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We consider state and parameter estimation for a dynamical system having bothtime-varying and time-invariant parameters. It has been shown that therobustness of the Markov Chain Monte Carlo (MCMC) algorithm for estimatingtime-invariant parameters alongside nonlinear filters for state estimationprovided more reliable estimates than the estimates obtained solely usingnonlinear filters for combined state and parameter estimation. In a similarfashion, we adopt the extended Kalman filter (EKF) for state estimation and theestimation of the time-varying system parameters, but reserve the task ofestimating time-invariant parameters to the MCMC algorithm. In a standardmethod, we augment the state vector to include the original states of thesystem and the subset of the parameters that are time-varying. Eachtime-varying parameter is perturbed by a white noise process, and we treat thestrength of this artificial noise as an additional time-invariant parameter tobe estimated by MCMC, circumventing the need for manual tuning. Conventionally,both time-varying and time-invariant parameters are appended in the statevector, and thus for the purpose of estimation, both are free to vary in time.However, allowing time-invariant system parameters to vary in time introducesartificial dynamics into the system, which we avoid by treating thesetime-invariant parameters as static and estimating them using MCMC.Furthermore, by estimating the time-invariant parameters by MCMC, the augmentedstate is smaller and the nonlinearity in the ensuing state space model willtend to be weaker than in the conventional approach. We illustrate theabove-described approach for a simple dynamical system in which some modelparameters are time-varying, while the remaining parameters are time-invariant.

Robust Bayesian state and parameter estimation framework for stochastic dynamical systems with combined time-varying and time-invariant parameters