Most of my work with RTKLIB has been done with differential solutions (RTK or PPK) using two receivers, a base and a rover. I have briefly explored static PPP solutions but have not previously looked at kinematic PPP solutions or analyzed the internal standard precision solutions of the u-blox F9P receiver. In this post, I will take a closer look at these options.
For this experiment I started by collecting a data set using an F9P receiver connected to a u-blox ANN-MB-00 antenna mounted on the roof of my car. The first 40 minutes were static followed by another 30 minutes of driving around residential and light industrial neighborhoods, all sparsely treed. The goal here was to start with something not overly challenging so I intentionally avoided any significant tree canopy, underpasses, or tall buildings. I enabled and logged u-blox raw observation and navigation messages (RXM-RAWX and RXM-SFRBX) as well as NMEA solution messages for the internal F9P standard precision solution ($GNGGA, $GNGLL, $GNGST).
I’ve uploaded this logged raw data file as well as all other necessary files to generate the solutions described below to the download section of my website in case anyone wants to download the data and duplicate my results. I did make some changes to the RTKLIB code as I worked through the experiment, so you will also want to download the executables for the latest b33f version of the demo5 RTKLIB code.
To generate a ground truth for the subsequent comparisons, I first converted the raw observation data file to rinex using RTKCONV and then ran a combined-mode PPK solution of the raw data against a nearby CORS station using the demo5 b33f version of RTKPOST and my standard configuration settings for the F9P (ppk.conf in the data download folder). The fix rate in the resulting solution is 99.9% and the CORS station is less than 10 km away, so I have a relatively high confidence in the accuracy of this solution. Note that the base coordinates in the CORS station rinex header are NAD83 while the single receiver solutions will all use the WGS84 datum. To correct for this, I have specified the base position in the config options in WGS84 coordinates.
[Note 1/11/21: As Brian pointed out in the comment section below, I made an error in this conversion. This adds a 5-10 cm DC bias to the E-W and N-S components in all the difference plots below. It doesn’t have a large effect on the first few plots but it becomes a significant percent of the error in the final PPP comparisons. I plan to make a follow-up post where I correct this error.]
In the image below, the raw observations are on the left, and the ground track of the PPK solution is on the right. The transition in the raw observations where the cycle slips (red ticks) begin indicate when the car started moving.
Since the raw log file from the F9P receiver includes NMEA position messages in addition to the raw observations, I can plot this file as a solution file directly with RTKPLOT. This will extract the NMEA positions from the file and ignore the raw observations.
If I use RTKPLOT to plot both the RTKLIB PPK solution and the F9P real-time (NMEA) solutions, I can then select the “1-2” button to plot the difference between the two solutions. Since the errors in the real-time solution will be much greater than the PPK solution, we can take this plot to indicate the error in the real-time solution.
Note that the errors are larger (and lower frequency) during the static portion of the data set on the left half of the plot than they are on the right when the car is moving. This may seem counter-intuitive but it is because the multipath component of the error gets randomized by the movement of the receiver antenna relative to the satellite signals.
If you look at the datasheet for the F9P, you will see that horizontal accuracy is specified as 1.5 m CEP accuracy for a PVT solution and 1.0 m CEP accuracy for an SBAS solution. I didn’t calculate the exact CEP value for the plot above, but it would correspond to where the square root of the sum of the squares of the two horizontal components was less than the spec for 50% of the time. In this case the solution included SBAS augmentation so I would expect the 1.0 m accuracy spec to apply. Just eyeballing the plot, it looks we are getting at least this accuracy during the static portion and even better accuracy during the dynamic portion. This makes sense since the spec is for a static case. I could not find an F9P spec for dynamic accuracy.
Note that I have upgraded the firmware in the F9P module to version 1.13 which was released fairly recently. SBAS support was added to the F9P with the 1.13 upgrade so I suspect if you are running older firmware on your F9P, you may see larger errors. You can check the firmware version running on your module by querying the UBX-MON-VER message from u-center.
Sometimes it’s hard, at least for me, to look at the raw error numbers and visualize what they mean in the real world, so I have shown a snapshot of the two ground tracks below, the green dots are the PPK solution, and the yellow dots are the real-time F9P solution. I suspect for many applications, the level of error in the real-time solution would be acceptable. I was actually surprised to see how good it is.
So next, let’s look at the RTKLIB single frequency post-processing solutions. I will start with the “Single” positioning mode solution. This mode gives a very coarse solution and is really only suitable for initial approximate locations for the other solution types but we’ll take a quick look at it anyways. I ran an RTKLIB solution using the same config file as for the PPK solution, I just changed the “Positioning Mode” option from “Kinematic” to “Single. I then plotted the difference between this solution and my reference solution as I did before. Below is a plot of the difference between the two solutions.
As you can see, the errors are much larger than the real-time F9P solution and so of very little use.
Next, let’s look at the RTKLIB Kinematic PPP solution to see if there is any opportunity to improve upon the real-time solution here. To create a kinematic PPP solution I used the raw observation and navigation file from the F9P, along with precise ephemeris and clock files, a recent DCB (differential code bias) file, an antenna calibration file, and the ppp.conf config file, all included in the uploaded data set folder. I used very similar configuration settings to the PPK solution with a few exceptions. First, I enabled or configured all the PPP relevant parameters. For now, you can see the details of these settings in the ppp.conf configuration file, I hope to cover them in more detail in a future post. Next, I increased the minimum elevation mask from 15 degrees to 20 degrees based on earlier experiences showing that the RTKLIB PPP solutions are more vulnerable to errors and cycle slips in the low elevation satellites than are the PPK solutions. Also, I increased the outlier threshold from 1 meter to 30 meters since the residuals are much larger in the PPP solution and the outlier handling is different. I then ran two solutions, one with the first rapid precise ephemeris/clock files I was able to find online published after the data was collected (SHAOMGXRAP*.*), and the second solution was run with the final precise ephemeris/clock files (ESAOMGNFIN*.*). Both solutions were run with the most recent DCB files I was able to find which were based on analysis from Nov 2020. There are a number of online repositories of precise ephemeris data but many of these are GPS and GLONASS only, it is more difficult to find precise files that include Galileo and Beidou as well. The CDDIS, ESA, IGS, CODE, and other websites all have different variations of precise ephemeris files available for download but I have not yet found any one site that is best for both rapid and final multi-constellation ephemeris files.
Below are the differences between the two PPP solutions and the same PPK reference solution as used above, with the rapid ephemeris solution on the top, and the final ephemeris solution below.
[Note 1/11/21: See note above regarding the biases in this plot, they are a large part of the remaining error especially in the final ephemeris comparison plot as well as the CSRS PPP plot below]
In this case the rapid ephemeris/clock files were available the following day, the final ephemeris/clock files were not available until a week after the data was collected. Both solutions show smaller errors than the F9P real-time solution and the errors in the final solution are smaller than in the rapid solution, as would be expected.
PPP solutions typically have long convergence times, so some readers might be asking themselves why they don’t see any signs of this in these PPP solutions. The answer is because they were run in “combined” solution mode meaning the solution is run forwards and backwards and the two combined. Typically in a combined solution, and this includes the 2.4.3 version of RTKLIB, the kalman filter states are reset between the forward pass and the backwards pass to insure the two solutions are independent. In the demo5 code I have chosen not to reset the filter states unless it is a PPK solution with fix-and-hold enabled. This means the filter states will be fully converged at the beginning of the backwards pass and this will improve the overall accuracy of the solution at the possible expense of some theoretical loss of integrity in the solution, although I have not found this to be an issue in my limited testing. The convergence still needs time to occur however, so I would not recommend using this technique on data sets less than half an hour and even that might be marginal.
As you might expect, the errors in the PPP solutions are a fair bit lower than the real-time solution, while still quite a bit larger than the PPK errors. I suspect there are situations where these solutions would be of use, particularly where local CORS stations are not available. The biggest caveat is that the PPP solutions are less robust than either of the other two solution types and it is also more difficult to detect larger errors in the PPP solutions compared to the PPK solutions since there is no verification step from the ambiguity resolution.
Use of static PPP solutions seem to be quite common, I see less use of kinematic PPP solutions, so I was somewhat surprised and pleased to see how well the RTKLIB kinematic PPP solutions did work.
For static PPP solutions I prefer to use the free online CSRS PPP solution service I’ve described in other posts rather than RTKLIB since it is simpler to just submit the observation file than it is to find the precise ephemeris file and I also have more confidence in the accuracy estimates of the CSRS solution. It does take longer to converge than the RTKLIB solution since it is only using GPS and GLONASS satellites but this is only a minor inconvenience for a static measurement. For a kinematic measurement, the smaller number of satellites is a bigger problem but I thought it was worth a shot so I submitted the raw data file to CSRS and specified a kinematic solution. The CSRS solution is not directly plottable with RTKPLOT but I wrote a short python script to convert it to RTKLIB solution format and plotted the difference from the reference solution below.
The solution is no better than the real-time F9P solution when the car is moving, so this is also probably not a useful solution. It is interesting that in this case, unlike all the other solutions, the errors are larger when the car is moving than when it is stationary. This is probably because of the increased number of cycle slips during this time.
While that is probably enough for an initial exploration, I hope to take a closer look at some of these results as well as potential improvements in future posts. Please comment below if you would like to add anything else to the discussion.