A state estimation algorithm for linear systems driven simultaneously by Wiener and Poisson processes

The state estimation problem for linear stochastic systems driven simultaneously by Wiener and Poisson processes is considered. The emphasis is on the case in which the incident rate of the Poisson driving process is low. A nonlinear, suboptimal smoothing algorithm for state estimation is developed based on a strategy combining linear conditional estimation with the detection and estimation of the incident times and marks of the Poisson input process. A first-order approximation technique is included in the scheme to eliminate the error propagation effects that result from the sequential structure of the approach. The performance of the overall scheme for the time-invariant case is obtained analytically and simulated numerically. Both results agree closely, indicating that the suboptimal sequential scheme performs better than both the optimal causal filter and the optimal noncausal linear filter for sufficiently small Poisson intensity.