Performance of the Kalman filter with Poisson measurements
Hamid M. Faridani · International Journal of Systems Science · 1985
In this paper the properties of a Kalman filter, when the measurements arrive at random points in time, are examined under the assumption that the number of measurements arriving in a given time interval can be modelled as a Poisson counting process. The filter error covariance is a function of the times at which the measurements arrive. Since the measurements arrive at random points in time, then the error covariance is a random process. A measure of the filter's performance is the expected value of the error covariance, which is found not to be self-propagating. The exact value of this measure is not found, but computationally feasible bounds are determined to nest it. Using a first-order example it is shown that in the steady-state the bounds are close over all values of the parameter mixes.