<pre>

Path: news.mathworks.com!newsfeed-00.mathworks.com!newsfeed2.dallas1.level3.net!news.level3.com!postnews.google.com!z16g2000prn.googlegroups.com!not-for-mail
From: dsp@myallit.com
Newsgroups: sci.stat.math,comp.soft-sys.matlab,sci.engr.control
Subject: Kalman filtering with multiplicative noise
Date: Sun, 20 Jul 2008 19:51:02 -0700 (PDT)
Organization: http://groups.google.com
Lines: 22
Message-ID: &lt;1309743c-3d5c-4165-9cdb-1ab51892727d@z16g2000prn.googlegroups.com&gt;
NNTP-Posting-Host: 202.7.166.175
Mime-Version: 1.0
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
X-Trace: posting.google.com 1216608662 25874 127.0.0.1 (21 Jul 2008 02:51:02 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Mon, 21 Jul 2008 02:51:02 +0000 (UTC)
Complaints-To: groups-abuse@google.com
Injection-Info: z16g2000prn.googlegroups.com; posting-host=202.7.166.175; 
User-Agent: G2/1.0
X-HTTP-UserAgent: Mozilla/5.0 (Windows; U; Windows NT 5.1; en-GB; rv:1.9.0.1) 
X-HTTP-Via: 1.1 syd-pow-pr12.tpgi.com.au:3128 (squid)
Xref: news.mathworks.com sci.stat.math:83479 comp.soft-sys.matlab:480591 sci.engr.control:50810


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 = x1 + v1 where v1 ~ N(0,e1)

Volume measurement model:
z2 = 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.

<pre>