of C, D and E sections, because QZSS provides a high-elevation-angle satellite to the 3D map method. As a result, the number of valid candidate points in C, D and E sections increases dramatically. The reliability in C, D and E sections is also much higher than that of GPS+GLONASS. In addition, the trajectory became smoother than before.
Table 2 compares the positioning results of both RTKLIB SPP and the 3D map method, showing the 3D map method using GPS, GLONASS and QZSS to have the best performance among three scenarios. The positioning error mean and availability are 3.89 meters and 96.72 percent, respectively. The positioning error mean could be further improved to 3.23 meters if selecting the position point with URA3Dmap ≤ 3 (yellow, orange and red points in Figure 6). This selection will lose about 17 percent of availability.
Table 2. Positioning results of the 3D map method using different combinations of satellite constellations in a middle urban canyon.
Shinjuku Deep Canyon. We conducted a similar experiment in the Shinjuku area of Tokyo, the most urbanized area in Japan (Figure 7). The positioning results and skyplot are shown in Figure 8 and the right of Figure 5, respectively. Table 3 compares the results of the two methods using the three constellation configurations.
Figure 7. Deep urban canyon environment, Shinjuku, Tokyo. (Courtesy Google Earth)Figure 8. Positioning results of the proposed 3D map method using different combinations of satellite constellations in a deep urban canyon.Table 3. Performance comparison of RTKLIB SPP and the proposed 3D map method using different combinations of satellite constellations in a deep urban canyon.
As shown in the left of Figure 8, only half of the GPS-only solutions are on the correct side of the street. A few points are incorrect due to the insufficient number of satellites. Adding GLONASS measurements greatly increases the availability, and most of the GPS-only outliers are corrected. The positioning error mean improves from 12.7 to 10.3 meters, and the availability improves from 53.2 to 75.9 percent. GLONASS measurements provide such a significant improvement because the distribution of GPS and GLONASS satellites are complementary.
After adding the QZSS measurements, availability further increases to 88.6 percent, and positioning error mean is reduced to 5.7 meters. The positioning error mean could be further improved to 4.2 meters if selecting the position points with URA3Dmap ≤ 3: the red, orange and yellow points in Figure 8. Although this selection will lose about 12 percent of availability, it could be easily compensated by a simple filtering technique.
Comparing Table 2 and Table 3, we find the positioning error of the proposed method in the middle urban canyon is about 1 meter worse than that in the deep urban canyon. This is because of the increase of multiple reflected signals.
The target application of this 3D map method is consumer-based pedestrian navigation. Most of these applications benefit from an integrated system of multiple sensors. The 3D map method could serve as one sensor for such an integrated system. The calculation of positioning accuracy is required to indicate the quality of the point solution estimated by this method. Figure 9 shows the relationship between the calculated accuracy and positioning error. We can find that the calculated accuracy is able to describe the performance of the proposed method.
Figure 9. Positioning error of the 3D map method using GPS+GLONASS+QZSS. The purple line denotes the calculated 68 percent accuracy of the proposed method.
The performance of the conventional method is very inaccurate in this deep urban canyon. Its positioning error is larger than 40 meters. Figure 10 shows the number of satellites in this data. Note the number of LOS satellites is determined by the ray-tracing simulation according to the ground truth trajectory.
Figure 10. Number of LOS satellites, the number of satellites used in the 3D map method, and the total number of satellites tracked by the commercial-grade receiver.
The number of LOS satellites means the light-of-sight path of satellite is not blocked by buildings. Note that the LOS signal also contains the multipath effect. In this deep urban canyon, the number of LOS signals is much less than that of all received satellites. This implies a lot of NLOS is received, which deteriorates the performance of the conventional method. The map-based method is able to correct most of the NLOS signals.
The number of satellites used in the map-based method is close to the number of all the satellites received. Therefore the map-based method can achieve better performance than the conventional method. Figure 11 demonstrates the comparison between the map-based method and the commercial GNSS receiver. The map-based method is simply smoothed by a moving average filter with 3 seconds data. It is difficult to understand the pedestrian trajectory by the commercial-grade receiver result. In some cases, the commercial receiver will estimate the pedestrian to be on the wrong side of the streets. The proposed method, instead, is capable of estimating the result at the correct side of the street.
Figure 11. Positioning results of the proposed 3D map method and commercial-grade receiver using GPS+GLONASS+QZSS in the deep urban canyon.
Li-Ta Hsu is a post-doctoral researcher at the Institute of Industrial Science of the University of Tokyo. He received his Ph.D. degree in aeronautics and astronautics from National Cheng Kung University, Taiwan.
Shunsuke Miura received an M.S. degree in information science from the University of Tokyo in 2013.
Shunsuke Kamijo received a Ph.D. in information engineering from the University of Tokyo, where he is now an associate professor.
A little more than a year ago, I became a part of a team of surveyors from across the country to offer testing and input on new technology and programing coming out of JAVAD GNSS. It has been a great honor to work along with Dr. Javad Ashjaee, the other surveyors and Javad’s staff at JAVAD GNSS. Why Javad chose me, I doubt that I will ever know. While I am proud to be a part of what Javad has dubbed “J-Team,” I have realized very quickly how little I know about GNSS. In this series of articles that I plan on putting together, I will chronicle my advances in GNSS and testing of JAVAD GNSS equipment.
As part of my testing, I have been using a JAVAD Triumph 2 base (with 4-watt external radio) and a TRIUMPH-LS rover. I had seen advertisements for this system for many months prior to becoming a member of the J-team. I was apprehensive at first with the difference in the appearance and learning the new software. However, it did not take long to realize how advanced this system, namely the TRIUMPH-LS, was.
One key feature that I use to determine the quality of my shots is the V6 engines. The V6 engines that it uses to fix the ambiguities is unlike anything I have seen in any other software or receiver. The V6 engines are six separate RTK engines running simultaneously. Basically, this is like having six separate receivers in one.
When in heavy multipath area, I tend to stay fixated on this screen. Each engine can fix at different times. When another engine gets fixed, the resulting epochs are averaged between the two fixed engines and so on with any of the other engines. (See above image.)
This is only one of many technological advancements that Javad has included in his newest receivers. Please continue to follow my articles on other advancements and general surveying practice topics.
For more information on Javad’s J-Field software, the TRIUMPH-LS or other JAVAD GNSS solutions, please feel free to visit www.javad.com, email [email protected], or call 1-888-550-5301 or 1-408-770-1770.
Matthew D. Sibole is a Professional Land Surveyor (PLS) and a member of the JAVAD GNSS J-Team.
Analysis of new Galileo signals at an experimental ground-based augmentation system (GBAS) compares noise and multipath in their performance to GPS L1 and L5. Raw noise and multipath level of the Galileo signals is shown to be smaller than those of GPS. Even after smoothing, Galileo signals perform somewhat better than GPS and are less sensitive to the smoothing time constant.
By Mihaela-Simona Circiu, Michael Felux, German Aerospace Center (DLR), and Sam Pullen, Stanford University
Several ground-based augmentation system (GBAS) stations have become operational in recent years and are used on a regular basis for approach guidance. These include airports at Sydney, Malaga, Frankfurt and Zurich. These stations are so-called GBAS Approach Service Type C (GAST C) stations and support approaches only under CAT-I weather conditions; that is, with a certain minimum visibility. Standards for stations supporting CAT-II/III operations (low visibility or automatic landing, called GAST D), are expected to be agreed upon by the International Civil Aviation Organization (ICAO) later this year. Stations could be commercially available as soon as 2018.
However, for both GAST C and D, the availability of the GBAS approach service can be significantly reduced under active ionospheric conditions. One potential solution is the use of two frequencies and multiple constellations in order to be able to correct for ionospheric impacts, detect and remove any compromised satellites, and improve the overall satellite geometry (and thus the availability) of the system.
A new multi-frequency and multi-constellation (MFMC) GBAS will have different potential error sources and failure modes that have to be considered and bounded. Thus, all performance and integrity assumptions of the existing single-frequency GBAS must be carefully reviewed before they can be applied to an MFMC system. A central element for ensuring the integrity of the estimated position solution is the calculation of protection levels. This is done by modeling all disturbances to the navigation signals in a conservative way and then estimating a bound on the resulting positioning errors that is valid at an allocated integrity risk probability.
One of the parameters that is different for the new signals and must be recharacterized is the residual uncertainty attributed to the corrections from the ground system (σpr_gnd). A method to assess the contribution of residual noise and multipath is by evaluating the B-values in GBAS, which give an estimate of the error contribution from a single reference receiver to a broadcast correction. Independent data samples over at least one day (for GPS) are collected and sorted by elevation angle. Then the mean and standard deviations for each elevation bin are determined.
Here, we evaluate the E1 and E5a signals broadcast by the operational Galileo satellites now in orbit. In the same manner as we did for GPS L5 in earlier research, we determine the σpr_gnd values for these Galileo signals. As for GPS L5, results show a lower level of noise and multipath in unsmoothed pseudorange measurements compared to GPS L1 C/A code.
DLR GBAS Facility
DLR has set up a GBAS prototype at the research airport in Braunschweig (ICAO identifier EDVE) near the DLR research facility there. This ground station has recently been updated and now consists of four GNSS receivers connected to choke ring antennas, which are mounted at heights between 2.5 meters and 7.5 meters above equipment shelters. All four receivers are capable of tracking GPS L5 (in addition to GPS L1 and L2 semi-codeless) and Galileo E1 and E5a signals. Figure 1 gives an overview of the current ground station layout, and Table 1 gives the coordinates of the antennas.
Figure 1. DLR ground facility near Braunschweig Airport, also shown in opening photo at left.Table 1. Ground receiver antenna coordinates.
Smoothing Techniques
The GBAS system corrects for the combined effects of multiple sources of measurement errors that are highly correlated between reference receivers and users, such as satellite clock, ephemeris error, ionospheric delay error, and tropospheric delay error, through the differential corrections broadcast by the GBAS ground subsystem. However, uncorrelated errors such as multipath and receiver noise can make a significant contribution to the remaining differential error. Multipath errors are introduced by the satellite signal reaching the antenna via both the direct path from the satellites and from other paths due to reflection. These errors affect both the ground and the airborne receivers, but are different at each and do not cancel out when differential corrections are applied.
To reduce these errors, GBAS performs carrier smoothing. Smoothing makes use of the less noisy but ambiguous carrier-phase measurements to suppress the noise and multipath from the noisy but unambiguous code measurements.
The current GBAS architecture is based on single-frequency GPS L1 C/A code measurements only. Single-frequency carrier smoothing reduces noise and multipath, but ionospheric disturbances can cause significant differential errors when the ground station and the airborne user are affected by different conditions. With the new available satellites (GPS Block IIF and Galileo) broadcasting in an additional aeronautical band (L5 / E5), this second frequency could be used in GBAS to overcome many current limitations of the single-frequency system.
Dual-frequency techniques have been investigated in previous work. Two dual-frequency smoothing algorithms, Divergence Free (Dfree) and Ionosphere Free (Ifree), have been proposed to mitigate the effect of ionosphere gradients.
The Dfree output removes the temporal ionospheric gradient that affects the single-frequency filter but is still affected by the absolute difference in delay created by spatial gradients. The main advantage of Dfree is that the output noise is similar to that of single-frequency smoothing, since only one single-frequency code measurement is used as the code input (recall that carrier phase noise on both frequencies is small and can be neglected).
Ifree smoothing completely removes the (first-order) effects of ionospheric delay by using ionosphere-free combinations of code and phase measurements from two frequencies as inputs to the smoothing filter. Unlike the Dfree, the Ifree outputs contain the combination of errors from two code measurements. This increases the standard deviation of the differential pseudorange error and thus also of the position solution.
Noise and Multipath in New GNSS Signals
GBAS users compute nominal protection levels (H0) under a fault-free assumption. These protection levels are conservative overbounds of the maximum position error after application of the differential corrections broadcast by the ground system, assuming that no faults or anomalies affect the position solution. In order to compute these error bounds, the total standard deviation of each differentially corrected pseudorange measurements has to be modeled. The standard deviation of the residual uncertainty (σn, for the nth satellite) consists of the root-sum-square of uncertainties introduced by atmospheric effects (ionosphere, troposphere) as well as of the contribution of the ground multipath and noise. In other words, these error components are combined to estimate σn2 as described in the following equation:
(1)
The ground broadcasts a value for σpr_gnd (described later in the section) associated with the pseudorange correction for each satellite. These broadcast values are based on combinations of theoretical models and actual measurements collected from the ground receivers that represent actual system characteristics. Unlike the ground, σpr_air is computed based entirely on a standardized error model. This is mainly to avoid the evaluation of multipath for each receiver and each aircraft during equipment approval.
In addition to the characteristics of nearby signal reflectors, multipath errors are mainly dependent on signal modulation and other signal characteristics (for example, power, chip rate). In earlier research, we showed that the newly available L5 signals broadcast by the GPS Block IIF satellites show better performance in terms of lower noise and multipath. This mainly results from an increased transmitted power and a 10 times higher chip rate on L5 compared to the L1 C/A code signal.
In this work, we extend this evaluation to the new Galileo signals and investigate their impact on a future multi-frequency, multi-constellation GBAS. Characterization of these new signals is based on ground subsystem measurements, since no flight data with GPS L5 or Galileo measurements are available at the moment. We assume that the improvements observed by ground receivers are also applicable to airborne measurements. This assumption will be validated as soon as flight data are available.
The measurements used were collected from the DLR GBAS test bed over 10 days (note that Galileo satellite ground track repeatability is 10 sidereal days) between the December 14 and 23, 2013. In that period, four Galileo and four Block IIF GPS satellites were operational and broadcast signals on both aeronautical bands E1 / L1 and E5a / L5.
In Figure 2, the suppression of multipath and noise on the Galileo signals can be observed, where the code multipath and noise versus elevation for GPS L1 C/A BSPK(1), Galileo E1 (BOC (1,1)) and Galileo E5a (BPSK(10)) signals are shown. The code multipath and noise was estimated using the linear dual-frequency combination described in equation (2), where MPi represents the code multipath and noise on frequency i, ρi the code measurement, and ϕi,and ϕj represent the carrier-phase measurements on frequencies i and j, respectively. Carrier phase noises are small and can be neglected.
(2)
Figure 2. Raw multipath function of elevation for GPS L1, Galileo E1 (BOC (1,1)) and Galileo E5a (BPSK(10)) signals.
The multipath on the Galileo E1 (BOC(1,1)) signal (the magenta curve) is lower than the GPS L1 C/A (BPSK(1))(black curve), especially for low elevation, where the advantage of the E1 BOC(1,1) is more pronounced. The lower values can be explained by the wider transmission bandwidth on E1 and the structure of the BOC signal. Galileo E5a (green data in Figure 2) again shows a better performance than Galileo E1. This was expected due to the higher chip rate and higher signal power. A comparison of the raw multipath and noise standard deviations for GPS L1, L5 and Galileo E1, E5a signals is presented in Figure 3.
Figure 3. Ratios of the multipath and noise standard deviation function of elevation.
The curves there show the ratios of the standard deviations for each elevation bin. The values for GPS L1 are almost 1.5 times larger than those for Galileo E1 BOC(1,1) (green curve) for elevations below 20°. For high elevations, the ratio approaches 1.0. This corresponds to the observations in the raw multipath plot ( Figure 2). With the same signal modulation and the same chip rate, E5a and L5 have very similar results (red curve), and the ratio stays close to 1.0 for all elevations.
The blue and the purple curves in Figure 3 show the ratio of GPS L1 C/A (BPSK(1)) and GPS L5 (BPSK(10)), and Galileo E1 (BOC(1,1)) and Galileo E5a (BPSK(10)), respectively. The ratio of GPS L1 to GPS L5 (blue curve) increases with elevation from values around 2.5 for low elevations, reaching values above 3.5 for elevations higher than 60°. As Galileo E1 performs better, the ratio between Galileo E1 and Galileo E5a (purple curve) is smaller, from a value of 1.5 for elevations below 10 degrees to a value of 3.0 for high elevations.
Until now, we have presented the evaluation of raw code noise and multipath. However, in GBAS, carrier smoothing is performed to minimize the effect of code noise and multipath. The value that describes the noise introduced by the ground station is represented by a standard deviation called σpr_gnd and is computed based on the smoothed pseudoranges from the reference receivers. In the following section, we focus on the evaluation of σpr_gnd using different signals and different smoothing time constants. Note that, in this study, σpr_gnd contains only smoothed multipath and noise; no other contributions (for example, inflation due to signal deformation or geometry screening) are considered.
B-values and σpr_gnd
B-values represent estimates of the associated noise and multipath with the pseudorange corrections provided from each receiver for each satellite, as described in Eurocae ED-114A and RTCA DO-253C. They are used to detect faulty measurements in the ground system. For each satellite-receiver pair B(i,j), they are computed as:
(3)
where PRCTX represents the candidate transmitted pseudorange correction for satellite i (computed as an average over all M(i) receivers), and PRCSCA(i,k) represents the correction for satellite i from receiver k after smoothed clock adjustment, which is the process of removing the individual receiver clock bias from each reference receiver and all other common errors from the corrections. The summation computes the average correction over all M(k) receivers except receiver j. This allows detection and exclusion of receiver j if it is faulty. If all B-values are below their thresholds, the candidate pseudorange correction PRCTX is approved and transmitted. If not, a series of measurement exclusions and PRC and B-value recalculations takes place until all revised B-values are below threshold. Note that, under nominal conditions using only single-frequency measurements, the B-values are mainly affected by code multipath and noise.
Under the assumption that multipath errors are uncorrelated across reference receivers, nominal B-values can be used to assess the accuracy of the ground system. The standard deviation of the uncertainty associated with the contribution of the corrections (σpr_gnd) for each receiver m is related to the standard deviation of the B-values by:
(4)
where M represents the number of the receivers and N represents the number of satellites used. The final sigma takes into account the contribution from all receivers and is computed as the root mean square of the standard deviation of the uncertainties associated with each receiver (Equation 4).
Figure 4 shows the evaluation of (σpr_gnd) for the Galileo E1, BOC(1,1) signal and the GPS L1 C/A signal for increasing smoothing time constants (10, 30, 60, and 100 seconds). Starting with a 10-second smoothing constant, Galileo E1 shows much better performance than GPS L1. The difference shrinks as the smoothing constant increases due to the effectiveness of smoothing in reducing noise and short-delay multipath. However, even with 100-second smoothing (the purple curves), Galileo E1 BOC(1,1) shows lower values of (σpr_gnd).
Figure 4. σ(pr_gnd) versus elevation for Galileo E1 (dotted lines) and GPS L1 (solid lines for different smoothing constants: red (10s), green (30s), cyan (60s), purple (100s).
A similar comparison is presented in Figure 5, of the performance of GPS L1 and Galileo E5a. The Galileo E5a signal is significantly less affected by multipath, and the difference stays more pronounced than in the Galileo E1 – GPS L1, even with 100-second smoothing. It can be also observed that the Galileo signals have a lower sensitivity to the smoothing constant. The Galileo E1 signal shows an increase of sensitivity for low elevations (below 40°), while on E5a, a smoothing constant larger than 10 seconds has almost no impact on the residual error. Thus, a shorter smoothing constant on Galileo E5a generates approximately the same residual noise and multipath a 100-second smoothing constant on GPS L1.
Figure 5. σ(pr_gnd) versus elevation for Galileo E5a (dotted lines) and GPS L1 (solid lines) for different smoothing constants: red (10s), green (30s), cyan (60s), purple (100s).
The values for (σpr_gnd) are, however, impacted by the number of satellites which are used to determine a correction. Since only a very limited number of satellites broadcasting L5 and Galileo signals are currently available, these results should be considered preliminary. The first evaluations strongly indicate that with the new signals, we get better ranging performance. Based on the performance advantage of the new signals, a decrease of the smoothing constant is one option for future application. This would reduce the time required (for smoothing to converge) before including a new satellite or re-including a satellite after it was lost.
In the current GAST-D implementation, based on GPS L1 only, guidance is developed based on a 30-second smoothing time constant. A second solution, one with 100 seconds of smoothing, is used for deriving the Dv and Dl parameters from the DSIGMA monitor and thus for protection level bounding (it is also used for guidance in GAST-C). During the flight, different flight maneuvers or the blockage by the airframe can lead to the loss of the satellite signal.
Figure 6 shows the ground track of a recent flight trial conducted by DLR in November 2014. The colors represent the difference between the number of satellites used by the ground subsystem (with available corrections) and the number of satellites used by the airborne subsystem in the GAST-D position solution. One of the purposes of the flight was to characterize the loss of satellite signals in turns. In turns with a steeper bank angle, up to 3 satellites are lost (Turns 1, 3, and 4), while on a wide turn with a small bank angle (Turn 2), no loss of satellite lock occurred. It is also possible for airframe to block satellite signals, leading to a different number of satellites between ground and airborne even without turns.
Figure 6. Ground track of a flight trial conducted by DLR. The colors represent difference between number of SVs used by the ground system and number of SVs used by the airborne.
With this in mind, a shorter smoothing constant would allow the satellites lost to turns or to airframe blockage to be re-included more rapidly in the position solution. However, a new smoothing constant would have to be validated with a larger amount of data. Data from flights trials has to be evaluated as well to confirm that similar levels of performance are reresentative of the air multipath and noise.
In a future dual-frequency GBAS implementation, an important advantage of lower multipath and noise is to improve the Ifree position solution. In earlier research, we demonstrated that the error level of the Dfree solution is almost the same as for single-frequency, but an increase in error by a factor of 2.33 was computed for the Ifree standard deviation based on L1 C/A code and L2 semi-codeless measurements.
If the errors on L1 (E1) and L5 (E5a) code and carrier phase measurements are statistically independent the standard deviation of the σIfree can be written as,
(5)
where α=1−f 21 ∕ f 25, and σL1,σL5 represent the standard deviations of the smoothed noise and multipath for L1 (E1) and L5 (E5a), respectively. Considering σpr_gnd,L1(E1)) = σpr_gnd,L5(E5a)) in equation (5), the noise and multipath error on Ifree (σIfree) increases by a factor of 2.59.
Figure 7 shows the ratio σIfree/σL1 using measured data. We observe that the measured ratio (the black curve) is below the theoretical ratio computed based on the assumption of statistically independent samples (the constant value of 2.59). This is explained by the fact that the multipath errors in the measurements are not independent but have some degree of statistical correlation. The standard deviations are computed based on the same data set used in the raw multipath and noise assessment using 100-second smoothed measurements sorted into elevation bins of 10° spacing.
Figure 7. Measured ratio σIfree/σL1 function of elevation.
Conclusion
We have shown how GBAS can benefit from the new signals provided by the latest generation of GPS and Galileo satellites. We have demonstrated improved performance in terms of lower noise and multipath in data collected in our GBAS test bed. When GBAS is extended to a multi-frequency and multi-constellation system, these improvements can be leveraged for improved availability and better robustness of GBAS against ionospheric and other disturbances.
Acknowledgment
Large portions of this work were conducted in the framework of the DLR internal project, GRETA.
Manufacturers
The ground facility consists of four JAVAD GNSS Delta receivers, all connected to Leica AR 25choke ring antennas.
Mihaela-Simona Circiu is is a research associate at the German Aerospace Center (DLR). Her research focuses on multi-frequency multi-constellation Ground Based Augmentation System. She obtained a 2nd level Specialized Master in Navigation and Related Applications from Politecnico di Torino.
MIchael Felux is is a research associate at the German Aerospace Center (DLR). He is coordinating research in the field of ground-based augmentation systems and pursuing a Ph.D. in Aerospace Engineering at the Technische Universität München.
Sam Pullen is a senior research engineer at Stanford University, where he is the director of the Local Area Augmentation System (LAAS) research effort. He has supported the FAA and others in developing GNSS system concepts, requirements, integrity algorithms, and performance models since obtaining his Ph.D. from Stanford in Aeronautics and Astronautics.
InvenSense Inc. is making available its InvenSense Positioning Library (IPL) software, designed to provide sensor-assisted positioning in places where GNSS alone cannot provide desired accuracy. Invensense is a provider of intelligent sensor system on chip for motion and sound in consumer electronic devices.
InvenSense made the announcement at Mobile World Congress, taking place in Barcelona, Spain March 2-5.
The IPL incorporates advancements in sensor-assisted positioning algorithms that allow use of inertial sensors to improve GNSS positioning in urban areas where satellite signals are either blocked or distorted by multipath, enabling continuous location availability while driving in underground parking lots, tunnels, or walking in urban canyons. The IPL enables continuous and accurate position, velocity and orientation in challenging operating environments.
These sensor-assisted positioning algorithms have been designed to operate under normal pedestrian and driving use without restrictions on the device orientation. Supported pedestrian use includes handheld, hand swinging, in pocket, call mode and belt holster. The algorithms also allow any use within the vehicle, such as in cradle, cup holder or simply left on a seat. The software was designed in a way to maximize accuracy and minimize constraints on the user.
The IPL is designed to operate with an IMU and GNSS receiver as minimum hardware. Integration with a magnetometer, barometer, and vehicle speed sensor is also available, which provides additional heading integrity as well as height and velocity accuracy for sensor-assisted positioning.
IPL is designed for smartphones using Android, iOS, Windows and general Linux operating systems and has already started shipping commercially. The underlying navigation technology comes from years of development at Trusted Positioning Inc., which was acquired by InvenSense this past summer.
“With more consumers using their smartphones for turn-by-turn navigation on foot or in vehicle, one of the most frustrating user experience issues is losing your GPS (GNSS) signal in an unfamiliar location or being re-routed erroneously due to multipath errors,” said Ali Foughi, vice president of Marketing and Business Development at InvenSense. “With IPL technology, high-accuracy location guidance is always available and provides smartphone OEMs with a differentiated user experience and consumers with a more reliable navigation solution.”
The InvenSense Positioning Library is available immediately.
InvenSense is exhibiting in booth #D61 in Hall 7 at Mobile World Congress.
A single-feed smart antenna (left) compared to the multipath rejection results of the new TW5340 smart antenna with Accutenna technology. Photo: Tallysman
Tallysman’s new TW5340 smart antenna is designed to pair Tallysman‘s Accutenna technology antenna with STMicroelectronics’ Teseo II receiver. The combination makes the smart antenna accurate for use in all environments, including urban canyons, according to the company.
The TW5340 is a multi-constellation GNSS Smart Antenna that provides simultaneous GPS/GLONASS/SBAS reception. It is designed for use in professional-grade applications such as precision timing, network synchronization, low current applications, and tracking/positioning applications.
To illustrate the advantages of this technology coupling, simultaneous recordings of vehicle position were conducted using two smart antennas — one with and one without Tallysman’s Accutenna technology — in an area of downtown Ottawa, Canada, notorious for high levels of multipath signals. Results show how the high multipath signal rejection capabilities of Tallysman’s Accutenna technology greatly improves accuracy, the company said.
The Tallysman TW5340 smart antenna.
The TW5340 supports STMicroelectronics Autonomous A-GPS, which accelerates GPS positioning by predicting satellite ephemeris data based on previous observations. This results in extremely fast time-to-first-fix. The TW5340 can be configured to output up to three NMEA 0183 message lists with navigation update rates up to 10 Hz. RS232, CMOS, and USB interfaces are available with input voltage options of 3,3V, 5.0V, and 12V. A standby-mode feature provides for very low current consumption (<100uA) and is particularly useful in battery-operated applications.
A standard one pulse-per-second 1PPS synchronized to UTC time is available as a single ended output or as a differential output at RS422 levels.
Tallysman’s Windows-based Configurator enables simple configuration of parameters such a baud rates, output message rates, constellation, tracking parameters, 1 PPS configuration and standby-mode parameters.
The TW5340 is housed in an IP67 housing and is REACH and ROHS compliant. A non-magnetic version is also available as Part Number TW5341.
Analysis of Signal Tracking Techniques for Multipath Mitigation
By Antonio Fernández, Mariano Wis, Pau Closas, Carles Fernández-Prades, José A. García, Francesca Zanier, and Massimo Crisci
INNOVATION INSIGHTS by Richard Langley
GETTING RID OF A NUISANCE. No, I’m not talking about your neighbor’s barking dog or the IT guy when he shows up to fiddle, yet again, with your computer. I’m talking about multipath. What is multipath, you ask? Herewith, Multipath 101. When a radio signal travels from a transmitting antenna to a receiving antenna, it will follow a direct line-of-sight path. But the signal might also travel to the receiving antenna after being reflected off a nearby building, say, resulting in a delayed signal or echo along with the line-of-sight one. Those of us of a certain age will remember ghost images on the screens of TVs connected to “rabbit ears” or outdoor antennas. That was multipath. These days, with TV signals primarily delivered by cable and satellite, we don’t see multipath much anymore. But we do hear it in our cars, from time to time, while listening to FM radio. Although the FM “capture effect” provides some margin against multipath, it is not uncommon to lose stereo reception or to experience fading out of the signal while driving in built-up areas as a result of reflections.
This same multipath phenomenon also affects GNSS signals. Unlike satellite TV antennas, the antennas feeding our GNSS receivers are omnidirectional. So we have the possibility of not only receiving a direct, line-of-sight signal from a GNSS satellite but also any indirect signal from the satellite that gets reflected off nearby buildings or other objects or even the ground. The related phenomena of diffraction and scattering can also generate multipath signals.
In a GNSS receiver, the line-of-sight and multipath signals combine to corrupt tracking of the line-of-sight signal resulting in increased pseudorange and carrier-phase measurement errors.
GNSS antenna and receiver manufacturers have developed techniques to minimize some of the impact of multipath on the GNSS observables. And tracking of some of the newer GNSS signals is a bit more resistant to multipath. But multipath, at some level, is still a problem looking for a better solution.
This brings us to ARTEMISA, which stands for Advanced Receiver Techniques: Multiprocessing Algorithms. It’s a European initiative to develop techniques to minimize the effects of multipath in GNSS receivers. For those of you who are a little rusty on your Greek mythology, Artemis (or Artemisa in Spanish — after all, she was a woman) was the Greek goddess of the hunt. You might better know her Roman equivalent: Diana. Her parents were Zeus and Leto, and Apollo was her twin brother. She is often depicted carrying a bow and arrows. How appropriate a name for a project whose goal is to try to kill off the effects of multipath in GNSS receivers.
In this month’s column, the team of researchers involved with ARTEMISA describe their efforts to generate synthetic multipath for GPS L1 and Galileo E1 signals and to test different signal tracking techniques in a simulated receiver to see which techniques best minimize the effects of multipath on positioning solutions and which might be feasible candidates for incorporating in real receivers. The hunt is on.
GNSS navigation in urban environments is usually challenged by a number of effects such as multipath and weak signal conditions. In particular, the pernicious effects of multipath on signal tracking and system accuracy are widely known. To mitigate these effects, there is a series of techniques that range from modified antenna design to combining the GNSS receiver with other sensors or subsystems. Another possibility is to implement advanced tracking techniques specifically designed for these purposes. Such techniques usually impose computational load and implementation complexity, which make them hard to implement in an application-specific-integrated-circuit-based receiver. However, given the current advances in computer technology and the possibilities of field-programmable-gate-array- (FPGA-)based hardware, it is possible to implement these new techniques in an operational receiver.
We have studied this possibility as part of the ARTEMISA project, carried out by DEIMOS Space and the Centre Tecnològic de Telecomunicacions de Catalunya, and supervised by the European Space Agency’s European Space Research and Technology Centre. We have implemented and tested a series of innovative techniques that are able to cope with, and even to estimate, multipath (MP) parameters, using a simulated software receiver based on the GRANADA (Galileo Receiver Analysis and Design Application) GNSS blockset for MathWork’s Simulink graphical programming language tool. These techniques are based on the maximum likelihood principle (as implemented in the Multipath Estimating Delay Lock Loop) or on online Bayesian techniques for the estimation of multipath (as implemented in the Multipath Estimating Particle Filter), involving architectural modifications of the tracking loops (as in vector tracking loops), or even constituting a new paradigm in receiver design (direct position estimation).
Our effort in this project has focused on two main tasks. The first task is the design and development of the simulation platform, the techniques to be tested, and a multipath model representative of the urban environment. The second task involves a simulation campaign that has been carried out to test the different techniques and to contrast the results obtained against the legacy delay lock loop / phase lock loop (DLL/PLL) tracking loop schemes. This article describes these tasks and some of the results we have obtained so far.
Keep in mind that at the time of writing, ARTEMISA is still ongoing. Therefore, more results are expected up until the end of the project.
Simulation Platform
The simulation platform has been developed in Matlab/Simulink with DEIMOS Engenharia’s GRANADA GNSS Blockset. This blockset is a collection of Simulink models and blocks that can be used to design and simulate any kind of GNSS receiver. The main block is the Factor Correlator Model (FCM), which implements the set of correlators through an analytical (set of equations) model. Carrier phase, code misalignment, autocorrelation function, and even the correlated noise and the multipath at the output of every virtual correlator are simulated for a given input trajectory. On the other hand, the tracking loops are implemented as independent modules representative of an actual receiver. This semi-analytical approach has the advantage of performing a fast simulation of the correlator output without the need for implementing the baseband correlation operation. In addition, its implementation in Simulink allows for the development of innovative tracking schemes. This approach also matches with the ARTEMISA project concept, where a series of innovative tracking loops has been implemented with the aim of replacing or improving conventional PLL/DLL schemes.
The main architecture of the simulation platform is shown in FIGURE 1. We use an external trajectory file to generate the reference data that will be used with the FCM block to generate the correlator output that will feed the tracking loop blocks. These trajectory files are also used to feed the multipath scenario generators, to test each technique under a number of defined scenarios so that we can assess their performances and find their limitations under multipath.
We used two statistical models for the description of the signal propagation: the Controlled Stochastic Channel Model (CSCM), which is a modification of the Land Mobile Satellite channel developed by Pérez-Fontán, and the well-known Land Mobile Channel Model, developed by the German Aerospace Center (Deutsches Zentrum für Luft- und Raumfahrt or DLR); see Further Reading. These models generate a series of scenario files, which can be loaded into the FCM to introduce the multipath effects in the correlator output.
These two statistical models are complementary. The CSCM model allows the user to set the multipath channel characteristics to be able to stress the tracking technique, while the DLR model permits evaluation of the technique’s response in realistic conditions.
A deterministic user-defined multipath generator was implemented to check the response of the tracking techniques under well-defined multipath conditions. The Multipath Error Envelope (MPEE) was also computed to evaluate the response of the technique under one echo with varying delay conditions.
The purpose of this article is not to explain all the developments performed with the platform. It focuses on the results obtained with the deterministic and statistical channel model. For this reason, the development of the CSCM generator will be explained in detail.
Controlled Stochastic Channel Model
The CSCM module was specifically created for this project. Its purpose is to generate a stochastic channel, but with the capability to control the multipath power levels and the number of echoes generated in the scenario, thus creating a set of realistic multipath signals, but with the capability of being easily controlled by the user. Time series for multipath echoes are generated, following a Rice or Rayleigh stochastic model, but the mean power levels, the amplification K factors, and the power switching times are chosen by the user.
The model allows the selection of the number of satellites (channels) that are generated in the model, the sampling period (related to the loop integration time), the length of the simulation, the receiver speed, the signal carrier frequency, and channel specific parameters such as the number of echoes, the average delay of the echoes and the decay slope (echo power loss ratio with signal delay).
One of the parameters the user can set implicitly is the multipath echo lifetime. What the user really sets is the channel transition time, or the time during which the channel keeps the multipath configuration. Every time the transition time is changed, a series of multipath echoes are canceled and other ones appear. This set of disappearing/appearing echoes is performed in pairs in such a way that the transition between echoes is smooth. FIGURE 2 illustrates this mechanism.
Figure 2. CSCM echoes smooth transition.
When an echo is disappearing (a red one in the figure), its associated echo is at its maximum value (a blue scatterer). In the next interval, a new echo appears in a different delay position (a green one) and the associated scatterer begins to decrease its power. This mechanism allows the user to easily associate the transition time to half the multipath echo lifetime.
Simulation Plan
The simulation plan is structured into different stages. The first stage of the simulation plan is based on the controlled multipath environment, with specific tests for each technique. The purpose of this stage is the tuning up of the techniques. As an example, for the Multipath Estimating Delay Lock Loop (MEDLL) technique, parameters such as the precorrelation bandwidth, the number of MEDLL iterations or the number of assumed multipath echoes are parameters that are adjusted after these tests are carried out. Another purpose of this first stage is to check the performance of the techniques under deterministic, fully controlled multipath. Parameters like signal-to-multipath ratio, multipath delay, and the number of multipath echoes can be controlled at any time.
Another test is the generation of the multipath envelope error plot. The utility of this test is to find the optimal configuration of the correlator position for each kind of signal, which is a trade-off between the obtained root-mean-square error (RMSE) and the number of correlators. This procedure is repeated for each signal considered in the plan.
The next stage of the simulation plan is the test with the CSCM model. This test consists of the generation of a series of scenarios characterized by the stochastic model, the number of echoes, and the user receiver dynamics. Scenarios presented in this article are shown in TABLE 1. Two types of user environments are defined: one for pedestrian and one for vehicular receivers. The dynamics (user speed) define the integration (sampling time) and the multipath Doppler spread. The stochastic model parameters include the type of stochastic model for the line-of-sight signal (LOSS) and multipath echoes, mean power level, and amplification K factor. These scenarios represent a moderate multipath level with four echoes.
Table 1. CSCM scenarios in the simulation plan.
Each scenario was run with different settings of carrier-to-noise-density ratio (C/N0) and with all the signals that were planned for the project: GPS L1 C/A, GPS L5, Galileo E1 and Galileo E5. In this article, we focus on L1 band signals, analyzing the results for GPS L1 and Galileo E1.
Table 2. GNSS signals considered in the analysis.
The final stage in the simulation plan is testing each technique under realistic channel conditions with the DLR model. In this case, an urban scenario is set, assuming two types of receiver dynamics (a pedestrian user and a vehicular user). No more details about this stage are given because these tests are currently ongoing.
Technique Descriptions
After an initial evaluation of the candidate techniques, the following techniques were selected for implementation and testing in the project.
Multipath Estimating Delay Lock Loop. MEDLL was proposed by Van Nee (see Further Reading). It is a robust statistical approach to the multipath problem, where the maximum likelihood principle is applied to a signal model consisting of LOSS and M-1 multipath rays or echoes. The key idea is to perform the estimation of the whole set of parameters of the incoming signals (that is, amplitude, delay, and phase) in an iterative manner. When their amplitudes, time delays, and carrier phases are estimated, the effect of the reflections in the correlation can be removed. Applying standard assumptions, the maximization of the likelihood function yields a set of interrelated equations from which one can estimate iteratively the LOSS and multipath parameters. The implementation of MEDLL considers a similar architecture as conventional DLLs, although in practice more than three correlators per loop are required for effective multipath mitigation. Despite its demanding requirements in terms of a large number of correlators and computational load, MEDLL was successfully implemented in NovAtel receivers because of its excellent performance in multipath mitigation.
The contributions of all signals (that is, LOSS and an unknown number of echoes) are not calculated simultaneously from the outset. First, the contribution of only one signal is calculated, then the contribution of a second signal is added with the contributions of both signals being optimized, then the contribution of a third signal is added and the contributions of all three signals are optimized, and so on. The process is repeated until a suitable stop criterion is fulfilled. A possible approach for deciding when to stop adding more rays to the signal model is to detect when the error increases; that is, observing that the signal-to-residual ratio when considering an extra path decreases with respect to the case of not considering it, or reaching a maximum number of considered paths, which is a design parameter of this technique.
Multipath Estimating Particle Filter. The MEPF shares with MEDLL the philosophy of estimating the parameters of multipath to mitigate its effect. The main difference is that in this case the statistical principle is not the ML (as in MEDLL) but Bayesian filtering. Here the term Bayesian means that the algorithm is using some sort of a priori information regarding these parameters (such as interdependencies and time evolution models). Therefore, instead of assuming that each integration period is independent of the others, a first-order Markov process is assumed for the unknown parameters (that is, amplitude, delay, and phase). The resulting problem is formulated as a nonlinear state-space model and can be solved by means of a Rao-Blackwellized particle filtering method.
The MEPF has a relatively high computational load, which is a function of the number of particles (Np), the number of correlation points, and the number of rays to be estimated (M). In all cases, the larger the values the more computationally demanding the algorithm is. According to the simulations performed, configurations with Np larger than 2000 are not worthwhile, because it implies a high computational cost and the results do not improve significantly the accuracy of a GNSS receiver. Also notice that the dimension of the state-space to be estimated is 3 × M ([amplitude, phase, delay] × M), and thus estimating an additional multipath ray implies augmenting the dimensionality by three. Theoretically, the convergence results of particle filters are independent of the dimensionality of the problem. However, it is agreed that in practice these methods fail when the problem increases in dimension. Therefore, setting M larger than 5 is not reasonable since the number of particles required for convergence would be too large to consider its implementation in a receiver.
Vector Tracking Loops. A conventional GNSS receiver consists of several parallel scalar DLLs, each of which independently estimates the individual pseudoranges. The parallel set of measured pseudoranges (plus Doppler or accumulated delta range measurements on the carrier) are then fed to a Kalman filter estimator, and thus each DLL effectively produces an independent estimate for each of the N pseudoranges for each of the N satellites. However, not all of their measurements are truly independent, although they are treated as such by the DLL, and if there are more than four measurements being made and four or fewer unknowns, the system is overdetermined. Furthermore, the geometry of the satellite-user paths generally prevents the measurements from being truly independent.
The concept of vector tracking loops firstly appeared in the early 1980s. Recently, the method has attracted the attention of many researchers (see Further Reading) due to its good performance in weak signal scenarios.
In this article, we present the implementation of a vector tracking loop that works with pseudorange and pseudorange-rate measurements and provides estimations for position, velocity, receiver clock error, and receiver clock drift. The vector loop has been integrated in a basic receiver based on the classical DLL and PLL/frequency lock loop (FLL)-assisted architecture, acting as an overlay procedure, which activates automatically once the basic receiver has obtained the first position fix. Then, the position/velocity/time solution is used to jointly estimate the synchronization parameters (time delay and carrier phase) for each of the received GNSS signals by means of an extended Kalman filter, and those values are re-injected into the tracking loop. By using position for deriving such synchronization parameters, the algorithm exploits the problem’s inherent geometric constraints, processing all the channels jointly and providing robustness in scenarios with weak receiving power, high multipath, or fast fading.
Direct Position Estimation. Although the conventional two-step position determination is the approach taken traditionally, it is seen to have a number of drawbacks. In contrast, direct position estimation (DPE for short) proposes an alternative where the estimation of a user’s position is performed directly from the received and sampled signal, thus avoiding intermediate steps and jointly considering signals from all satellites when estimating the position solution. By merging the two-step approach into a single estimation problem, DPE addresses some of the inherent drawbacks of the conventional approach where the dependencies between channels are efficiently exploited, in the sense that signals from visible satellites are jointly processed to obtain the user’s position. At the time of writing, this technique is being implemented and its analysis is left for future publications.
Results
Not all the results that we have obtained have been included in this article; only the most relevant ones for L1/E1 CBOC and BPSK signals are given.
MEDLL. Optimal Correlator Configuration. As stated previously, the test consisted of executing different correlator configurations. TABLE 3 shows the correlator configuration ID, the number of correlation samples, and the location of the late correlators with respect to the prompt one and normalized to the chip time (Tc). The corresponding early samples are defined analogously. For all these configurations, it is assumed that there is a correlator at zero chips.
Table 3. MEDLL correlator configurations tested.
These configurations were selected in order to test different possibilities as regular spacing between correlators (MP31, MP61, or MP91), setting the correlators to inflexion points of the autocorrelation function (ACF) (NC37 or NC43 for CBOC modulation), or variable spacing (as configurations AR01 to AR05 and GE01) that optimize the number of correlators. The results of the tests can be observed in FIGURE 3 for a BPSK(1) signal and for a CBOC(6,1,1/11) signal.
Figure 3. MPEE for MEDLL with BPSK and CBOC signals for different correlator configurations (Tc=chip time).
In general, it is observed that the greater the number of correlators, the smaller is the spacing and therefore, the area covered by the multipath error envelope is smaller. However, the greater the number of correlators, the greater is the processing time. Therefore, it is necessary to find an optimal configuration that best fits the multipath variation.
After having analyzed the tests for these configurations, we found that the optimal configurations are AR01 for the BPSK signal and NC37 for the CBOC(6,1,1/11) signal. These configurations are shown in FIGUR 4, and were used for the remaining tests.
Figure 4. Correlator configurations for CBOC and BPSK signals.
CSCM. As mentioned in the simulation plan description, the tests for a pedestrian and a vehicular user in a moderate multipath environment were performed with a scenario file generated with the CSCM tool. These scenarios are characterized by a series of multipath echo levels, number of echoes, and specific stochastic models that are detailed in Table 1. In this table, the pedestrian scenario is known as SP1 and the vehicular scenario is shown as SV1. The results with these scenarios are presented in this article.
The RMSE for range estimates in these scenarios is shown in FIGURE 5 for SP1 and SV1. For comparison, these plots show also the theoretical lower bound (Nunes bound) computed for each technique.
Figure 5. Range RMSE for MEDLL in pedestrian and vehicular scenarios.
The plots show that MEDLL outperforms the conventional DLL results above a minimum C/N0 value. This happens beyond 32 dB-Hz for a CBOC signal and 35 dB-Hz for a BPSK(1) signal for low dynamics (pedestrian) environments.
In the case of vehicle scenarios such as SV1, it is observed that it requires significantly higher values of C/N0 in order to outperform the DLL RMSE. This result makes the technique impractical for vehicular applications.
Time Performance. A collateral result that has been obtained with CSCM scenarios is the time performance of the technique, compared to the legacy DLL/PLL scheme. The ratios of the execution times needed for the techniques have been computed. This is an indicative measure of the computational load. The time performance of MEDLL with the selected correlator configuration against DLL is 10:1. That is, 10 times more time is required for the MEDLL technique than the DLL to run the same scenario. It is also observed that the ratio for BPSK modulation is slightly larger than the ratio for the CBOC signal, because more correlators are used in that case.
MEPF. Performance Under Controlled Channel. FIGURE 6 shows an example of the performance of the MEPF technique tested in a controlled channel environment.
Figure 6. Results of the MEPF in the controlled multipath environment with 2 and 3 estimated rays including the line-of-sight. For comparison purposes, DLL/PLL results are also included (blue line in upper plot).
It can be observed how the DLL/PLL technique has an error, which grows as the number of rays is increased. However, when the MEPF is applied, it can be observed how the technique is capable of dealing with a multipath-changing environment despite the fact that it is varying in time with the number of rays increasing. It can also be noticed that the response of the technique is practically the same independent of the number of estimated rays (M). These results were achieved with a BPSK signal and 500 particles.
Covariance Matrix Adjustment. Before starting the specific test for the evaluation of the scenario performance, it is necessary to calibrate the particle filter. The calibration procedure consists of the adjustment of the process covariance matrix. The observation covariance can be adjusted, simply by analyzing the raw observables, or it can even be done automatically.
The critical point is the adjustment of the states’ covariance. It has been observed that an improper adjustment of the covariance may cause an increment in the range RMSE or even the divergence of the filter. For that reason, a systematic procedure for the adjustment of the covariance matrix has been followed. This procedure evaluates the performance using different configurations of the covariance matrices of the line-of-sight and multipath parameters in two stages, and allows us to find a set of optimal values for each scenario.
Optimal Correlator Configuration. We also analyzed the optimal correlator configuration for the MEPF technique. A number of configurations in Table 3 were used under CSCM scenarios. It was found that the correlator configuration does not have a strong influence on the performance of the MEPF technique. It is worth mentioning that in cases where fewer than five correlators were used, the performance degraded. Despite the weak influence of the range RMSE with the correlator configuration, it was observed that there is a minimum for the BPSK signal that can be chosen for the MEPF technique (MP31). For the CBOC signal, the same configuration used for MEDLL is finally chosen (NC37), provided that it is the optimal configuration that balances range RMSE and the number of correlators.
Number of Particles. It is important to notice that an initial set of tests was performed with 500 particles. However, it was found that by increasing the number of particles to 2000, the performance of the technique with CSCM was remarkably better. Because of this, for the remaining tests using the CSCM, this number of particles was the default value. Using a higher number is not worthwhile since results are not much improved and the computational load becomes too high.
CSCM Results. The range RMSE results for the pedestrian scenario SP1 with the MEPF technique are shown in FIGURE 7. In this case, it is observed that for the CBOC signal, MEPF outperforms the DLL/PLL technique for low C/N0 values. This result could not be reproduced for the BPSK signal because of the adjustment of the covariance matrix, which in this test was optimized for CBOC.
Figure 7. Range RMSE for MEPF and pedestrian scenario.
These promising results for CBOC open the possibility of using this technique in applications where the LOSS is very weak or where the multipath signals are very strong. More tests with this technique are currently being executed for a better adjustment of covariance settings for BPSK.
Time Performance. The previous time performance analysis was performed with the MEPF technique. The performance ranges among 180:1 and 340:1, when compared to DLL/PLL schemes using three correlation samples. The extremely long time required to simulate the scenario makes this technique inadvisable for implementation within an operational receiver using current technology.
VTL.CSCM Results. The same CSCM scenarios were performed for the VTL technique, but using a multi-channel receiver. Results for pedestrian SP1 and vehicular SV1 scenarios are shown in FIGURE 8.
Figure 8. Position RMSE for VTL with pedestrian and vehicular scenarios.
It must be noted that, in order to perform fair comparisons, the results of ordinary DLL/PLL tracking used a conventional KF for the computation of the position instead of the least squares module available in the GRANADA GNSS Blockset.
In our numerical simulations, a significant improvement in the performance of VTL with respect to the DLL/PLL+KF scheme was not observed in pedestrian environments, due to the low dynamics. Under those dynamic conditions, both systems exhibited similar (statistically equivalent) behavior.
In the case of scenario SV1, the velocity applied to the receiver was higher than in the pedestrian case, and the VTL exhibited a remarkable improvement over the DLL/PLL+KF-based receiver. For the BPSK modulation, it was observed that for low values of C/N0 , the VTL performs better than DLL/PLL+KF. However, for stronger signals, both techniques have the same behavior as shown for the pedestrian scenario results. On the other hand, for the CBOC modulation, it is observed that VTL performs better than DLL/PLL+KF for the whole range of C/N0 values. The precorrelation bandwidth was set to 8 MHz in the case of BPSK, while for CBOC it was set to 14 MHz. That wider bandwidth of the CBOC receiver has an impact in the estimation of the measurements covariance matrix. In can be observed that in such higher dynamic stress conditions, the VTL outperformed DLL/PLL+KF in our numerical simulations.
It must be mentioned that for all the simulations, we assumed the same C/N0 for all satellites. However, we plan to run tests with LOSS fading (variation of C/N0). It is expected that the VTL technique will show its advantage in those simulations.
It was also observed that settings of the KF covariance have an important effect on the results. This covariance must be adjusted according to the multipath signal level. Therefore, a calibration operation, which adapts the KF to a particular scenario should be performed. While the measurement covariance matrix can be adaptively estimated from the output of the DLLs and the PLLs, the process covariance matrix should be adjusted depending on the trajectory characteristics.
Time Performance. The time performance analysis also shows that the time performances of VTL and DLL/PLL+KF are very similar. Only a small increment of 15% of the computational cost for vehicular scenarios has been observed. This makes this technique a good candidate to be implemented in an operational software-based receiver.
Results Overview
After analyzing the current results from the different techniques, some general conclusions on their performance can be made.
MEDLL can be useful to mitigate and improve the pseudorange measurement provided that the C/N0 value is greater than a threshold value. An intuitive reasoning for this is that the estimation of multipath rays is easier at high C/N0 values. Below this value, the MEDLL technique does not present an important advantage over ordinary DLL/PLL given the time performance it has (a ratio of 10:1). MEDLL is especially well-suited for static and pedestrian environments.
MEPF is a technique that still needs research before it can be used operatively. Results show that it works quite well for low C/N0 values when compared to DLL/PLL. Results show that for the CBOC signal, at least 2000 particles are needed to give good results for low C/N0 values. However, its time performance is very poor (around 200:1 with respect to DLL with 2000 particles)
VTL does not present an advantage in the pseudorange measurement domain, but it clearly improves the position solution with respect to a classical DLL/PLL+KF tracker. This improvement is remarkable under dynamic conditions. It is also observed that the time performance is very similar to the DLL/PLL+KF one. Therefore this technique is a good candidate for implementation in a receiver prototype based on embedded hardware, an FPGA implementation, or software-based radio.
For the sake of completeness, a performance comparison in the range domain of the different techniques with the BPSK and CBOC signals for the pedestrian SP1 scenario are presented in FIGURE 9. The metric used is the range RMSE.
Figure 9. Compared range RMSE for different techniques: pedestrian scenario with BPSK(1) and CBOC(6,1,1/11) signals.
Conclusions and Future Work
This article has presented a series of innovative multipath-estimating techniques using non-conventional approaches in the tracking algorithms. These non-conventional approaches are based on maximum likelihood (MEDLL) or non-linear online filtering algorithms (MEPF). Alternative approaches in the positioning algorithms have also been analyzed (VTL and DPE).
To check the performance of these techniques, we have developed a simulation platform, able to carry out deterministic multipath simulations, in which the multipath environment can be controlled deterministically, and stochastic simulations based on tested multipath models (CSCM and DLR). The CSCM model is capable of simulating realistic multipath environments but with the capability to control the multipath ray parameters and the number of these rays. The DLR model allows us to perform simulations based on the conditions in realistic urban environments.
This article has focused on the CSCM model. It shows simulations for a pedestrian and a vehicular scenario that represent typical dynamic conditions for each kind of user.
These results show that the MEDLL technique performs very well in a static multipath environment under low dynamics with good visibility conditions.
Concerning the MEPF, it has been found that the adjustment of the covariance for the observables is very important for achieving good results for the range RMSE. If this adjustment is done well, the results for low values of C/N0 outperform the ordinary DLL/PLL technique. This adjustment has been successfully achieved for a CBOC signal, but a BPSK signal still requires additional work. This may open the possibility of using this technique in applications in which the LOSS is very weak.
It has also been observed that the VTL technique is very effective in high dynamics applications and noisy environments, provided that the internal KF process noise covariance has been properly estimated. VTL also shows a performance very similar to the DLL/PLL+KF scheme in mild-condition scenarios. That makes this technique a good candidate for implementation in a real-time software-based receiver.
Finally, it is necessary to remark that ARTEMISA is still a work in progress. An extensive simulation campaign in a realistic urban environment under different conditions using the DLR multipath model is ongoing. In addition to the techniques presented in this article, other advanced techniques such as direct position estimation are under evaluation.
Acknowledgments
The ARTEMISA project, funded by the European Space Agency (ESA) is being carried out by DEIMOS Space, with the Centre Tecnològic de Telecomunicacions de Catalunya as subcontractor. The content of the present article reflects solely the authors’ views and by no means represents official ESA policy.
The authors of this article would like to thank Tiago Peres, Joao Silva, and Pedro Silva from DEIMOS Engenharia; José Antonio Pulido from DEIMOS Space; and Roberto Prieto-Cerdeira from ESA’s European Space Research and Technology Centre for their support in the adaptation of the GRANADA GNSS Blockset and the simulation platform to the requirements of the techniques and multipath environments tested in the project.
ANTONIO FERNANDEZ co-founded DEIMOS Space with headquarters in Madrid, in 2001, where he is currently in charge of the GNSS Business Unit.
MARIANO WIS is currently working for DEIMOS Space as a project engineer in the GNSS Business Unit. He is also a Ph.D. candidate in the Aerospace Science and Technology Program of Universitat Politècnica de Catalunya in Barcelona.
PAU CLOSAS is a senior research associate and head of the Statistical Interference Department in the Communications Systems Division of the Centre Tecnològic de Telecomunicacions de Catalunya (CTTC) in Barcelona.
CARLES FERNANDEZ–PRADES is serving as head of the Communications Systems Division at CTTC, where he holds a position as senior researcher.
JOSE A. GARCIA is with the Radio Navigation Systems and Techniques Section at the European Space Agency’s European Space Research and Technology Centre (ESA/ESTEC) in Noordwijk, The Netherlands.
FRANCESCA ZANIER is also with the ESA/ESTEC Radio Navigation Systems and Techniques Section.
MASSIMO CRISCI is the head of the ESA/ESTEC Radio Navigation Systems and Techniques Section.
FURTHER READING
• ARTEMISA
“ARTEMISA: New GNSS Receiver Processing Techniques for Positioning and Multipath Mitigation” by A.J. Fernandez, J.A. Pulido, M. Wis, F. Zanier, R. Prieto-Cerdeira, M. Crisci, P. Closas, and C. Fernández-Prades in Proceedings of Navitec 2012, the 6th ESA Workshop on Satellite Navigation Technologies, and the European Workshop on GNSS Signals and Signal Processing, Noordwijk, The Netherlands, December 5–7, 2012, doi: 10.1109/NAVITEC.2012.6423092.
• GRANADA GNSS Blockset
“Factored Correlator Model: A Solution for Fast, Flexible, and Realistic GNSS Receiver Simulations” by J.S. Silva, P.F. Silva, A. Fernández, J. Diez, and J.F.M. Lorga in Proceedings of ION GNSS 2007, the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 25–28 2007, pp. 2676-2686.
• Signal Propagation Statistical Models
“A Location and Movement Dependent GNSS Multipath Error Model for Pedestrian Applications” by A. Steingass, A. Lehner, and F. Schubert in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of The Satellite Division of the Institute of Navigation, Savannah, Georgia, September 22–25, 2009, pp. 2284-2296.
“Statistical Modeling of the LMS Channel” by F.P. Fontan, M. Vazquez-Castro, C.E. Cabado, J.P. Garcia, and E. Kubista in IEEE Transactions on Vehicular Technology, Vol. 50, No. 6, November 2001, pp. 1549–1567, doi: 10.1109/25.966585.
• Multipath Estimating Delay Lock Loop
“The Multipath Estimating Delay Lock Loop: Approaching Theoretical Accuracy Limits” by R.D.J. Van Nee, J. Siereveld, P. C. Fenton, and B. R. Townsend in Proceedings of PLANS 1994, the Institute of Electrical and Electronics Engineers Position, Location and Navigation Symposium, Las Vegas, Nevada, April 11–15, 1994, pp. 246–251, doi: 10.1109/PLANS.1994.303320.
• Multipath Estimating Particle Filter
“Nonlinear Bayesian Tracking Loops for Multipath Mitigation” by P. Closas, C. Fernández-Prades, J. Diez, and D. de Castro in International Journal of Navigation and Observation, Vol. 2012, Article ID 359128, 15 pages, 2012, doi:10.1155/2012/359128.
“A VDLL Approach to GNSS Cell Positioning for Indoor Scenarios” by F.D. Nunes, F.M.G. Sousa, and N. Blanco-Delgado in Proceedings of ION GNSS 2009, the 22nd International Technical Meeting of the Satellite Division of The Institute of Navigation, Savannah, Georgia, September 22–25, 2009, pp. 1690–1699.
• Direct Position Estimation
“Maximum Likelihood Estimation of Position in GNSS” by P. Closas, C. Fernández-Prades, and J.A. Fernández-Rubio in IEEE Signal Processing Letters, Vol. 14, No. 15, May 2007, pp. 359-362, doi: 10.1109/LSP.2006.888360.
• Some Previous Innovation Columns on Multipath Mitigation
The September “Innovation” column in this magazine, “It’s Not All Bad: Understanding and Using GNSS Multipath,” by Andria Bilich and Kristine Larson, mentions the use of multipath in studying soil moisture, ocean altimetry and winds, and snow sensing. An experiment the authors conducted, designed to study soil moisture, yielded a surprise bonus: a new methodology for measuring snow depth via GPS multipath. It has important implications for weather and flood forecasting, and could also bring new insight to bear on GPS antenna design.
In the “Innovation” column, the authors wrote, “Motivated by our studies showing that multipath effects could clearly be seen in geodetic-quality data collected with multipath-suppressing antennas, we proposed that these same GPS data could be used to extract a multipath parameter that would correlate with changes in the reflectance of the ground surface. . . .
“We carried out an experiment designed to more rigorously demonstrate the link between GPS signal-to-noise ratio (SNR) and soil moisture. Specifically, we were interested in using GPS reflection parameters to determine the soil’s volumetric water content — the fraction of the total volume of soil occupied by water, an important input to climate and meteorological models. Traditional soil moisture sensors (water content reflectometers) were buried in the ground at multiple depths (2.5 and 7.5 centimeters) at a site just south of the University of Colorado.”
Here Comes the Storm. During the experiment, two late-season snowstorms swept over Boulder. Larson and colleagues discovered that changes in multipath clearly correlated with changes in the snow’s depth, as measured by hand and with ultrasonic sensors at the test site. While it has been long recognized that snow can affect a GPS signal, this demonstrates for the first time that a standard GPS receiver, antenna, and installation — deliberately designed to suppress multipath — can be used to measure snow depth.
On September 11, Geophysical Research Letters, published by the American Geophysical Union, featured an article titled “Can We Measure Snow Depth with GPS Receivers?” by Larson and Felipe Nievinski of the Department of Aerospace Engineering Sciences, University of Colorado; Ethan Gutmann and John Brown of the National Center for Atmospheric Research; Valery Zavorotny of the National Oceanic and Atmospheric Administration; and Mark W. Williams, from UC’s Department of Geography, all based in Boulder.
The authors adapted an algorithm used for modeling GPS multipath from bare soil to predict GPS SNR for snow, introducing a uniform planar layer of the snow on the top of soil. The algorithm treats both direct and surface-reflected waves at two opposite circular polarizations as plane waves that sum up coherently at the antenna. They write:
“The amplitude and the phase of the reflected wave is driven by a polarization-dependent, complex-value reflection coefficient at the upper interface of such a combined medium with a known vertical profile of the dielectric permittivity e. The reflection coefficient is calculated numerically using an iterative algorithm in which the medium is split into sub-layers with a constant e. For the soil part, we use a known soil profile model that depends on the soil type and moisture. For frozen soil, soil moisture (liquid water) is low, as for very dry soil. For the snow part, we take a constant profile with e, considering relatively dry and wet snow layer thicknesses.
“After calculating the complex amplitude of the reflected wave at each polarization, we multiply it by a corresponding complex antenna gain. The same procedure is applied to the complex amplitude of the direct wave. After that, the modulation pattern of the received power, or the SNR, as a function of the GPS satellite elevation angle is obtained by summing up coherently all the signals coming from the antenna output and taking the absolute value square of the sum.”
Figure 1(a) shows GPS SNR measurements for one satellite on the day immediately before and the day immediately after an overnight snowfall of 35 centimeters (roughly 10 inches). Figure 1(b) shows the corresponding model predictions for multipath. The two figure portions amply demonstrate that the multipath has a significantly lower frequency if snow is present as compared with bare soil. The authors further noted that the model amplitudes do not show as pronounced a dependence on satellite elevation angle as the observations, and state the necessity of further work on antenna gains in order to use model amplitude predictions.
Figure 1. (a) GPS SNR measurements for PRN 7 observed at Marshall GPS site on days 107 (red) and 108 (black) after direct signal component has been removed. Approximately 35 centimeters of snow had fallen by day 108. (b) Model predictions for GPS multipath from day 107 with no snow on the ground (red), and day 108 after 35 centimeters of new snow fall had accumulated (black) using an assumed density of 240 kg m-3 (figures reproduced by permission of American Geophysical Union).
How Deep the Snow. The authors propose that the hundreds of geodetic GPS receivers operating in snowy regions of the United States, originally installed for plate deformation studies, surveying, and weather monitoring, could also provide a cost-effective means to estimate snow depth.
Currently, a few conventional monitor points measure snow depth, but only at that point, and the data does not extrapolate well. Snow forms an important component of the climate system and a critical storage component in the hydrologic cycle. Accurate data of the amount of water stored in the snowpack is critical for water supply management and flood control systems. As more snow falls at higher elevations, varying greatly even within one valley or watershed, current remote-sensing snow monitors do not supply adequate data. Further, snow may be redistributed by wind, avalanches, and non-uniform melting, so that continuous data would be very helpful.
Using GPS multipath to map snow depth could improve watershed analyses and flood prediction — and, carried steps further, produce data to help better understand multipath, bringing innovation to future antenna designs.
FIGURE 2. Snow depth derived from GPS (red squares), the three ultrasonic snow depth sensors (blue lines), and field measurements (black diamonds). Bars on field observations are one standard deviation. GPS snow-depth estimates during the first storm (doy 85.5–86.5) are not shown (gray region) because the SNR data indicate that snow was on top of the antenna.
Kristine Larson was featured as one of the “50 GNSS Leaders to Watch” in the May 2009 issue of GPS World.
Manufacturer
For the experiment a Trimble NetRS receiver was used with a TRM29659.00 choke-ring antenna with SCIT radome, pointed at zenith.
Telltale signs of multipath are the fluctuations in the signal-to-noise ratios (SNRs) reported by some GNSS receivers. In this month’s column, the authors look at how an analysis of SNR values can be used to map the multipath environment surrounding an antenna so that models of multipath can be constructed to further minimize its effect. Also, although an annoyance for most GNSS users, it turns out that multipath has its positive points.
INNOVATION INSIGHTS by Richard Langley
CAST YOUR MIND BACK 30 OR 40 YEARS. (Sorry, students, this exercise is for the older folks.) What was one of the most striking features of the suburban landscape? Virtually every house was topped with a Yagi TV antenna. The only way to receive TV signals before cable and satellite TV was directly from the transmitter tower. And, unless you had one of those fancy antenna rotors, reception wasn’t always that great. Not only did we have to put up with weak signals, there was the problem of multipath. Besides a direct signal from the transmitter, the antenna could pick up a signal reflected off a nearby building, say, resulting in a delayed ghost image to the right of the main image on the TV screen. Even those out in the country weren’t immune from multipath as a fluttery image might be seen caused by reflections from passing aircraft.
These days, with TV signals primarily delivered by cable and satellite, we don’t see multipath much anymore. But we do hear it in our cars, from time to time, while listening to FM radio. (Students can tune back in now.) Although the FM “capture effect” provides some margin against multipath, it is not uncommon to lose stereo reception or to experience fading out of the signal while driving in built-up areas as a result of reflections.
This same multipath phenomenon also affects GNSS signals. Unlike satellite TV antennas, the antennas feeding our GNSS receivers are omnidirectional. So we have the possibility of not only receiving a direct, line-of-sight signal from a GNSS satellite but also any indirect signal from the satellite that gets reflected off nearby buildings or other objects or even the ground. GNSS antenna and receiver manufacturers have developed techniques to minimize the impact of multipath on the GNSS observables. Nevertheless, there is typically some residual multipath afflicting the pseudorange and carrier-phase observables that limits the precision and accuracy of position determinations.
Telltale signs of multipath are the quasi-periodic fluctuations in the signal-to-noise ratios (SNRs) reported by some GNSS receivers, and in this month’s column, we learn how an analysis of SNR values can be used to map and better understand the multipath environment surrounding an antenna.
And, although an annoyance for most GNSS users, it turns out that multipath is not all bad. By analyzing the SNR fluctuations due to multipath, characteristics of the reflector can be deduced. If the reflector is the ground, then the amount of moisture in the soil can be measured. GNSS for measuring soil moisture? Who would have thought?
“Innovation” is a regular column that features discussions about recent advances in GPS technology and its applications as well as the fundamentals of GPS positioning. The column is coordinated by Richard Langley of the Department of Geodesy and Geomatics Engineering at the University of New Brunswick.
We often hear “multipath” blamed as the last great source of unmodeled errors in GNSS observations, and therefore positions. But what is multipath? And what can we do about it? Can we remove multipath, or understand its temporal and spatial nature, or use it in new and novel ways? In this article, we address some of these outstanding multipath questions through the lens of the signal-to-noise ratio, or SNR. This article begins with background on the multipath phenomenon and discusses how carrier-phase multipath is related to SNR, an observable that is routinely collected by GNSS receivers but rarely used. The remainder of the article details a few new applications of SNR observations for multipath analysis. With this single observable type and a few assumptions about its relation to tracking loops and the environment surrounding the antenna, we can understand the multipath environment, remove multipath errors from carrier-phase measurements, and in some cases even transform this error into a new source of environmental information.
Multipath is exactly what it sounds like — a signal that travels along more than one path. When GNSS radio waves propagate from the GNSS satellite toward the receiving antenna, it is possible for the incoming signal to travel more than one path via reflection, diffraction, scattering, or a combination of these. Although all these phenomena contribute to multipath, in this article we limit multipath to reflections of a specular nature. Specular reflections occur when an electromagnetic wave hits an object (such as the surface of the Earth, a building, or a car) that is smooth relative to the signal wavelength. Upon reflection from the smooth surface, the outgoing energy is coherent, discrete, and sent in a single direction. From this point forward, multipath is taken to mean specular reflections from a large object.
When received by a GNSS antenna, this coherent reflected signal will disturb the tracking loops and distort the measured code and phase. The code and phase distortions occur because the GNSS receiver tracks a composite signal, which is the sum of the direct or line-of-sight signal and one or more multipath signals. The composite signal is biased from the direct signal simply because the multipath signal travels a longer path length than the desired direct signal. GNSS tracking and positioning rely upon the assumption of direct line-of-sight between satellite and receiver, thus tracking a composite signal will result in mismeasurement of the carrier and code ranges.
Why is multipath still an unsolved problem with GNSS positioning? As discussed below, multipath is a site-specific phenomenon — each GNSS site or satellite or vehicle will have a unique multipath-generating environment. Multipath is also dynamic — errors evolve with motion of the GNSS satellites and change as the reflecting surfaces (such as growing vegetation, moving cars, dry or damp ground) around the receiving antenna also change. Multipath errors cannot be simply differenced away — multipath at one station will not cancel out upon differencing with observables from another station. Nor can multipath always be “averaged out” — with real-time or rapid static GNSS positioning, the spatial and temporal complexity of site-specific multipath environments can adversely affect position determination.
Simplified Multipath Model
On the most basic level, multipath errors are driven by the geometric relationships between the receiving point (the GNSS receiver antenna), the sending point (the GNSS satellite antenna), and the reflecting object. We illustrate these geometric relationships using simple ray tracing; for a more involved ray-tracing technique, see the paper “Development and Testing of a New Ray-Tracing Approach to GNSS Carrier-Phase Multipath Modelling” listed in Further Reading. The geometric relationships between the satellite, receiving antenna, and reflecting objects dictate the additional path length traveled by the multipath signal, and how this path length changes as the satellite moves.
In an ideal, multipath-free world, this geometry is described only by the line-of-sight betwxeen satellite and receiver, which we describe via the azimuth and elevation angle of the satellite relative to the receiver. The geometry becomes more complicated when a reflecting/multipath object is introduced. TABLE 1 introduces some multipath terms and FIGURE 1 shows how these factors combine to create a forward-scatter multipath environment where a single reflected signal is received by the GNSS antenna. This illustration shows an antenna receiving two signals from one GNSS satellite, the desired direct ray and a second ray that reflects off a tilted, planar object before reception. For this example, we assume all angles are coplanar and disregard the third dimension.
FIGURE 1. (a) Forward-scatter multipath geometry, where the red arrows indicate the longer path traveled by the multipath signal relative to the direct signal. See Table 1 for definition of terms. (b) Signal amplitudes after including antenna gain pattern (green line) effects and attenuation upon reflection at a surface; see Table 2 for definition of terms.
Using the multipath terms listed in Table 1 and the geometric relationships depicted in Figure 1a, the additional distance traveled by the reflected/multipath signal relative to the direct one is the path delay. The phase of the multipath signal (again, relative to the direct signal) is the angular equivalent of path delay:
[1]
Already, we see that the path delay and multipath relative phase are a function of the antenna-reflector distance (h) and the angle of reflection from the surface (β), and that the same multipath object will result in different multipath phases for different GNSS signals due to the dependence on λ.
As discussed below, the time-varying nature of multipath is key to understanding and mitigating its effects. Thus we examine the multipath frequency, that is, the rate of change of the multipath phase:
[2]
If we assume a single stationary reflecting object, the only time-varying factor in Figure 1 is the satellite — as the satellite moves relative to the receiving antenna, the reflection point also moves, changing the path delay and multipath relative phase. Substituting the angular relationships (see Figure 1a) between the satellite, receiver, and reflecting object into the previous equation makes this more obvious:
[3]
But how is “multipath frequency” related to quantities measured by our GNSS receivers: the code range, carrier phase, and signal-to-noise ratio (SNR)? To answer that question, we must introduce another set of multipath quantities, which describe the dominant signal strength factors (TABLE 2) for the direct and multipath signals; we ignore thermal noise, cable losses, etc.
The amplitude of the direct signal (Ad) is equivalent to the GNSS signal strength as it is received and is affected by the antenna gain pattern (Figure 1b). The multipath signal comes through the antenna gain pattern at a different angle; by design, most GNSS antennas will apply less gain at angles consistent with common multipath geometries, such as below the antenna horizon. The multipath signal will also experience some amount of attenuation upon reflection; the combination of attenuation and antenna gain yields the amplitude of the multipath signal (Am). Note that the broadcast GNSS signals are right-hand circularly polarized (RHCP), which are largely converted to left-hand polarization upon reflection. Thus the simplified “gain pattern” introduced here must incorporate both RHCP and LHCP patterns.
Under the simplified model of GNSS receiver response to tracking direct plus short-delay (smaller than 1.5 code chips) reflected signals, the multipath relative phase and signal amplitudes describe both the code and carrier-phase multipath errors, respectively denoted ρMP and δφ:
[4]
. [5]
These equations are derived from code and carrier tracking behavior in the presence of multipath. Look in Further Reading for precise derivations and additional background material.
In addition to carrier phase and code observables, GNSS receivers routinely record SNR (or the related carrier-to-noise-density ratio — C/N0) for each satellite. As the term indicates, SNR is a ratio of signal power to the noise floor of the GNSS observation, and has conventionally been used only for comparison of signal strengths between channels and satellites or to assess interference. Like code and carrier-phase multipath errors, SNR is a function of multipath phase and signal strengths:
. [6]
If we remove the effects of the direct signal, the remaining SNR is due only to multipath and is reduced to a simple function of multipath signal amplitude, relative phase, and a time-invariant phase offset:
. [7]
Note that the equations for code multipath, carrier-phase multipath, and SNR contain the cosine or sine of the multipath relative phase, ψ. Therefore all three GNSS observables will have quasi-sinusoidal behavior driven by ω. To illustrate this, FIGURE 2 gives an example for a rising satellite reflecting off horizontal ground 1.0 meters below the antenna. All three GNSS observables oscillate at the same frequency; however, pseudorange error and SNR are in phase while carrier-phase error is 90 degrees out of phase.
FIGURE 2. Simulated carrier-phase error, code error, and SNR (recorded direct-plus-multipath SNR in green; SNR due to multipath alone in blue in linear amplitude units for a horizontal surface 1.0 meters below the antenna, assuming Rs 5 0.2 reflection coefficient and a choke ring antenna gain pattern.
In this article, we use SNR observations to understand and quantify multipath effects. We choose SNR over the other observable types because multipath effects on SNR have the most unambiguous relationship to multipath. Typical levels of pseudorange noise will swamp all but the most extreme of multipath errors; carrier-phase data are more precise, but extracting multipath from these data requires first modeling clocks, orbits, and atmospheric delays. SNR data are directly related to carrier-phase multipath, are largely independent of the above effects, and are determined independently for individual satellites. Unfortunately, not all GNSS receivers provide SNR data with the requisite precision and accuracy to clearly observe the multipath relationships; see “Scientific Utility of the Signal-to-Noise Ratio (SNR) Reported by Geodetic GPS Receivers” in Further Reading for information on high-utility SNR. When SNR data are of sufficient quality, they can provide a unique and direct window on the multipath errors affecting the code and carrier observations.
SNR Multipath Applications
A number of new scientific applications of SNR data are evolving to exploit the above multipath relationships. In the following sections, we describe three different SNR-multipath applications and provide relevant (although not exhaustive) references. All of these applications draw upon the above relationships and require precise and accurate SNR data that conform to the simplified multipath model described above.
Multipath Corrections. Recall that the multipath errors in GNSS observables are simply a function of signal amplitudes and the relative phase between direct and multipath signals. It stands to reason that if these amplitudes and phases can be estimated, we can model and remove multipath errors from our code and carrier observations. SNR data allow us to do just that. After extracting the direct signal (Ad) to reveal the SNR due only to multipath (SNRMP), this remaining time series depends only on Am and ψ. As shown in Figure 2 and Equation 7, SNR due to multipath oscillates with a constituent frequency ω, which is the time derivative of ψ, and has an amplitude envelope equivalent to Am. Therefore, from SNR due to multipath we can estimate multipath relative phase and multipath amplitude as a function of time.
This idea of modeling SNR data to estimate multipath parameters as time-varying quantities was first explored in a multi-antenna differential environment. This concept was extended to undifferenced SNR data so that carrier-phase errors at single-antenna GPS stations could be modeled and removed. In our implementation, we used wavelet analysis to first separate the direct amplitude from the multipath signal, then estimated the frequency content ω(t) of SNRMP as a function of time. Using as the primary input to an adaptive least-squares algorithm, we then estimated multipath amplitude and relative phase as a function of time. Substituting these Ad, Am, and ψ estimates into Equation 5 for carrier-phase multipath yielded a multipath-error correction profile.
A simple example from the Salar de Uyuni, a large salt flat in Bolivia, illustrates the process. For PRN8 observed during September 2002 with an antenna about 1.4 meters above the salt surface, the SNR due to multipath has very clear oscillations with a constituent frequency of approximately 0.0021 Hz (470 second period) (see FIGURE 3). Using frequency estimates as an input, the adaptive estimation algorithm estimates direct and multipath signal amplitudes as well as the multipath relative phase, which is approximately linear with time due to the relatively constant frequency estimate. Figure 3 shows that the modeled SNRMP closely matches the SNR data, and the carrier phase correction profile closely matches the phase errors.
FIGURE 3. SNR modeling example from the Salar de Uyuni data set, PRN8, ascending arc, in seconds since the beginning of the satellite pass. Real data are given in black, while estimated quantities are colored lines; estimation uses SNR due only to multipath, i.e., after the direct signal has been removed, in linear amplitude units. The goal of SNR modeling is to generate a phase-multipath correction profile, shown in the bottom panel as a red line overlaying phase residuals.
SNR-based phase-error estimation techniques show great promise for removing multipath errors from phase data. For the Salar de Uyuni test session, we derived SNR-based carrier-phase corrections for all satellites in view. By applying these corrections, we achieved a reduction in carrier-phase postfit residual root-mean-square error of up to 20 percent for static positioning, and 1–7 dB reduction in spectral power at multipath periods for kinematic positions.
Power Spectral Maps. Sadly, the complex and time-varying nature of multipath error cannot always be removed. In those cases, a better understanding of the multipath environment (the direction of and distance to reflecting objects) may aid the GNSS analyst. With this information, an analyst could discern the effect of multipath on position solutions, or de-weight multipath-corrupted observations, or simply choose one solution strategy (static, real-time kinematic or RTK, long vs. short occupation, etc.) over another to minimize or avoid multipath effects. For example, short duration but high-frequency multipath errors would be unimportant to someone solving for a single position using 24 hours of data, but that same multipath source could wreak havoc in an RTK survey. A method to evaluate the multipath environment at different frequencies and with a sense or orientation is therefore of great value.
As with the phase-error modeling example above, we accomplish multipath characterization via the frequency content of SNR oscillations, but this time backing out the distance, h (see Equation 3). This distance is directly related to the multipath frequency — nearby objects yield low-frequency errors, distant objects lead to high-frequency errors. By relating the distance, h, to angles (θ,γ) describing the direction and orientation of reflecting objects (Figure 1a), we can fully describe the multipath environment.
In this application, dubbed power spectral mapping, a wavelet transform is applied to each satellite’s SNR time series to extract multipath power estimates over a range of frequencies or height values. The 3-D power vs. frequency vs. spatial coordinate data cube is then sliced into frequency bands of interest (i.e., height ranges), and all data contributing to a frequency band are combined. The signal power is assigned to the satellite’s location and projected onto a “sky plot.” This type of plot has four quadrants for north, south, east and west; concentric rings indicate satellite elevation angle; the center of the plot is the zenith while the outer ring is the horizon. This combination and projection process forms a map depicting the multipath characteristics of a GPS site.
These maps can help the analyst determine the source of multipath errors. For example, at first glance the permanent International GNSS Service (IGS) GPS station MKEA (see PHOTO) on Mauna Kea volcano in Hawaii seems to be multipath-free as it is surrounded by nothing but jagged rocky ground — uneven ground (relative to the GNSS wavelength) should create a diffuse multipath signature.
Mauna Kea GPS station MKEA, facing northwest
The SNR data tell a different story, with strong coherent oscillations (see FIGURE 4) over a range of frequencies. By conducting wavelet analysis for all satellites in view, the combined power spectral maps (see FIGURE 5) show very strong reflections coming from the south-southeast and northwest, the location of volcanic cinder cones. Although rocky, these cinder cones generate strong multipath reflections. The sloped hillsides can be broken into a set of discrete reflectors at different distances, creating multipath oscillations at different frequencies over each satellite pass. For a more in-depth discussion of MKEA multipath and other power spectral map examples, see “Mapping the GPS Multipath Environment Using the Signal-to-Noise Ratio (SNR),” listed in Further Reading.
FIGURE 4. Example SNR profile from MKEA (top panel) as a function of time, in linear amplitude units after direct signal contributions have been removed. The bottom panels show wavelet power at different periods (colored lines), which are averaged together to form the wavelet power over 30–60 and 60–90 seconds-period bands of interest (heavy black lines).FIGURE 5. GPS L1 power spectral maps for MKEA SNR data for four different frequency bands (given as periods in upper right-hand corner of each plot). Figure is reproduced from “Mapping the GPS Multipath Environment Using the Signal-to-Noise Ratio (SNR).”
Soil Moisture. Manuel Martin-Neira is credited with introducing the idea, in 1993, that reflected GPS signals could be used for scientific studies. Since then, GPS reflection studies for ocean altimetry and winds, soil moisture, and snow sensing have all been discussed in the literature. These studies typically use an antenna pointed to optimize Earth reflections and specifically designed to track reflected (LHCP) signals. This means that antennas designed to suppress ground reflections, such as those used by the geophysical, geodetic, and surveying communities, are not used.
Motivated by our studies showing that multipath effects could clearly be seen in geodetic-quality data collected with multipath-suppressing antennas, we proposed that these same GPS data could be used to extract a multipath parameter that would correlate with changes in the reflectance of the ground surface. In our initial study, we used data from an existing IGS GPS site in Tashkent, Uzbekistan, and concentrated on SNR reflectance changes caused by rain and subsequent drying of the soil. While the correlation between the SNR data and precipitation models was strong, we lacked proper ground instrumentation to demonstrate that we were measuring true soil moisture changes.
Subsequently, together with other colleagues, we carried out an experiment designed to more rigorously demonstrate the link between GPS SNR and soil moisture. Specifically, we were interested in using GPS reflection parameters to determine the soil’s volumetric water content — the fraction of the total volume of soil that is occupied by water, an important input to climate and meteorological models. Traditional soil moisture sensors (water content reflectometers) were buried in the ground at multiple depths (2.5 and 7.5 centimeters) at a site just south of the University of Colorado in Boulder. Precipitation data were also collected. Using a fixed frequency, Equation 7 was used to model the SNR data and estimate an amplitude and phase offset on each day. FIGURE 6 shows phase estimates converted to water content for six satellites that pass over the same ground south of the GPS antenna. We specifically concentrated on these six satellites because they transmit the new L2C signal, which yields superior SNR data compared to the L1 C/A-code signal.
FIGURE 6. Variation in volumetric water content (VWC) from multiple GPS satellites (colored dots) and water content reflectometers buried at 2.5-centimeter depth (data range given by grey shaded region). Daily precipitation totals in blue. Figure is reproduced from “Use of GPS Receivers as a Soil Moisture Network for Water Cycle Studies.”
Figure 6 shows excellent agreement between in situ sensors and the GPS multipath parameters. Soil moisture values rise within hours of a precipitation event, and then drop over approximately one week as the soil dries. It is important to note that the GPS SNR data are sensing much larger spatial regions (hundreds of square meters) whereas the soil probes measure values over a very small soil region (100 centimeters square). Climate scientists desire soil moisture measurements that have large footprints, and SNR data from some existing GPS stations are uniquely poised to provide this scale of soil moisture measurements.
Conclusions
Under the simplified multipath model discussed here, SNR data have a defined relationship to both carrier-phase and pseudorange multipath errors. Although SNR is traditionally used only as a measure of signal tracking, we have demonstrated some applications that use this common but underutilized observable to identify potential multipath sources, model and remove phase multipath errors, or retrieve soil moisture content from ground reflections. All of these applications are predicated upon accurate and precise SNR measurements, which conform to the simplified multipath model. Not all receivers are created equal in this respect, thus care must be taken in selecting reliable SNR data for analysis.
Acknowledgments
We acknowledge technical support from UNAVCO and funding from the National Science Foundation. We thank our colleagues Eric Small, John Braun, Ethan Gutmann, Valery Zavorotny, and Penina Axelrad.
Manufacturers
The Salar de Uyuni and Mauna Kea data sets were obtained from Ashtech (now Magellan Professional) Z-12 receivers using Allen Osborne Associates (acquired by ITT Communications Systems) AOAD/M_T element antennas while the soil moisture experiment data set was from a Trimble NetRS receiver fed by a model TRM29659.00 choke ring antenna with SCIT radome.
ANDRIA BILICH is a geodesist with the National Geodetic Survey’s Geosciences Research Division in Boulder, Colorado. Her research interests include GPS multipath characterization, antenna calibration, and precision improvements to high-rate positioning for geoscience applications. She received her B.S. in geophysics in 1999 from the University of Texas and a Ph.D. in aerospace engineering in 2006 from the University of Colorado. Dr. Bilich was the recipient of the 2007 Parkinson Award from The Institute of Navigation for her dissertation titled Improving the Precision and Accuracy of Geodetic GPS: Applications to Multipath and Seismology.
KRISTINE M. LARSON received a B.A. in engineering sciences from Harvard University in 1985 and a Ph.D. in geophysics from the Scripps Institution of Oceanography, University of California at San Diego, in 1990. Since 1990, she has been a faculty member in the Department of Aerospace Engineering Sciences at the University of Colorado at Boulder. The primary focus of her work is developing and improving GPS applications for measuring plate tectonics, episodic slip, volcanic deformation, ice-sheet motion, timing, seismic waves, soil moisture, and snow depth.
“GPS Receiver Architectures and Measurements” by M.S. Braasch and A.J. van Dierendonck in Proceedings of the IEEE, Vol. 87, No. 1, January 1999, pp. 48–64.
“Conquering Multipath: The GPS Accuracy Battle” by L.R. Weill in GPS World, Vol. 8, No. 4, April 1997, pp. 59–66.
“Multipath Effects” by M.S. Braasch in Global Positioning System: Theory and Applications, edited by B.W. Parkinson, J.J. Spilker Jr., P. Axelrad, and P. Enge, Vol. 1, Chp. 14, American Institute of Aeronautics and Astronautics, Washington, D.C., 1996.
• Multipath Ray Tracing
“Development and Testing of a New Ray-Tracing Approach to GNSS Carrier-Phase Multipath Modelling” by L. Lau and P.A. Cross in Journal of Geodesy, Vol. 81, No. 11, pp. 713–732, 2007 (d
oi: 10.1007/s00190-007-0139-z).
• Assessing and Modeling Multipath Using Signal-to-Noise Ratios
“Mapping the GPS Multipath Environment Using the Signal-to-Noise Ratio (SNR)” by A. Bilich and K. M. Larson in Radio Science, Vol. 42, RS6003, 2007 (doi:10.1029/2007RS003652).
“Scientific Utility of the Signal-to-Noise Ratio (SNR) Reported by Geodetic GPS Receivers” by A. Bilich, P. Axelrad, and K. M. Larson in Proceedings of ION GNSS 2007, the 20th International Technical Meeting of the Satellite Division of The Institute of Navigation, Fort Worth, Texas, September 26–28, 2007, pp 1999-2010.
“Modeling GPS Phase Multipath with SNR: Case Study from Salar de Uyuni, Bolivia” by A. Bilich, K. M. Larson, and P. Axelrad in Journal of Geophysical Research, Vol. 113, B04401, 2008 (doi:10.1029/2007JB005194).
• Using GPS to Estimate Soil Moisture
“Using GPS Receivers to Measure Soil Moisture Fluctuations: Initial Results” by K.M. Larson, E. E. Small, E. Gutmann, A. Bilich, P. Axelrad, and J. Braun in GPS Solutions, Vol. 12, No. 3, pp. 173–177, 2008 (doi: 10.1007/s10291-007-0076-6).
“Use of GPS Receivers as a Soil Moisture Network for Water Cycle Studies by K.M. Larson, E. E. Small, E. D. Gutmann, A. L. Bilich, J. J. Braun, and V. U. Zavorotny in Geophysical Research Letters, Vol. 35, L24405, 2008 (doi:10.1029/2008GL036013).
• Measuring Reflected GPS Signals from Space
“Reflecting on GPS: Sensing Land and Ice from Low Earth Orbit” by S.T. Gleason in GPS World, Vol. 18, No. 10, October 2007, pp. 44–49.
“A Passive Reflectometry and Interferometry System (PARIS): Application to Ocean Altimetry” by M. Martin-Neira in ESA Journal, Vol. 17, No. 4, 1993, pp. 331–355.
