Glonass Ambiguity Resolution with RTKLIB Revisited

To get a high precision fixed solution in RTKLIB we need to resolve the integer ambiguities that come from the carrier phase measurements.  Resolving the integer ambiguities for the GLONASS satellites is more challenging than resolving them for the other constellations.  This is because, unlike the other constellations, the GLONASS satellites all transmit on slightly different frequencies.  This introduces an additional bias error in the receiver hardware.

These hardware biases are constant, generally the same for all receivers from the same manufacturer, are proportional to carrier frequency and are similar between L1 and L2.

In the demo5 version of RTKLIB, there are four choices for how to handle GLONASS ambiguity resolution (AR). I will cover all four briefly, but then focus on the “autocal” setting which I have enhanced in the most recent version (b29c) of the demo5 code.

Off:  If Glonass  AR is set to “Off”, then the raw measurements from the Glonass satellites will be used for the float solution but ambiguity resolution will be done only with satellites from the other constellations.  If you are not using the demo5 version of RTKLIB, this is usually your only choice when using receivers from different manufacturers for the rover and the base.  However, you are giving up a significant amount of information by ignoring the GLONASS ambiguities and so I would not recommend this setting if you are using the demo5 code, unless of course your receivers don’t support the Glonass satellites.

On:  If Glonass AR is set to “On” then RTKLIB will treat the Glonass ambiguities the same as the ambiguities from the other constellations and will not make any attempt to account for the additional hardware biases.  Use this setting if your base and rover receivers are from the same manufacturer, since in this case, the biases will cancel and can be ignored.  There are also some cases in which different manufacturers have equal or nearly equal biases as we will see later, in which case you can also use this setting.  This is your best solution for dealing with Glonass ambiguities.  I always try to use matched receivers for base and rover if possible.

Fix-and-Hold: This is an option I have added to the demo5 code for Glonass AR.  It is an extension to the “fix-and-hold” method used for other constellations but instead of using the additional feedback to track the ambiguities, it uses it to null out the hardware biases.  I recommend this setting when using the demo5 code with unmatched receivers.  It takes advantage of the additional information in the Glonass ambiguites most of the time.  However, fix-and-hold is not enabled until after a first fix has been achieved, and so the Glonass ambiguities are not available until then.  This can mean longer time to first fix and less robustness compared to the “On” option, so don’t use this option for matched receivers.

Auto-cal:  This option adds additional states to the kalman filter to estimate the receiver hardware biases as a function of carrier frequency, one state for L1, another for L2.  In previous experiments I had not had any success with it.  Recently, however, I discovered that if I adjusted the filter settings, it can be effective for a zero baseline case, where base and rover are both connected to the same antenna so that almost all other errors are completely cancelled.  With a little more experimentation I also found that for short baselines it can also be effective if the kalman filter state is pre-set to something close to the final value before the solution is started.  It will then usually converge to the correct bias value.  However, there is currently no mechanism in the code to adjust any of these values, so I have not found this mode to be useful in its current implementation.

To make the auto-cal option more flexible, and hopefully more useful, I made a few modifications to it in the b29c code.  I added the capability to pre-set the initial state value and also to adjust the internal filter settings, specifically the initial variance and process noise for this state.  The units for the state, and hence for the initial value are in meters per frequency channel and values generally are within +/-5 cm per channel.  I used some existing config parameters that are currently unused to reduce the amount of code I needed to change.  Unfortunately it means that the names are not as descriptive as they could be.  The new config parameters are:

pos2-arthres2 = relative GLONASS hardware bias in meters per frequency slot
pos2-arthres3 = initial variance of GLONASS hardware bias states
pos-arthres4 = process noise for GLONASS hardware bias states

Bias values have been published for some of the most popular geodetic quality receivers but are generally not available for lower-cost or less popular receivers.  Here is a table of values from a paper published by Lambert Wanninger in 2011 for nine receiver manufacturers.

biases

I was able to verify these results for Trimble, Leica, and Novatel, but I found a much lower value for Septentrio so I suspect the biases may have changed in their newer receivers.

To demonstrate the modified autocal option, I will start with a zero baseline case between a ComNav receiver and a Tersus receiver.  It is easiest to measure the hardware biases in the zero baseline case because most other errors will cancel and the hardware biases will be the dominant error.  In this case, I have significantly reduced the initial variance setting from the original value of 1.0 to 1E-7 and increased the process noise from 1E-6 to 1E-3.

I have run the solution several times with the initial bias value set to different numbers between -.05 and 0.06.  Here are the results for both L1 and L2.

biases1

The convergence occurs just after first fix is achieved.  If a fix is not achieved, then the state will not converge as you can see above for the 0.06 example.   In this case, the initial value was too far from the correct value and prevented getting a fix.  As you can see, all the other cases converged towards a single value around -.022, both for L1 and for L2.

Another way to visualize the error in the initial value is to look at the GLONASS residuals after first fix is achieved.  The plot below shows the GLONASS L1 carrier phase residuals  for different initial values, for 0.03 on the left, -0.05 in the middle, and what I believe is the correct value for this receiver combination of -.022 on the right.

 

acal1

Here are the same plots for the L2 carrier phase residuals.

acal2

Through a slightly tedious process, I am fairly easily able to iterate the residuals down to near zero for different pairs of receivers in my possession.  Note that this gives me the relative difference in biases for each receiver pair, and not absolute values for each receiver, unlike Wanniger’s table which is for absolute biases.

Extending the table to receivers used in nearby CORS stations is a little more challenging because the initial bias value needs to be fairly close to get a first fix and hence a convergence, but still possible if the base station is not too distant.   I found data sets that included CORS data from Leica, Novatel, Trimble, and Septentrio receivers.  Using the above procedure to iterate the residuals down to near zero, I was then able to extend my table and make the values absolute by choosing the unknown offset to make my bias pairs align with Wanninger’s table.  This is the resulting table I created.

ComNav    =   2.3 cm
Leica          =   2.3 cm
Novatel      =  2.3 cm
Septentrio = -0.3 cm
SwiftNav   = -0.2 cm
Tersus        = -0.1 cm
Trimble      = -0.7 cm
u-blox         = -3.2 cm 

To generate an initial value for the bias state from this table for an RTKLIB solution, subtract the base station bias from the rover bias, then divide by 100 to convert from centimeters to meters.  This value can then be used to set the “pos2-arthres2” config parameter in the config file.  For the RTKPOST and RTKNAVI GUI option menus I have labeled this “Glo HW Bias”.

To test this code on an independent set of data after generating the table, I used a data set recently sent to me by a reader.  It consists of a u-blox  M8T receiver for rover and Leica receiver just a few kilometers away for base, and was collected in Europe.  The rover position was static but I ran the solution in kinematic mode to make the solution a little more challenging and to make any errors in the solution more visible.

To generate the correct config value for RTKLIB I  subtracted the Leica bias of 2.3 cm from the above table from the u-blox bias of -3.2 cm to get a relative bias between receivers of -5.5 cm or -0.055 m.  I added “pos2-arthres2=-0.055” to the config file and then ran the solution four times, with pos2-gloarmode set to “off”,”fix-and-hold”,”autocal”, and “on”.  Although I left the bias value set for all runs it is ignored unless gloarmode is set to autocal.

Here are the times to first fix, the number of satellite pairs used for the initial fix, and the number of satellite pairs being used for fix after 10 minutes.

  Time to # sat pairs used # sat pairs used for
GLO AR mode first fix for initial fix fix after 10 min
OFF 4:10 7 7
Fix&Hold 4:10 7 11
Autocal 1:05 14 14
On 6:47 14 14

As you would expect, the time to first fix for gloarmode=”off” was the same as “fix-and-hold” since “fix-and-hold” does not use the GLONASS satellites for initial fix.  After 10 minutes it was still only including four of the GLONASS satellites in the ambiguity resolution which was a little unusual, typically I would have expected more GLONASS satellites to be included.

With gloarmode=”autocal”, the time to first fix was reduced from 250 seconds to 65 seconds and the number of satellites included in the first fix increased from 7 to 14., both significant improvements.

The most surprising thing in this data is that when gloarmode was set to “on” it acquired a fix at all.  In many similar cases it will never get a fix.  The GLONASS carrier phase residuals after initial fix were very high though as can be seen below.  The left plot is with gloarmode set to “on”, and the right plot is with it set to “autocal”.

biases3

The ambiguity resolution ratio was also much higher when autocal was enabled as can be seen below (yellow/green=autocal, olive/blue=on) which improves robustness.

biases2

The large residuals did not affect the solution position, as the two solution did not differ by more than 2 mm at any time.  The autocal solution however is much more robust in the sense that it is less likely to lose fix.

Although I have found the results with autocal enabled are generally excellent with relatively short baselines (<10 km), I have found the results less encouraging for longer baselines (>25 km).  In these case I have found that I often get better results with pos-gloarmode set to “fix-and-hold” then I do with “autocal”.  I don’t understand exactly why this is, but suspect that the fix-and-hold correction is more general and may be correcting for more than just the GLONASS hardware biases.

The code changes for this feature are included both in my Github repository and in the newest (demo5 b29c) executables available to download from the rtkexplorer website.   If you choose to experiment with this feature, please let me know if you find any errors in my table, or can add values for any additional receivers.

[Note 6/17/18:  I had a issue with uploading the executables to the website.   If you downloaded them prior to 6/17/18, please download again to get the updated version.] 

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