Recursive State Estimation for Discrete-Time Nonlinear Systems With Binary Sensors: A Locally Minimized Variance Approach

In this paper, the locally-minimized-variance state estimation problem is investigated for a class of discrete-time nonlinear systems with Lipschitz nonlinearities and binary sensors. The output of each binary sensor takes two possible values (e.g. 0 and 1) in accordance with whether the sensed variable surpasses a prescribed threshold or not. The purpose of this paper is to design a state estimation algorithm such that an upper bound of the estimation error covariance is firstly guaranteed and then minimized at each sampling instant by properly designing the estimator gain. The valid information of sensed variables is extracted from binary measurements, and a novel state estimator is constructed in a recursive form, which is suitable for online computations. Moreover, a sufficient condition is established to ensure the exponential boundedness of the prediction error in the mean square sense. Finally, two examples are presented to verify the effectiveness of the proposed method.