A Bayesian Filter Switching Strategy for Simultaneous State and Parameter Estimation

Recent advances in high-speed computing technology have lead to the frequent use of stochastic nonlinear models to represent complex system dynamics. The design and implementation of advanced control or monitoring strategies using such complex models require real-time estimation of the key system states and parameters that are either unmeasured or unknown. In situations, where the parameters are precisely known, the states can be estimated un- der the Bayesian framework by computing the state posterior density. The state posterior density is often computed by solving a state filtering problem [1]. A closed-form solution to the fi ering problem exists for linear state space models (SSMs) under the Gaussian noise settings or when the state space is finite [1]. Unfortunately, in many engineering systems, the model is often nonlinear and the parameters are not known or time-varying, and therefore need to be estimated before the states can be estimated. In practical settings, simultaneous state and parameter estimation is often the only realistic solution for it avoids processing of large data set and also allows for adaptation to the time-varying system behavior [2, 3].

The choice of an efficient Bayesian filter for simultaneous state and parameter estimation in nonlinear stochastic systems is still an open problem. This is because there is no single tractable Bayesian filter that is guaranteed to provide a consistent performance for a given system under all operating conditions [4]. A practitioner is thus left with no clear substitute for the optimal Bayesian filter.

This paper develops a filter switching strategy for simultaneous state and parameter estimation in systems represented by nonlinear, stochastic, discrete-time state space models (SSMs). The proposed strategy considers a bank of plausible Bayesian filters for simultaneous state and parameter estimation, and then switches between them based on their performance. The performance of a Bayesian filter is assessed using a performance measure derived from the posterior Cramer-Rao lower bound (PCRLB). The efficacy of the filter switching strategy is illustrated on a practical simulation example.

References

[1] M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A tutorial on particle filters for online nonlinear/non-gaussian bayesian tracking,” IEEE Transactions on Signal Processing, vol. 50, no. 2, pp. 174–188, 2002.

[2] H. He, R. Xiong, X. Zhang, F. Sun, and J. Fan, “State-of-charge estimation of the lithium-ion battery using an adaptive extended kalman filter based on an improved thevenin model,” IEEE Transactions on Vehicular Technology, vol. 60, no. 4, pp. 1461–1469, 2011.

[3] C. Kravaris, J. Hahn, and Y. Chu, “Advances and selected recent developments in state and parameter estimation,” Computers & chemical engineering, vol. 51, pp. 111–123, 2013.

[4] P. Minvielle, A. Doucet, A. Marrs, and S. Maskell, “A Bayesian approach to joint tracking and identificafition of geometric shapes in video sequences,” Image and Vision Computing, vol. 28, no. 1, pp. 111–123, 2010.