Model-Based Robust Filtering and Experimental Design for Stochastic Differential Equation Systems

Abstract

We derive robust linear filtering and experimental design for systems governed by stochastic differential equations (SDEs) under model uncertainty. Given a model of signal and observation processes, an optimal linear filter is found by solving the Wiener-Hopf equation; with model uncertainty, it is desirable to derive a corresponding robust filter. This article assumes that the physical process is modeled via a SDE system with unknown parameters; the signals are degraded by blurring and additive noise. Due to time-dependent stochasticity in SDE systems, the system is nonstationary; and the resulting Wiener-Hopf equation is difficult to solve in closed form. Hence, we discretize the problem to obtain a matrix system to carry out the overall procedure. We further derive an intrinsically Bayesian robust (IBR) linear filter together with an optimal experimental design framework to determine the importance of SDE parameter(s). We apply the theory to an SDE-based pharmacokinetic two-compartment model to estimate drug concentration levels.