Robust filtering for continuous-time uncertain nonlinear systems with an integral quadratic constraint

This paper formulates a robust state estimator for continuous-time uncertain nonlinear systems with an integral quadratic constraint noise/uncertainty description. The model uncertainty and exogenous disturbances enter the state dynamics and observation channel in a unified fashion that includes the case of multiplicative noise. The robust filtering problem is formulated as a set-valued state estimation problem which is recast into an optimal control problem. An approximate solution to the resulting Hamilton-Jacobi-Bellman equation is obtained by using quadratic optimization with linearization of the observation equation. The approximate information state of the robust filter is organized as a triple of scalar, vector and matrix-valued parameters governed by a differential Riccati equation.