State Estimation for Linear Systems Driven Simultaneously by Wiener and Poisson Processes.
ILLINOIS UNIV AT URBANA-CHAMPAIGN COORDINATED SCIENCE LAB
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The state estimation problem of linear stochastic systems driven simultaneously by Wiener and Poisson processes is considered, especially the case where the incident intensities of the Poisson processes are low and the system is observed in an additive white Gaussian noise. The minimum mean squared error MMSE optimal filter is derived via the Doleans-Dade and Meyer differentiation rule for discontinuous semi-martingales and its corresponding basic filtering theorem for white Gaussian observation noise. The nonclosedness property and performance of the filter are investigated. The results together with the performance of the linear optimal filtering schemes lead to the conclusion that causal filters and noncausal linear filters are inherently unsuitable for the state estimation for such class of systems. A noncausal nonlinear suboptimal scheme is developed for the estimation problem based on a combined estimation and detection strategy. A first-order approximation scheme 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 is obtained analytically and simulated numerically. Both results agree closely indicating that there exists a lambda such that if the Poisson intensity lambda an element of 0, lambda, the suboptimal sequential scheme performs better than the causal optimal filter and the noncausal linear filter.
- Statistics and Probability