Kalman Filter- practical way to get the measurement error covariance R

emily.d.show@googlemail.com wrote:

You need to set up an experiment that lets you have a well-controlled
independent parameter, or that lets you measure the independent
parameter significantly more accurately than you expect in practice.
Then measure the same parameter by the method that you're going to use
in practice.  Use your 'good' value of the parameter vs. your 'practical
measurement' to determine the variance.

Exactly how you set up your experiment depends on what parameters you're
trying to measure, of course.

--

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

Posting from Google?  See http://cfaj.freeshell.org/google/

Do you need to implement control loops in software?
"Applied Control Theory for Embedded Systems" gives you just what it says.
See details at http://www.wescottdesign.com/actfes/actfes.html

thanks up there,

and Tim, I am quite new in the field of stochastic estimation and
control, actually I only had some lectures.

I think I did the experiments you mentioned, the parameters needed to
be estimated is the stator resistance of the BLDC motor, I actually
know the value of it and I measured the value in a Simulink model,
which is without any noises. the value is equal to the real one.

I estimated the resistance with KF as a observer and I added some
Gausian noise simulated the measurement noise. I got the variance of
the estimated resistance vs. the real resistance.

The problem is, as I used the current and rotor speed as for the
measured value, the structure of R is like R=[a,0;0;b], how to choose
a, and b using the variance I got from experiments?

And like Matt said, how to choose the initial a and b?

thanks again.

Emily

(...)

(...)

If you know it (or you really trust to your measurements)
then R doesn't exist.



--
Mikolaj

Hi.
You might also try starting with the product specifications to get the
general structure of the R matrix. Then you can evaluate its performance on
the motor hardware while varying R by multiplying it by a coefficient until
you are satisfied that you've achieved the fastest estimation response you
can get for your system.

As a simple example, say you had R=[a 0;0 b], with a and b being the
corresponding measurement error variances from your sensor specifications.
Then, set R_test = k*R and turn the crank on your Kalman Filter gain
computations. Test that out in your hardware setup. Try several conservative
values of k until you are satisfied with the estimation output. The more you
decrease k, the faster your filter will respond -- but it will also be much
noisier.

Matt

: hello all,
:
: I just get into a project about BLDC motor state and parameter
: estimation using Kalman Filter. And I have already finished the
: calculation of KF, now the problem is to estimate or tune the KF
: measurement error covariance R.
:
: I read some materials and also my boss told me it is possible to
: estimation R in a practical way, and I assume, I should take some
: sample measurements and estimation of the motor states or parameters
: to determine the variace of the measurement noise, that is something
: like: varERROR=f(x-\hat x).
:
: But I really dont know how to achieve this 'practical estimation of R'
: in PRACTIC.
:
: Anyone knows how to deal with that??

We have calculated the measurement error for an encoder by simulating motion
at various speeds, sample rates and resolutions.   As it turns out
quantizing is the biggest source of error.  We sampled data the sample times
plus or minus a little jitter.  The sampled data was then quantized to the
resolution of the encoder. The errors are then calculated between the
simulated sampled and quantized data and the true data.  The variance was
computed from that.

Peter Nachtwey