A Fokker-Planck approach to joint state-parameter estimation

The problem of joint estimation of parameters and state of continuous time systems using discrete time observations is addressed. The plant parameters are assumed to be modeled by a Wiener process. The a priori probability density function (pdf) of an extended state that comprises the plant state variables and the parameters is propagated in time using an approximate solution of the Fokker-Planck equation that relies on Trotter’s formula for semigroup decomposition. The a posteriori (i. e., given the observations) pdf is then computed at the observation instants using Bayes law.