Tag: RTK

Carrier Phase Compensates for Wind and Wave Motion

Limited landing area as well as interference due to wind disturbance and wave motion make shipboard landings of unmanned aerial vehicles (UAVs) extremely difficult. Use of UAVs at sea can enhance the efficiency of intelligence gathering and surveillance, and could also increase long-range air-strike capability. To successfully land aircraft in such a challenging environment requires a high-precision navigation system; this prototype applies RTK measurements.

By Chiu-Jung Huang and Shau-Shiun Jan

UAVs can perform functions such as surveying, imaging, detection, sensor work, rescue, and geographic information systems (GIS) data collection. The exploitation of UAVs with portable launching and recovery systems using an automatic guidance equipment can enhance their flexibility in many practical applications. In particular, UAVs can achieve great effectiveness from launch and recovery aboard ships at sea. However, the landing area is narrow on a ship, and interference related to the maritime environment due to wind disturbance and wave motions varies greatly, making maritime UAV landings quite difficult. Recovering these aircraft in such a rapid-dynamic environment requires a high-precision UAV navigation system.

Generally, UAVs use a differential GPS (DGPS) aiding station to continuously transmit positioning correction information during landing approach; this method can provide about 0.7 to 1-meter accuracy. However, shipboard landings require more stringent accuracy. According the Joint Precision Approach and Landing System (JPALS), the requirements of shipboard landing include vertical accuracy on the order of 0.3 meters, and the requirement for the vertical protection level is 1.1 meters. To fulfill these accuracy requirements, we have chosen the real-time kinematic (RTK) technique. Recently, researchers have studied the use of RTK satellite navigation. The Boeing Unmanned Little Bird program has been examining shipboard launch and recovery using related navigation techniques.

The accuracy of using RTK navigation is 1 centimeter + 1 part per million.

Since development of shipboard landing is costly in terms of time and many resources, including human resources, this research is an attempt to evolve a software-in-the-loop (SIL) simulation system to analyze the accuracy of using RTK for landing navigation. The SIL system uses the MATLAB Simulink interface becasue of its helpfulgraphic user interface and block diagrams. A flowchart of the SIL system is shown in Figure 1.

The simulated RTK message provides the navigational data used as the analysis results from the experiments. To ensure the stability of the landing process, the aircraft models were control by a linear quadratic Gaussian regulator (LQG), which is able to reject the environmental disturbances encountered in the landing process. The ship motions were simulated using the factors and the model formulated by the International Towing Tank Conference. A combined position error consisting of the aircraft controls and ship motions was calculated and then fed back to the RTK navigation message.

RTK Performance

RTK navigation provides high positioning performance in the range of a few centimeters; the technique can eliminate main errors, including ionospheric and tropospheric errors and satellite clock errors, among others. A base station and a rover station can cover a service area of about 10 to 20 square kilometers. The data transition should be in real time using a wireless VHF or Wi-Fi modem.

Because data for shipboard landings are difficult to acquire, the navigation message in the SIL was simulated using experiments involving a variety of conditions. In this article, four kinds of experiments were included to help verify the availability and reliability of using RTK information as a navigational message.

We started with a basic kinematic experiment, which was simply used to assess the RTK performance. Next, a relative positioning experiment was conducted to ensure the RTK relative positioning accuracy was adequate. After that, an antenna reversal experiment was designed in order to understand the ship’s swing effect in which aircraft altitude might cause a lack of common view satellites. Finally, an antenna forward flip experiment was conducted intended to show the different RTK positioning results for a variety of sea state effects.

All of the experimental data were collected by a workshop computer through a program data file. The analyses of the results included the mean, standard deviations of positioning error, unavailable RTK percentages and the positioning accuracy when RTK was unavailable. All of the analysis results were imported to the SIL simulation using the Gaussian random variable model.

Kinematic Experiment. The base station setup included an antenna, tripod, and receiver. The rover station setup included a portable vehicle with a battery, antenna, and receiver placed as shown in Figure 2. The data were transmitted and received using a wireless modem for which the transmitted rate was 115200 bps. The receiver was connected to a laptop used as a workshop to monitor satellite quality and collect the data. The region in which the experiment took place is shown in Figure 3: on the roof of the Aeronautics and Astronautics department building at National Cheng Kung University in Taiwan. The red star is the known position of the base station. The broken rectangular red line is 25 meters by 10 meters along which the moving rover station moved clockwise.

However, it is difficult to show the true positions of the experiment. In this article, we tried to get the true position by using a linear regression method which used the time, t, as the explanatory variable and the position, y(t), as the dependent variable. The linear regression used the past five epoch positions as the dependent variables by which to obtain the linear polynomial, and the fifth position was put into the polynomial to get the position error. For example, in order to calculate an error at t=4, the position results from t=0 to t=4 must be taken into Equation (1) to form the second order polynomials with parameters P, Q, and R

 (1)

The experimental results are shown in Figure 4, which is the ENU positioning error, and Table 1 shows the analysis error mean and standard deviations. The experimental results show that the horizontal positioning accuracy is 0.037 meters (95 percent).

Relative Experiment. This experiment had one base station as before and included two rover stations which were placed on a T-bar, the relative distance being known, on a portable cart as shown in Figure 5. The region of the experiment is shown in Figure 6, where the star marks the location of the base station, with the rover station moving along the black arrow.

The relative error was calculated using a known distance, 0.72 meters, to compare the two rover station positions. Figure 7 shows the relative results of the experiment for which the mean value and standard deviations were recorded in Table 2. In this experiment, only about 4.5 percent of the positioning results failed to meet the requirement of 0.3 meters.

Common-View Satellite Experiment. Aircraft landing altitude and the ship’s swing motion caused by the state of the sea might affect GNSS information received by the antenna. This experiment had one base station and one rover station at fixed positions as before, but we attempted to flip the antenna of the base station toward the north by 80 degrees, as shown in Figure 8, and the rover station changed direction according to Table 3. The antenna directional change of 80 degrees were chosen for the extreme case that the base station and rover station could experience completely different satellites in view.

Results of the experiment are shown in Figure 9, in which the vertical lines indicate antenna directional changes. For this experiment, every change is 30 seconds. This experiment demonstrates that the position performance definitely varies. The position analysis is shown in Table 4, which shows a horizontal error of 0.116meters (95 percent).

Sea-State Experiment. In this experiment, one base station and one rover station were required in a fixed position, but the rover station changed the direction of the antenna, as shown in Figure 10, where the angle of x is decided according to the sea state in Table 5. On the other hand, the antenna changing toward a different direction simulated the swing motion of the boat.

The experimental results shown in Table 6 are the mean values, and Table 7 shows the standard deviations. The simulation provides the analysis results in order to authenticate the integration simulations. The results show that the sea state slightly influences RTK positioning.

UAV and Ship Motion Simulations

During shipboard landing processing, many complicated conditions must be taken into account, including crosswinds, an air-wake model, wind gusts, and deck motion. The ship deck motion and crosswind effects are two key factors that further increase the difficulty of ship-borne operations.

For this reason, the UAV controller must have anti- interference features. An LQG controller is able to reject the environmental disturbances encountered during landing in a lateral motion. For the ship deck motion, the chosen spectrum (the International Towing Tank Conference, or ITTC two-parameter spectrum) was used as the power spectrum of the sea waves to be simulated.

Aircraft Simulation. The aircraft was in the simulation, the SP.X-6, was designed by the Remotely Piloted Vehicle and Microsatellite Research Laboratory of National Cheng Kung University (see opening photo and cover). For the longitudinal motion, a combination of a linear quadratic integral (LQI) controller and a Kalman filter in the inner-loop system was used to control the vertical velocity and height mainly using an elevator. For the lateral motion, the LQG autopilots were designed with guaranteed robustness properties that allowed quick return to the designed point.

The SP.X-6 aircraft state functions are shown in Equation 2, in which the x, u, y, w, and v mean the system state vector, input, measurement, process error vector, and the measurement error, respectively. A, B, C, and K refer to the system state matrices, which can be evaluated by the system identifications that are derived by using the subspace identification to obtain an initial model. After that, the initial model will feed into the recursive prediction error method algorithm in order to arrive at further refined models.

 (2)

After obtaining the aircraft’s model, the LQG controller is used, a block diagram for which is shown in Figure 11 and for which the close-loop dynamic is given by Equation 3. The  means the estimated states are feedback by which to form the optimal control law, u=−K. The y means the output command with the LQG variables F, G, K, and L.

 (3)

The aircraft landing controls were divided into the longitudinal and lateral dynamics. For the longitudinal dynamics, the landing command was the vertical discrete height. In the case of the lateral dynamics, the stable condition was used when disturbances were encountered.

Up till now, navigation of SP.X-6 relied solely on the GPS signal. Using RTK technique for the landing process will enhance navigation accuracy. The navigation method is the point-to-point guidance law illustrated in Figure 12.

The basic concept of the point-to-point guidance law can be derived from the aircraft initial position A and the target position B in two-dimensional coordinate frame at every epoch. Desired heading angle θ_T and the distance between two points d can computed at each control loop via Equation 4.

 (4)

The navigation signal used in the simulation is of 20 Hz.

Deck Motion Simulation. Variations in waves are formed by the wind, and waves do not propagate only in one direction; the other direction will also affect wave propagation. The wave always is set as a stationary random process for the purpose of processing. The Longuet-Higgins model assumes that random waves are composed of many different wavelengths and harmonic amplitude superposition. Assuming the wave travels in a fixed direction, the peaks and troughs of the wave lines are parallel to each other and perpendicular to the forward direction of the waves, which are called two irregular waves or crested waves. Crested waves cause greater ship motion. The crested wave model indicates that point a at t epoch on a random sea wave height can be expressed as Equation 5, where a_i -th represents harmonic waves with ω_i frequency and ε_i initial condition.

 (5)

It can be seen that the wave function can be expressed as a superposition of individual harmonics, so as long as waves establishing harmonic amplitudes and harmonic frequencies can be simulated in order to create the wave model. In this research, the amplitudes and the initial conditions are obtained from the sea wave spectrum of the ITTC model:

 (6)

Four different sea state conditions were designed, as shown in Table 8 in the integrated simulation. Using the parameters from the spectrum analysis and the frequency divide method, the sea wave simulation could be obtained. Figures 13 and 14 show the simulation results of sea state A. Figure 15 shows all four state spectrum simulations results, and Figure 16 shows the sea wave height.

Integrated Simulations

In the integrated simulation, first the health of the RTK information was examined, and then, according the environment parameter settings, sea wave simulations were conducted. Subsequently, the aircraft landing process errors were presented using the experimental positioning analysis.

The integrated simulation system is shown in Figure 17; it can be divided into three parts. The first part is the sea state options shown in the black line region, and the sea wave change is displayed and the maximum changing rate is calculated after the sea state option is selected. The second part is shown in the green line region that is the landing analysis which includes RTK health status, ENU error size. The last part is the landing animation which is enclosed in the red line region.

Four sea-wave height simulation statuses can be selected, and the chosen sea state can be used to determine the corresponding landing environment, as shown in Figure 18, which illustrates the ship motion simulated by the wave height.

RTK health information was simulated according to the experimental results in Table 9, in which the RTK information unavailability was 1.1 percent. A random Gaussian number was used to simulate the health of the RTK satellite information.

After the sea-wave simulation and the RTK health simulation, the second concern was the landing process simulation. The landing process simulation has two conditions, namely the “normal landing” condition and the “landing with common-view satellite problem” condition. The normal landing process errors were presented using the Sea State Experiment results, while the landing with common-view satellite problem process errors was simulated by the result of Common View Satellite Experiment positioning analysis.

For example, a ship was traveling at a velocity of 10 m/s in East, and an aircraft was cruising at a velocity of 20 m/s toward the East. The initial position of the ship was at (E_S, N_S, U_S) = (200, 0, 0) and the aircraft was at (E_A, N_A, U_A) = (0,150,100). In the landing process, the desired heading angle and the distance to the waypoint were evaluated every epoch. The simulated landing process example is shown in Figure 19; the blue line is the ship’s trajectory and the red line indicates the aircraft’s trajectory.

The guidance accuracy includes the control accuracy and the navigation sensor measurement accuracy. In the simulation result, the control accuracy (that is, controller error) was neglected. Therefore, the error for the landing process becomes only the navigation sensor measurement error which was the RTK error in this article. Users have the options to add different controllers as well as the controller error in the simulations.

The landing positioning error was simulated using the imported analysis results in the correspondence sea state included in the RTK status shown in Figure 20 and the landing ENU errors are shown in Figure 21.

Red stars in Figure 20 indicate the warning window when the simulated RTK statuses were unhealthy. For example, the 114th, 126th, 169th and 240th epochs in Figure 21 indicate that RTK data is unavailable during this time simulation. The unhealthy RTK signal might cause interruptions in navigation service in the landing process, as shown as the red stars in Figure 21. For the epochs with red stars, the simulated position results were exceeding the performance requirement for RTK shipboard landing. When this situation happened, the monitoring system might raise a flag to the aircraft’s guidance system not to use the RTK signal for landing at this period of time. Excluding these unhealthy RTK epochs, the simulated landing errors were well met the performance requirement for RTK shipboard landing, as shown in Figure 22.

An overall simulation result is illustrated in Figure 23, when the successful landing message was shown in a pop-up window, the landing information of the whole landing process would be shown in the graphic user interface.

Conclusions

Experimental results showed that 99 percent of the horizontal positioning was in the range requirement of 0.3 meters. Using the common view satellite experiment and the sea state variation experiment conducted in this study, the limitations of RTK positioning can be understood. Monitoring the RTK status can provide high-quality accuracy with regard to guidance of the landing process. We hope that the results of this study will become a reference for building a shipboard landing system in Taiwan.

Manufacturers

All of the experimental data were collected by a workshop computer through a NovAtel (www.novatel.com) Connect program data file. The base station setup included a NovAtel GPS-703-GGG antenna with a Sokkia tripod and the NovAtel Propak-V3 RT2-G receiver. The rover station setup included a portable vehicle with a battery, a NovAtel GPS-703-GGG antenna and the NovAtel Propak-V3 RT2-G receiver.

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Chiu-Jung Huang received her B.S. degree from National Cheng Kung University (NCKU) in Taiwan. She is currently studying for her M.S. degree in aeronautics and astronautics at NCKU.

Shau-Shiun Jan is an associate professor of aeronautics and astronautics at NCKU. He directs the NCKU Communication and Navigation Systems Laboratory (CNSL). His research focuses on GNSS augmentation system design, analysis, and application. He received his Ph.D. degree in aeronautics and astronautics from Stanford University.