Tag: pseudolites

In the battle for reliable positioning and timing, the U.S. Army is engaged in a multitude of activities, including mounted and dismounted A-PNT (assured position, navigation and timing) systems, anti-jam technology and pseudolites.

The idea is simple: Take some GPS satellites, and put them on or near the ground. Now you have a navigation system where you have full control over the locations and power of the transmissions. You can ensure that the transmissions reach places that GPS normally struggles with, such as deep urban canyons, forests and valleys.

You can turn up the transmit power, so they are much harder to jam than spaceborne GPS signals. These pseudo-satellites, commonly referred to as pseudolites, have seen steady interest over the years for a variety of applications.

Now the U.S. Army is pursuing the use of pseudolites as part of its initiative to maintain operation in GPS-denied environments.

Pseudolite Basics

There are various types, and use-cases, of pseudolites. In this column we’ll consider the direct-ranging pseudolite, which can be simply considered as a ground-based GPS satellite. If we deploy several pseudolites on the ground, we can imagine that a normal GPS receiver would be able to receive the GPS-standard transmissions and derive a position, just as we would from the space-based satellite transmissions.

The fact that the pseudolites are ground-based introduces us to the first consideration: The locations of the transmitters are no longer described by orbital parameters. Instead of calculating the position of satellites, we need to describe the location of the pseudolites in geographical terms, perhaps with a fixed position described in Earth-centered, Earth-fixed (ECEF) coordinates.

The transmitted navigation data message, which would normally contain almanac and ephemeris information, may now need to contain the geographical position of the pseudolite. Not a problem, but our GPS receivers will need a software upgrade to be able to handle this situation.

The deployment of the pseudolites themselves poses an interesting problem. Imagine a military scenario, where the army is deployed to a region of interest. Navigation warfare is taking place, and GPS is frequently jammed in the region.

High-power pseudolites are deployed to allow the army to navigate despite the jamming, using the same standard-issue GPS receivers that soldiers are familiar with.

The first problem is, having placed your pseudolites in position, how do you know where they are?

You might choose to place your pseudolites at locations that have previously been surveyed, so you know where they are in advance. But this isn’t likely, particularly if you’ve just moved your troops into an unfamiliar area. You might also want to move the pseudolites regularly, as the army moves to new ground. So the pseudolites need to determine their own position, and the easiest way for at pseudolite to determine its own position is with GPS, of course.

Isn’t this a bit incestuous? If we’re using pseudolites because GPS is jammed, how does the pseudolite get its position? This is why military pseudolites will typically be fitted with some form of anti-jam technology, such as a controlled radiation pattern antenna. This allows the pseudolite to receive GPS satellite signals in the presence of jamming, determine its own position, and transmit that as part of its own navigation message.

So, now that we can get pseudolite locations, the next consideration is: Where should pseudolites be placed?

A-DOP-ting a Good Layout

If you know about GNSS, you’ll be familiar with the concept of dilution of precision (DOP). This is essentially a measure of how accurate your position estimate is likely to be, due to the geometry of the satellites: a good wide spread of satellite positions gives us better accuracy.

The DOP can be easily calculated by forming a covariance matrix of the geometry, expressed in an appropriate coordinate frame. If (x_n, y_n, z_n) denotes the position of the n^th pseudolite, and (x, y, z) the position of the receiver, we can express the unit vectors from the receiver location to the pseudolite location:

We then form a matrix of these unit vectors:

Finally, we form the covariance matrix from which we can extract the DOP values:

From the elements of this matrix we can determine the various DOP metrics. Let’s concentrate on horizontal DOP (HDOP), given by:

When positioning using GPS satellites, we are blessed with a Walker constellation that generally gives us a nice spread of satellite locations (unless we’re in an urban canyon). On the battlefield, using pseudolites, we do not have the same luxury.

Let’s consider a scenario: a conflict in Helmand province, Afghanistan. An operating base is established at Camp Shorabak, where a pseudolite is operating, and three further pseudolites are deployed in the field. This is shown in figure Figure 3.

Taking a look at Figure 4, we can see what this means for HDOP. The regions shaded green represent locations where our HDOP is less than 2.5, and the red areas represent an HDOP greater than 50.

Soldier #1 is surrounded by the four pseudolites, which is a pretty nice arrangement: We get an HDOP of around 2.4. But if we now consider soldier #2, located a bit further out, we get a very different picture.

Here we have an HDOP of 64, which is fairly terrible. It’s not really that surprising looking at the geometry — to soldier #2 the pseudolites all appear in a similar direction. Soldier #2 cannot expect to achieve good positional accuracy in this arrangement.

So getting a good geometric spread of ground-based pseudolite locations could be a bit of a challenge, especially if the operating area is constantly moving and changing. The next thing to think about is getting enough height.

Getting the Height Right

When we perform positioning using GPS, we typically track several satellites, which have a range of elevations. Many GPS receivers will choose to ignore the satellites at low elevations, such as those within 5 degrees of horizontal, because those satellites are generally the least reliable. They may be partially obscured, and subject to more noise and fading.

Ground-based pseudolites all have very low elevations by definition. Unless the terrain is perfectly flat and smooth, pseudolites quickly become obscured. Even with flat ground, pseudolite signals will disappear behind the horizon after a few kilometers.

Let’s go back to our Afghanistan scenario again. This time, instead of looking at DOP, let’s look at the geographical coverage of our four pseudolites. Here we’ll assume that our user, the soldier, is 2 meters (m) high, and the pseudolite antennas are mounted at a height of 20m above the ground. That’s pretty high — the army will need to erect some masts.

Figure 5 shows what we get. The green areas are locations where our soldier can see all four pseudolites; yellow three, orange two, and red one. At all other locations, no pseudolite signals can be seen at all. You can quickly see that the range isn’t great — terrain, even small undulations in the ground, is a line-of-sight killer. Add some buildings and trees and the situation gets worse. Reduce the height of our pseudolites below 20m, and the situation gets worse. Soldier #1 can receive three pseudolite signals, but soldier #2 has no hope in this case.

Let’s raise the height of the antennas to a fairly crazy 100m above ground (Figure 6). As expected, we get much better coverage, but soldier #2 still has a problem. To get good signal coverage over any sizable area, you really do need to get those antennas as high as possible.

Augmenting GPS

Often, we don’t want to rely on pseudolite signals alone. If GPS is available, we clearly want to make use of it, and so we want to use a mixture of both GPS satellites and pseudolites. Consider working in a region of sporadic GPS reception, such as an urban environment or forest. We can usually receive a couple of good GPS satellites, but we also need a couple of pseudolites to help us get a complete navigation solution.

Coming back to one of our original objectives, which is to avoid redesigning the GPS receiver hardware, we need to make sure that our receivers can receive and process both GPS satellite signals and pseudolite signals simultaneously. To achieve this, we can decide to make our pseudolites transmit GPS-standard signals, and make use of unassigned spreading codes to essentially create new satellites in the constellation.

But we quickly run into a problem. GPS satellites are always a distance of around 20,000 kilometers away, and the received signal strength is also fairly constant: around –158.5 dBW. This is a very small signal, as we all know, sitting well below the noise floor. When we suddenly bring high-power pseudolites into the mix, we have quite a nasty problem to deal with.

Near, Far, Wherever You Are

Let’s say, for argument’s sake, we have a pseudolite transmitting with a power of 1 watt. Conducting a basic link budget analysis gives us the plot below and suggests that, at a distance of 10 km from the pseudolite, we can expect to receive the signal at around –112 dBW. This is way above our GPS satellite signal level, but might be manageable by a receiver. Now consider a receiver at a distance of 100 m from the transmitter: we receive a power of –72 dBW, which is huge.

In our quest to augment GPS and make it more robust, we have in fact created a GPS jammer, and achieved exactly the opposite. As with any radio communications link, the received power is extremely sensitive to the distance (varying with the square of distance). In pseudolite terminology, this is known as the near/far problem.

The near/far problem has given engineers headaches for quite some time. Essentially, the problem comes down to: How can our GPS receivers handle such a massive dynamic range of expected signals? Especially if our objective is to avoid modifying the GPS receiver hardware, if at all possible.

How can a receiver handle the high power of a close-up pseudolite, which is to all intents a jammer, whilst simultaneously receiving the tiny GPS satellite signals from space? Various solutions have been proposed over the years, but one of the current favorite techniques involves pulsing the pseudolite signal.

The idea, then, is to only turn on the pseudolite periodically, essentially applying a duty cycle to the transmission. If a pseudolite isn’t transmitting, it can’t interfere with the normal GPS signals. There are a couple of things to take into consideration here:

1. What should the pulse duty cycle be, to enable both satellites and pseudolites to be tracked?
2. How does the GPS receiver behave when presented with alternating large and small signals?

A mathematical analysis of duty cycle effects is beyond the scope of this column, but consider Figure 8 for a qualitative view. Here we have two pseudolites operating alongside GPS satellites. The duty cycle chosen here is for the pseudolite to be operational for 10% of a 1 millisecond integration period. This gives enough time, when the pseudolite is not transmitting, for the low-level GPS satellites to be tracked.

The second pseudolite, which is closer and therefore higher power, transmits for a further 10% slot after the first pseudolite. You can see that each additional pseudolite eats into the time available for tracking GPS satellites, and degrades the signal-to-noise ratio. There are some tricks you can play, such as transmitting multiple pseudolites at the same time if you know they will be similar power levels, but it can get complicated.

The Importance of Gain Control

How the receiver copes with the large differences in received power level depends largely on the design of the RF front-end in the receiver. Most GPS receivers will have a certain amount of automatic gain control (AGC), which is a feedback loop designed to keep power levels constant. Many GPS receivers, though, simply aren’t designed with enough AGC to handle pseudolite-level signals (think GPS jammers again).

Military receivers, though, tend to have greater RF handling capabilities, and more bits in the ADC, so are better-suited to the situation. It is then a question of making sure the AGC loop responds in an appropriate time, compared to the duty cycle of pulses.

Figure 9 illustrates a slow AGC response, which is not particularly suitable. Compare this with Figure 10, where we have a fast AGC response, quickly adapting to the switches in power level. A receiver with this characteristic will be better able to track both pseudolite and satellite signals.

Airborne Pseudolites

If you’ve read this far, you’ll now know that the main problems with ground-based pseudolites are lack of good geometry, signal blocking by terrain, and the horrendous near/far issues. Wouldn’t it be nice if we could raise the pseudolites to a really high altitude, and all these problems would go away? Wait, that’s the GPS satellite constellation!

Ok, let’s not put them that far up. But how about carrying pseudolites on high-altitude airborne platforms instead? Great idea, and that’s why this is a current thread of defense activity in various countries. High-altitude long-endurance (HALE) or HAPS (high-altitude pseudo-satellite; the clue is in the name) unmanned platforms can be used to carry pseudolites at high altitude.

This solution can provide excellent coverage, the pseudolites can be repositioned as necessary, and the near/far problem is also far less pronounced.

I leave you once again with our Afghanistan scenario, from the point of view of a high-altitude airship at 18,000 meters.

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Figures: Michael Jones