Collocation and Kalman filtering - references please

> I am hoping that some of our more savvy forum-goers might provide some references so I can understand why the estimated standard errors of RTK vectors are optimistic compared to a least squares adjustment.

You mean why processor-estimated standard errors of GPS vectors tend to be unrealistic, I believe. Using least squares adjustments, it is possible to compare those unrealistically-weighted vectors to many other different measures of the same coordinate differences contained in the GPS vector and to figure out just how unrealistic the processor estimates were, typically correcting them by some factor.

The biggest reason Trimble error estimates are overly optimistic is that they're reported at 1 sigma; when you look at the exact same data in TBC, which defaults to 2 sigma, the error estimates approximately double - as they should. I've never received a good explanation of why 1 sigma is reported in the field and there is no option to change it.

Wikipedia has a pretty good article on Kalman filtering; they explain it in terms that even I can understand...

From the top few recommendations from Google I like those listed below.. You might also want to examine the documentation for the software package GLOBK (at http://www-gpsg.mit.edu/~simon/gtgk/Intro_GG.pdf and http://www-gpsg.mit.edu/~simon/gtgk/GLOBK_Ref.pdf )

For Kalman filtering in general see

http://www.cs.cmu.edu/~motionplanning/papers/sbp_papers/integrated3/kleeman_kalman_basics.pdf

http://www.cs.unc.edu/~welch/kalman/

http://gpsinformation.net/main/kalman2.htm

1 sigma vs 2 sigma history

lee, i don't know all of the details, but sum it up to this. one of the manufacturers (i don't know which) changed the coordinate quality display from 2 sigma to 1 sigma as a 'false' way to boast better results.

rather than contest it, the other manufacturers simply followed suit.

hopefully some others can corroborate this for me.

No, I meant what I said.

> No, I meant what I said.

Well, the necessary clarification is *how* a standard error estimate is derived. I assumed that, although you didn't say it, you meant "processor-estimated" or "RTK-controller-estimated" standard errors. If you didn't have that in mind, it would be nice to know what you were thinking of since it wasn't clear from your post.

Perhaps more details than you want are here: http://geoweb.mit.edu/~simon/gtgk/help/kalman.hlp.htm

> Well, the necessary clarification is *how* a standard error estimate is derived.

I doubt a reference on collocation and Kalman filtering would yield any clues to how any manufacturer is calculating the standard error estimate of RT vectors. I would think that information could only be supplied by the manufacturers. I think Lee's assertion that the uncertainties are reported at the 1 sigma level is a very reasonable explanation for the optimistic error estimates.

>I want to learn more about the application of collocation and Kalman filtering, specifically with regard to RT surveying.

I am interested in learning about the impact that collocation and Kalman filtering may have (if any) on the estimated uncertainties (from vendor software, whether that comes from a data collector or desktop software doesn't really matter to me) of RT vectors. The techniques applied in any measurement system invariably have an impact on the accuracy of the measurement. Collocation and Kalman filtering are two processes that I don't fully understand.

:good: Thanks!

I see that there are assumptions made to allow the filter to function. That is exactly the kind of information I was looking for. Obviously when assumptions are made there are implications to be considered regarding the results from the filter. Understanding why the assumptions are made in Kalman filtering is something I want to learn more about. Surely, this will require more than one reading, one source, or one seminar!

I have chopped, folded, spindled and mutilated our data every which way I can. At the end of the day I see two consistent issues in error reporting.

The QC numbers displayed in the field (on most data collectors I've used) are inflated by the mis-application of 'square root of the number of observations'. Each Epoch is treated as an individual measurement. The result is an over-optimistic QC number. I am reluctant to call it anything standard, because the numbers don't match any analysis exactly.

The number reported as 'QC' by Leica may well be based on 1 Sigma, but again it doesn't match anything else exactly. It is consistent across brands to closely match 40% of the 2 sigma numbers. I would expect it to be 34 to 38% if that were the only issue.

At the end of the day a good rough number is QC X 2.5 = nominal standard error. I used to export everything to Starnet. Now if it includes GPS data I leave it native and look for RTK errors of around 0.03 x 0.03 x 0.03. I then know I'm within a tenth.

It's easier in the field if the guys just run dual base rapid static. I have yet to return for better data that way...

Looks like you've gotten some good answers/pointers. I only read the forum every few days, so I'm a little slow to make a post.

It might be worthwhile to peruse the publications at:

University of New Bruswick:

Lecture Notes
Technical Reports

The Ohio State University:

OSU Reports

For Collocation (at least applied to gravimetry), Helmut Moritz' book, Advanced Physical Geodesy, is considered a classic text.

For Kalman Filtering, a good text is the one edited by Arthur Gelb and written by folks at TASC, called Applied Optimal Estimation, published by MIT Press.

These latter two references can occasionally be found in used form through ABE (Advanced Book Exchange).

Have fun - good stuff!

Some more:
http://ocw.mit.edu/courses/mechanical-engineering/2-160-identification-estimation-and-learning-spring-2006/lecture-notes/