Mean-square state and parameter estimation for stochastic linear systems with Gaussian and Poisson noises

Abstract

This paper proposes new mean-square filter and parameter estimator design for linear stochastic systems with unknown parameters over linear observations, where unknown parameters are considered as combinations of Gaussian and Poisson white noises. The problem is treated by reducing the original problem to a filtering problem for an extended state vector that includes parameters as additional states, modelled as combinations of independent Gaussian and Poisson processes. The solution to this filtering problem is based on the mean-square filtering equations for incompletely polynomial states confused with Gaussian and Poisson noises over linear observations. The resulting mean-square filter serves as an identifier for the unknown parameters. Finally, a simulation example shows effectiveness of the proposed mean-square filter and parameter estimator.

Keywords:

• Parameter estimation
• linear systems
• white noise

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors thank the Mexican National Science and Technology Council (CONACyT) for financial support [grant number 232814], [grant number 129081]; PRODEP for financial support [grant number 336234].