FPGA Central

Could you explain how to combine two different measurements with two
different sample rates to make an estimate with a Kalman filter?



Lets say I have want to estimate a position and I have an eccelerometer and
something else that measures position (a radar or something). The position
(radar) measurement has a rate of 1 measurement per second and the
eccelerometer has 1000 measurements per second.



Must the 1 Hz be up sampled to 1000 Hz before the measurements are used by
the Kalman filter to estimate position? Or how does it work?

Sven wrote:
> Could you explain how to combine two different measurements with two
> different sample rates to make an estimate with a Kalman filter?
>
>
>
> Lets say I have want to estimate a position and I have an eccelerometer and
> something else that measures position (a radar or something). The position
> (radar) measurement has a rate of 1 measurement per second and the
> eccelerometer has 1000 measurements per second.
>
>
>
> Must the 1 Hz be up sampled to 1000 Hz before the measurements are used by
> the Kalman filter to estimate position?

No

> Or how does it work?

Oh my. You'd have to dig a bit into Kalman filter theory, but I think
you could make this work quite well.

The basic idea of Kalman filtering is that you take an input, and at
each time step you update your best estimate of the state vector of your
system, x, and you update the covariance matrix of x, which expresses
how good a measurement of x you have.

The way that you derive the Kalman filtering equations is to say "Given
the known covariance of the estimate that I have, the estimate, and a
noisy measurement of the process, what is my new estimate, and my new
covariance?"

So you just do that -- but you recognize that you have one set of
equations that only takes accelerometer input (no gyro?) that you
implement 999 times, and another one that uses the accelerometer input
and your position measurement that you implement once.

I'm currently expanding my knowledge of Kalman filtering by reading
"Optimal State Estimation" by Dan Simon, Wiley 2006. If you're up to
understanding Kalman filtering at all it should be just the book for
you. You _will_ have to extend it's results somewhat, but I think it'll
be straightforward.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

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