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.

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.