A nonlinear continuous-discrete filter with model parameter uncertainty and application to anesthesia

This paper addresses the problem of joint estimation of the state and parameters for a deterministic continuous time system, with discrete time observations, in which the parameter vector is constant but its value is not known, being a random variable with a known distribution. Along time, the uncertainty in the parameter induces uncertainty in the plant state. The joint probability density function (pdf) satisfies the Liouville partial differential equation that is a limit case of the Fokker-Planck equation for vanishing diffusion. The continuous-discrete filter proposed operates as follows: Between two consecutive output sampling time instants, the pdf is propagated by solving the Liouville equation for an augmented state and is then corrected by using the last observation and Bayes law. An application to state estimation of the neuromuscular blockade of patients subject to general anesthesia, where parameter uncertainty is due to inter-patient variability, is described.