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From: pnachtwey <pnachtwey@gmail.com>
Newsgroups: sci.stat.math,comp.soft-sys.matlab,sci.engr.control
Subject: Re: Kalman filtering with multiplicative noise
Date: Mon, 21 Jul 2008 20:39:24 -0700 (PDT)
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On Jul 20, 7:51=A0pm, d...@myallit.com wrote:
> I'm trying to implement a Kalman filter in MATLAB that will use two
> types of measurements: volume and in/out flow rate. For the flow rate,
> the measurement error is additive Gaussian, but for the volume the
> measurement error is expressed as a percentage of the volume, so that
> the volume measurement is less accurate when its value is higher. I
> think the measurement model should therefore be:
>
> Flow rate measurement model:
> z1 =3D x1 + v1 where v1 ~ N(0,e1)
>
> Volume measurement model:
> z2 =3D x2*v2 where v2 ~ N(1,e2)
>
> I assumed the volume filtering should be done in the log domain to
> make the noise additive but how do I deal with a noise mean of one
> when the Kalman filter assumes a mean of zero? And how can I have a
> Kalman filter using both the measurements if one is in the log domain
> and the other one isn't?
>
> I am also dealing with a system where measurements will usually be
> missing (they are arriving sequentially) and at an uneven sampling
> rate, any other pointers on these too would be appreciated.

If this is a student project then why not assume there will be a set
point and the controller will maintain that set point with little
variation.  Now the volume is fixed and the variance is therefore
fixed.  Now you can assume the system is linear around that set point.

Peter Nachtwey