Optimal mean-square state and parameter estimation for stochastic linear systems with Poisson noises

This paper presents the mean-square state and parameter estimation problem for stochastic linear systems with unknown multiplicative and additive parameters over linear observations, where unknown parameters are considered Poisson processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed optimal state filter and parameter identifier is verified for both, stable and unstable, stochastic linear systems and compared against the mean-square estimator designed for polynomial systems with white Gaussian noises.