I'm using Kalman filters to segment the loudness of an acoustic signal from surrounding noise. The problem I've encountered is that muffled or faulty microphones measuring 'silence' (-70dB, -69dB, -71dB, ...) have low variance and so the Kalman filter relies on them as being more stable, "pulling down" the true value.
To solve this, I had the idea to pass in the offset-from-mean of all the signals, which would increase the variance of the "dead sensors" and I could add back the mean to the state estimate delta. But then it occurred to me that maybe the Kalman filter is already doing this by minimising "least squares error"?
A secondary problem I have is dynamically adding or removing sensors without losing my covariance matrix. Currently when sensors leave, I keep the same matrix, but I set it's observation variance
R_ij = Infinity, which seems to work. However, I would love to know how to re-arrange my matrix values when adding or removing additional sensors.