Accession Number : ADA077149
Title : State Estimation for Linear Systems Driven Simultaneously by Wiener and Poisson Processes.
Descriptive Note : Technical rept.,
Corporate Author : ILLINOIS UNIV AT URBANA-CHAMPAIGN COORDINATED SCIENCE LAB
Personal Author(s) : Au,Samuel Poriza
Report Date : Dec 1978
Pagination or Media Count : 120
Abstract : 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.
Descriptors : *LINEAR FILTERING , *POISSON DENSITY FUNCTIONS , ALGORITHMS , STOCHASTIC PROCESSES , WHITE NOISE , GAUSSIAN NOISE , KALMAN FILTERING , THESES , SEQUENTIAL ANALYSIS , ITERATIONS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE