I am trying to use the Kalman filter for my task: During the time, I receive data from different sensors. The state of the model may change over time according to the Const Velocity model, or the Const Acceleration model. The data is a true value with Gaussian noise. The main problem is that the Gaussian noise of the sources has a non-zero mean. For the Kalman filter to work properly, I have to calculate the noise characteristics for each source (mean and variance).
It is necessary to calculate the characteristics of sources not by a separate process before filtering, but during it. How can I do this? The most important thing for me is to calculate the mean value, as it represents a systematic error of the source. If we consider the mean value to be the same for two different sources, then with each new measurement, the filter will jump in the direction of one mean value, then the other.
I would like to find some simple and not very demanding algorithms for calculating the necessary noise characteristics. So far, I do not know anything better than to accumulate discrepancies between filter predictions and incoming measurements from sources. (Then you can try to analyze them somehow, but the discrepancies from the filter forecast are hardly useful enough to calculate the measurement noise characteristics)
P.S.: If I know the variance and mean noise of each source, then I will do the following things:
When a measurement arrives from some source, I will subtract the mean noise value (systematic error) from the measurement that came.
I will use the error variance to initialize the noise covariance matrix of the measurement R in the Kalman filter.
