Evaluating the quality of moving position solutions

Stationary position solutions are easy to evaluate, an ideal solution is a single point, any deviation from this point must be error. It is possible that the point itself is in error in an absolute sense but since I am only interested in the distance between receivers I am not concerned with absolute error.

Evaluating a solution for a moving receiver is more difficult since it is not easy to know what is the correct solution to compare to. If I had an expensive high precision receiver/antenna I could mount it on the same platform as the test receiver and use that as a reference, but I don’t have that, so I need to come up with another solution.

Mounting two low cost receivers on the moving platform gives us a couple of options for evaluation. First of all, since I have data from two nearby base stations, I can calculate two solutions, each using one of the low cost moving receivers as rover, and one of the COREX base stations for base data. Since the two low cost receivers remain a fixed distance apart, the difference between the two solutions should be constant in magnitude. The direction of the difference however is varying as the orientation changes. This means the difference between the two solutions should be a circle with radius equal to the distance. Since each solution is based on different base stations, and different receivers they should be fairly independent. The fact that one of the base stations is reporting GPS only, and the other is reporting GPS and GLONASS should also increase the independence of the solutions, since they are also using different sets of satellites,at least if we include GLONASS satellites in the solution. This not the case at the moment since the default config has GLONASS turned off, but we will turn it on soon.

RTKPLOT has a nice feature which allows us to plot the difference between two solutions. Click on the “1-2” button on the menu bar to see this, after opening both solutions from the file menu.

Below are the two solutions plotted on top of each other. Since the scale is 20 meters per division, it is impossible to see any difference between them.

Here is a plot of the difference between the two solutions while the car was stationary and driving in low velocity circles. Now the scale is 10 cm per division. We can see the expected circle, and the error from that circle is generally less than 5 cm once the solution converges to a fixed solution. I’ve jumped ahead a bit, since the solution in the plots includes some input parameter changes as well as some code changes, so the default solution we just calculated won’t be as clean, but we’ll get to those changes soon. The good news is that it looks like we are getting errors of only a few centimeters after the solution has converged, even when both receivers are moving.

There is also another, simpler way to evaluate the quality of the solutions if, as in my case, we are interested only in relative error and not absolute error. Instead of generating absolute solutions using the COREX base stations, we can calculate a differential solution directly, using one of the low-cost receivers as the base and the other as the rover. The result will then be the position difference between the two receivers. Since the distance between the two receivers is fixed but the orientation between them is varying as the platform they are on is moving, the solution should be a circle, again with radius equal to the distance between the two receivers. In this case, unlike the previous one, we do not get any absolute position information, only the distance between the two receivers. Note that even though the base is moving in this case, we do not use the “Moving-Base” solution option from the positioning mode choices, but stick with “Kinematic”. The solution algorithm does not need exact position of the base, only approximate location. We use the approximate starting location of the base receiver which is in the header of the RINEX observation file and ignore the fact that the base is moving. As long as we are concerned only with relative position between the two receivers and the base does not move a large distance from its starting point, this is a valid assumption to make.

Here is a plot of the result from using both base and rover on the moving platform. Note that it is very similar to the previous plot, generated from the difference between two absolute solutions, and again the error is only a few centimeters once the solution has converged.  As in the last plot, it does include some changes from the default input parameters and code that we will get to later.

This is the form of solution I will use for evaluating the effectiveness of various input parameters and algorithm changes.