Kalman Help 2

[msilverm23]

I am trying to use a Kalman filter to filter the AWGN noise in measuring clock offsets between two clocks for synch. Since, frequency jitter acts as process noise, the filter is trying to operate in the presence of both measurement noise and process noise. From my understanding, the filter can only take a ratio of the two and weight the kalman gain accordingly (low gain if Q/R is high and high gain if Q/R is low). Many of the papers I have read make it seem like the Kalman is more sophisticate than I am describing. Is it? In the presence of a great deal of process noise, could the Kalman filter filter out measurement noise well?

 

[2dye4]

That Kalman Filter is indeed a stinker. I have been trying to get a good grasp for some time.
I think there is indeed a lot more to it than your post suggests.


Still in order to provide some help to you i suggest peeling off the clock signal and building a PLL circuit to sync to it and provide a filtered version of the clock. Then the original can be compared with the PLL output to determine the characterisics of the jitter.

Also the Kalman filter is still just a least squares error estimation tool, processing without storing samples. If you can analyze your data in batch format you can achieve the same with much simpler analysis. The Kalman shines in real time processing of incoming data.

 

[msilverm23]

2dye4,

Thanks for the response. Right now, this is all just Matlab modeling and we are trying for a wireless synchronization method. We have modeled the jitter from the oscillator specification. I am beginning to believe that the Kalman is actual as I described it before bec. I found this passage in "Estimation with Applications to Tracking and Navigation" by Bar-Shalom, Li and Kirubarajan:

"A large gain indicates a "rapid" response to the measurement in updating the state, while a small gain yields a slower response to the measurement. In the frequency domain it can be shown that these properties correspond to a higher/lower bandwidth of the filter.
A filter whose optimal gain is higher yields less "noise reduction," as one would expect from a filter with a higher bandwidth."

Large optimal gains occur if Q is high and R is relatively low--small gains if the opposite. So, I think I may be out of luck.

Thanks again,

Matt

 

[IRstuff]

As posted earlier, the Kalman filter is AT BEST, a least-squares estimator. It's primary strength is the algorithm approach to determining the weighting by which new samples are incorporated, hence, it automatically changes its frequency response to accommodate changing noise conditions.

For what you are describing, you would probably need a phase-locked loop type filter.

TTFN

FAQ731-376

 

[Rtricci]

Still Kalman filter is very important, extended Kalman filter EKF and UKF are almost irreplacable.

Tricci
System Engineer,

http://www.celliz.com