Min-plus techniques for set-valued state estimation

This article approaches the deterministic filtering problem for a discrete-time nonlinear system (nonlinear dynamics and output functions) with a sum quadratic constraint on the process and the measurement disturbances. The problem is formulated using an optimal control framework and the solution to the associated Hamilton-Jacobi-Bellman (HJB) equation is obtained. This approach enables the design of the filter without recourse to linearization of the system dynamics/ output equation and yields a set-valued state estimator. A computationally tractable numerical algorithm is introduced by utilizing the min-plus linearity of the corresponding dynamic programming operator.