Proof of Concept test - Extremely accurate 3D velocity measurement with a ublox 6T module.

 

When the ublox 6 series modules were released, I noted that the 6T and 6P modules provided access to the raw carrier phase measurements, and I started thinking about how to use this capability.  My connections through my university research appointment weren't strong enough to get ublox to sample a dev kit to me (they generally don't sample them at all).  Jordi and Chris from 3DRobotics.com were kind enough to use their customer relationship with ublox to get a sample 6T module and provided it to me mounted on the standard DIYDrones ublox LEA-6 module.  So mine looks just like the one above, except it has a 6T module instead of a 6H.

 

My prime curiosity was how good the carrier phase measurements from this module were.  The datasheet indicates that carrier phase measurements are available, but gives no specs about their accuracy.  So I had no idea if they would be of value.  Well, with a module in hand, some measurements made, and post-processing completed, I can tell you that there is tremendous potential here, but a lot of work before this is something ready for everyday use.

 

OK, what is carrier phase and why do I care?

A carrier phase measurement is a measurement of the phase of the arriving carrier wave signal from the gps satellite.  Think of it this way - as the radio signal from the GPS satellite travels from the satellite to your receiver it completes some fractional number of cycles of oscillation.  That means that the distance from the satellite receiver to you is some fractional number of wavelengths - say 100 million and 1/2 wavelengths.  The carrier phase measurement gives you the fractional value of 1/2 wavelength, or 180 degrees of phase.  That in itself is almost useless.  Fortunately the gps module gives us something a little better than that.  What it reports is the phase change (or the number of wavelengths of distance change) between the satellite and the receiver from one measurement epoch to the next.  So what we really have is a measurement of the change in distance between the satellite and the receiver over a known period of time.  And so theoretically, given that we know something about the location and velocity of all the satellites we should be able to use this information to calculate the (3D) velocity of the receiver.  Just one more thought on this topic - we could do the same thing with pseudo-range or Doppler measurements, which the receiver also makes, but carrier phase measurements have the potential to be orders of magnitude more accurate.

 

Nice, but what about position?

Well, the technique that I will describe below has some applicability to making very accurate position measurements, but lets just say it is really hard and is the kind of thing that only happens (still a relatively small number of) military gps with very large price tags.  I'll say some more about this later.  For now, we will just be looking at making velocity measurements.

 

OK, but what will we do with a great velocity measurement?

Well, imagine how much better position hold could work in a copter if the autopilot knew its 3D velocity vector to an accuracy of 5 millimeters per second.  Yeah, time for a double-take.  I said millimeters per second.  My initial test yielded a velocity resolution of 1 millimeter per second and an accuracy of better than 5 millimeters per second at a 5 Hz update rate.

 

There are lots of other things we can do with a better velocity estimate, like better acceleration modelling in the AHRS system, etc.

 

Let's see the data.

OK.  I have run two tests so far.  The first turned out fantastic.  The second had some difficulties, but still shows immense promise.  Below is a plot of the velocity estimate error during the first test.  This represents a bit over 5 minutes of data with samples at 5 Hz.

 

OK - let me describe a few things in this plot.  First, note that there are 5 `spikes' where the error is above 0.1 m/s.  These are 5 samples where the receiver did not have carrier phase lock on at least 4 satellites, and you need 4 satellites to get a valid solution.  For individual samples like this you can generally re-use the last velocity estimate.  There are also around 10 samples where the error is on the order of 4 or 5 cm/s.  These are samples where the receiver only had 4 satellites with carrier phase lock.  The accuracy gets better when the receiver has more satellites with carrier phase lock.

You may be wondering what my "truth data" was.  Well, it was simply that the module was just sitting on the ground in my back yard, so the truth was 0 velocity in the Earth centered Earth fixed (ECEF, WGS84 for example) frame.  This is not at all cheating as the velocity relative to the ground is irrelevant - we are still making a velocity estimate based on measurements of the velocity between the satellites and the receiver, and the satellites are all moving at roughly 14,000 km/hour in various directions.  The relative velocities between the satellites and the receiver are on the order of thousands of kilometers per hour, and from this we are able to deduce motion on the millimeter per second scale.

 

Unfortunately maintaining carrier phase lock is not as easy as tracking a satellite.  On the second test in similar conditions I only got carrier phase lock on 4+ satellites about 75% of the time, leaving many periods of several seconds with no valid measurements available.  On the second test the reduced accuracy of the velocity measurement was more apparent with accuracy on the order of 0.1 m/s with 4 satellites and 0.02 m/s with 5 satellites.  Even so, 0.02 m/s is a very impressive number.

How did you do it?

I did all this with data recorded using ublox UCenter and post processing using MATLab.  There is no reason that C code cannot be developed to do this in real time, although it probably requires too much processing power to add to an 8 bit autpilot.  Fortunately 32 bit hobbyist autopilots are becoming reality.  My method was really a reflection on my lack of time for this sort of project at present.  So, here is what I did:

  • I used the 6T module to collect raw carrier phase measurement data.  Tridge supplied a Python script to convert the ublox formatted file to a human readable file.  I did some further formatting on it and imported it into MATLab as a data structure.
  • I used the GPS broadcast Ephemeris to compute the position of all the GPS satellites for which there were measurements at each time epoch, and translated these positions into the ECEF coordinate frame.
  •  I differenced the computed ranges between adjacent epochs and set up a linearized least squares estimate of the receiver velocity using unit vectors in the directions from the receiver to the various satellites as a weighting matrix.  The final estimate can be translated into the ENU or NED navigation frame for use.

I thought that approach would work great, but it failed completely, and it took me a while to figure out why.  The reason is that although the receiver clock bias is not needed in a velocity solution like it is in a position least squares solution, the receiver clock drift rate is not insignificant for inexpensive modules like ublox and it completely messes up the velocity estimate if it is not accounted for in the sample to sample carrier phase change.  Simply put, the receiver clock is not only running at a somewhat incorrect frequency (the clock bias - which is an error in the pseudo-range measurements) but its frequency is moving around and the rate of change of the frequency shows up as a velocity error in the carrier phase measurements.  So, I modified my least squares estimation to estimate both the 3D velocity vector and the drift rate of the receiver clock.  This worked great.

Work left to do

Several things need to happen to move this forward.  First, I need to investigate how big a problem exists with the module not being able to maintain carrier phase lock on enough satellites and what conditions make that better/worse.  Second, the issues with running this in real time on a drone need to be hashed out.  I don't really know how processor intensive this code will be when optimized, but likely it will need to wait for the 32 bit processors as it is fairly math intensive.  Finally code needs to be developed as I did this all with MATLab and borrowed a lot of proprietary scripts from research associates…

A few more things if you are interested - Cycle slip, Integer ambiguities...

The reason that it is difficult to use carrier phase measurements in a position solution is because of the "Integer Ambiguity".  The Integer Ambiguity is the unknown number of full cycles of the carrier wave between the satellite and the receiver.  See the picture below.

Here we see a satellite in motion and the phase measurement at two times.  The carrier phase measurement gives us the number of "Counted Cycles", but we have no idea how many cycles are in the Ambuguity.  There are techniques available to resolve the ambiguity, but generally these take a very large amount of processing power, take a long time, and are difficult to implement for platforms with dynamic motion.  We can maintain a sum of the Counted Cycles and do a variety of things with it.  This is one method used in RTK in a lot of agricultural applications, etc.  But every time we loose carrier phase lock we have to discard the sum and start over.  This is termed cycle slip.

I mentioned that gps receivers have a harder time maintaining carrier phase lock than just tracking a satellite.  The tracking loops in a gps receiver are fairly complicated.  There are simultaneous loops tracking both the code delay and Doppler frequency for both the in-phase and quadrature channels.  These loops use a power measurement from the combined I and Q channels in their discriminator to maintain lock in these loops.  However the carrier phase lock generally has to rely on a single channel and has other challenges. This is too bad because it is commonplace for the receiver to be able to track between 8 and 10 satellites in an open sky.  However, my 2nd test showed as poor as only 75% of the time with 4+ satellites maintaining carrier phase lock.  This will be the critical factor to investigate to move forward.

 

Views: 12232


Developer
Comment by Doug Weibel on December 2, 2012 at 5:42pm

I forgot to mention that the dev team will be looking at turning this into a product :)


3D Robotics
Comment by Chris Anderson on December 2, 2012 at 6:01pm

Awesome work, Doug! The 3DR team will indeed be looking at productizing that ;-)

Comment by Curt Olson on December 2, 2012 at 6:23pm

Cool stuff.  Any rough estimate for what the cost difference will be between the 6H and the 6T?  I have done some work with a professor at the U of MN who has run 3 receivers on an airplane and apparently there is an algorithm that can figure out the relative integer ambiguity and then use carrier phase to determine the relative positions of the 3 receivers to accurately determine an attitude "truth" reference.  As far as I know they have worked out the solution in post processing (I don't know if they have tackled real time.)  The other interesting thing they've worked on is setting up a remote base station (one fixed receiver and one mobile receiver) and accurately computed their relative positions.  So for example if you park your base station anywhere nearby, then walk your plane out to the target landing position and mark that, you could (in theory) get back to it with cm level accuracy.  So these things can be really helpful if you can recast your problem in a way that doesn't require absolute position accuracy, just relative position accuracy.


Developer
Comment by Doug Weibel on December 2, 2012 at 7:01pm

Hi Curt,

The cost question is one that someone who can talk to ublox about volume needs to ask.  I think for single pieces the cost difference is like a hundred bucks. 

The "attitude truth" problem is relatively simple if it is part of an integrated INU, and I would have tackled it already if not for the difficulty of Jordi only being able to convince ublox to give him a single sample and the modules being around $300 each in small quantity ;)

I know of other real time solutions for relative positioning similar to your "walk it out" approach.  The difficulty is when you have your sat count with carrier lock drop below 4 you loose the solution and can't get it back.  I know Tridge and Michael O are working on a ublox PPP solution using a "base station" receiver and I think that will be a much more robust approach.  It probably won't get centimeter level accuracy, but should get decimeter level.  Coupled with this speed estimate approach you could put together a killer position hold.

Comment by Jack Crossfire on December 2, 2012 at 7:24pm

Another RC modeler discovers the uBlox developer modules, which happen to cost the same as a fully RTK configured Hemisphere module.  uBlox just sells those to torment you.

Comment by Tim Wilkin on December 2, 2012 at 7:50pm

Hi Doug,

I might be able to help with your problem of dealing with <4 satellites...

It's well known that linear least squares regression is highly sensitive to outliers. In your case, when obtaining data from less than four satellites you're substituting an erroneous value to complete the computation, with the hope that the regression is stable. From your data it would appear that these events are transient, but the result is a significant spike in the error, since the estimator cannot identify this point as an outlier.

LLS regression is equivalent to monotonic averaging aggregation using arithmetic mean. I'm working presently on non-monotonic averaging functions for aggregation which are insensitive to outliers. I'd be happy to run your data through some of my code to see if it can produce a more stable and reliable estimate. Depending on its performance we can then discuss possible application of this method (note that computational complexity is equivalent to LLS). let me know if you'd like to look into this further.

Cheers,

Tim

Comment by Pbreed on December 2, 2012 at 8:02pm

I don't want to be a spoil sport, but if you choose your messages properly the normal 3DR ublox 6 with give you three dimension ECF V. These are derived from the internal Ublox measurement of carrier phase and Doppler and really help with the hovering accuracy without having to do integer ambiguity or watch for cycle slips... My personally developed helicopter uses 3D V for hvoer and it is much more stable than the jdrones Quad I bought to compare it to.... (I've been harping on the fact that the old 3DR GPS module did not give you proper 3D velocity for awhile) I actually bough the jdron thinking I could use my well tuned hover code to help with the current APM hover code only to discover that the data needed from the GPS was not availibe in a useful form at the needed rate.  I'm in the process of redoing the IMU code on my copter and within the next moth or so I'll let you know how the stock 3DR ublox compares to a nice hemisphere unit and or a nive high dynamic novatel.


Developer
Comment by Sandro Benigno on December 2, 2012 at 8:37pm

That is fan.tas.tic!
I've enjoyed how clearly you've explained it in details.

I think it makes me start to understand some talks I've heard about DJI's solution bug.
That was something about erratic readings because of "reflections" or something like that.


Developer
Comment by Andrew Tridgell on December 2, 2012 at 9:16pm

Hi Doug,

For a cheaper receiver that does raw, look at the uBlox-6P here:

http://www.csgshop.com/product.php?id_product=103

I have one of those on my roof for testing against a 6H.
The big advantage of the 6P is it has PPP builtin, so it already does a lot of the hard work of a good GCS reference station.

I've looked at some of the logs from my 6P, and the VECNED figures don't look nearly as good as yours. I would expect it to be calculating its internal velocity numbers using essentially the same method as you are, but perhaps VELNED is done only with doppler? I see typical figures of around 10cm/s from the 6P when stationary on my roof with PPP enabled.

I'll capture some VELECEF and POSECEF messages and see if they are any better.

Cheers, Tridge

Comment by Pbreed on December 2, 2012 at 11:22pm

4 yrs ago or so with ~$1K L1 RTK GPS receivers I was never able to keep RTK lock once the helicopter took off. The vibe seemed to kill it. With a $5K L1./L2 RTK GPS it could keep RTK lock about 90% of the time in flight.

Both systems got lock almost immediately when sitting still on the ground.

When the L2 GPS was working hover looked like you set the helicopter down on an invisible stepladder, even in wind it barely moved. When it lost RTK lock in hover it behaved very badly.... it generated momentary velocities that were WAY too high and the helicopter thinking it had been hit with a big gust took off in random directions, it was unnerving and a bit scary... (This was a Trex 600) If that project had continues I could have probably used the RTK status to tell the software to filter out these deviations.....

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