Adaptive range tracking

[walker1]

This was first posted under the "Signal Processing" group yesterday, but not much seems to go on there :-(

I am working on a range tracker for a scientific radar.

I have tried a full kalman filter and found, that it performed fairly well, as long as the tracked object did not change dynamics during the track.

I am now using a much simpler g-h-k (equ. alpha-beta-gamma or Simpson) filter, which requires much less (and simpler) code in Pascal.

In Eli Brookner's "Tracking and Kalman filtering made easy"
the range gain, g, in the filter is said to be equal to the variance of the range estimate divided by the variance of the input range samples.
It is, however, not just to calculate this during a track. If the input becomes more 'noisy', (the target starts moving more dramatically, say), this division will result in a lower gain, not a higher one. Or have I misunderstood something ?

Is there a way to more or less directly calculate the optimal gain on the fly?

I have figured out a way to change the filter gain up and down in small steps (2-5% at a time) based uppon the behaviour of the tracking error, and it seems to work, but ....

Searching the web results in very little, and what shows up seems to be for people like Einstein. (pure theory and math


In

 

[sreid]

Try posting your question at Wise DSP.

http://www.dsp-bg.info/

Several Einstienian DSP'ers lurk there.

 

[Higgler]

A note on Eli Brookner,
I worked in the same building back in 1980 (as opposed to working with him), he's got a great sense of humor, he always told a good joke to start his technical talks.
I always enjoyed his speeches.

kchiggins

 

[rsbuck]

It's been a long time but as I remember it you take the time and divide it by the speed of light at sea level. Thus range. Any doppler effects can be negated unless it is incomming.

 

[IRstuff]

If you reread Brookner's first couple of chapters, you may recall that the tracking error is a function of the model you use for the the target. A default constant velocity model "performed fairly well, as long as the tracked object did not change dynamics." A 2nd or 3rd order model is required to track through target dynamics.

TTFN

 

[walker1]

I have now done some further experiments with a full Kalman filter.

I have discovered that the 3-state (range, speed and acc.) filter, I have used so far, is much more lively and eager to follow input noise than a 2-state (range and speed only), given the same parameters.

I may not have entered the Q matrix (specifying target dynamics) with the exactly correct data in order to hit the same dynamics, but the trend is surely there.
The 2-state filter seems to be the way forward for most of my needs. Aircrafts may need the 3-state version, though.

I have now found a document talking about modifying the Q-matrix on the fly in order to change the filter dynamics.

My fist experiments with adaptable Kalman just put an x-tra gain (during one or a few iterations only!) in the CoVar.loop, which for a short while raised the Kalman gain. It actually worked quite fine, but of course, lowering or raising the gain for longer periods was not possible that way.