Kalman filtering with multiplicative noise

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.

Any ideas?

On Jul 20, 7:03&#4294967295;am, "ac123" <d...@myallit.com> wrote:
> Any ideas?

The missing measurements\uneven sampling rate is usually a matter of
being able to express your state transition matrix as a function of
the sampling time. This is easiest to understand when you are
filtering, a bit more complicated when you are predicting.

Chris

On Jul 22, 12:44&#4294967295;am, Chris Maryan <kmar...@gmail.com> wrote:
> On Jul 20, 7:03&#4294967295;am, "ac123" <d...@myallit.com> wrote:
>
> > Any ideas?
>
> The missing measurements\uneven sampling rate is usually a matter of
> being able to express your state transition matrix as a function of
> the sampling time. This is easiest to understand when you are
> filtering, a bit more complicated when you are predicting.
>
> Chris

So if my state transition is given by:

F = [dt 1
     1  0]

where dt is the time step, then you mean I just alter dt at each step?
Do I also need to alter the measurement matrix to account for the
missing measurements?

On Jul 21, 7:55�pm, d...@myallit.com wrote:
> On Jul 22, 12:44&#4294967295;am, Chris Maryan <kmar...@gmail.com> wrote:
>
> > On Jul 20, 7:03&#4294967295;am, "ac123" <d...@myallit.com> wrote:
>
> > > Any ideas?
>
> > The missing measurements\uneven sampling rate is usually a matter of
> > being able to express your state transition matrix as a function of
> > the sampling time. This is easiest to understand when you are
> > filtering, a bit more complicated when you are predicting.
>
> > Chris
>
> So if my state transition is given by:
>
> F = [dt 1
> &#4294967295; &#4294967295; &#4294967295;1 &#4294967295;0]
>
> where dt is the time step, then you mean I just alter dt at each step?
> Do I also need to alter the measurement matrix to account for the
> missing measurements?

If this is a typical state-space system, then the observation equation
should be independent of the time step.