Past Measurement‐Based Robust Nonlinear Observers With Application to Bearing‐Only Target State Estimation in Switched Systems

This paper presents the design of robust nonlinear observers that utilize both current and past measurements of outputs and inputs in the error injection term to estimate the states of a class of discrete‐time dynamical systems. Initially, for generic systems with Lipschitz nonlinearities, we design past‐measurement‐based observers to ensure input‐to‐state stability (ISS) of the estimation error dynamics. The proposed observer design is then applied to the bearing‐only target motion analysis (BOTMA) scenario, where a source agent estimates the states of a maneuvering target agent using only a sequence of noisy bearing measurements and input values. Assuming that the source and target agents navigate in a plane with multiple admissible observable and unobservable modes, we design mode‐dependent observers by modeling the source‐target maneuvers within a switched systems framework. The ISS of the overall switched BOTMA error dynamics, in conjunction with the proposed observer, is guaranteed under average dwell time switching. Simulation results demonstrate the effectiveness of the proposed observers in achieving accurate state estimation.