State Estimation for Dynamic Systems With Unknown Process Inputs and Applications

Abstract

The problem of state estimation for discrete-time stochastic time-varying systems in the presence of unknown process inputs or disturbances is addressed in this paper. A Kalman-type filter is proposed, and the optimal oracle filter gain in the sense of minimizing the mean squared error of the state estimate is obtained. To tackle the unknown quantities in the gain matrix, a nonlinear equation is introduced and its solution is taken as the estimate of unknown inputs, and then, a novel nonlinear equation-based unknown input filtering (NEUIF) is proposed. A scalar-based iterative algorithm for related fixed point problem is developed so that the dichotomy method is employed to solve the above nonlinear equation very efficiently. Adopting the same strategy for the dynamic systems with unknown inputs or disturbances, we provide two applications of the proposed state estimation algorithm. One is for a class of nonlinear dynamic systems with linear observations by taking the residual term in linearizing the transition function as an unknown input in the derived linear system. The other is for tracking maneuvering targets in which the bias between the real motion and modeled motions is regarded as an unknown input in the state transition equation. Some numerical simulations demonstrate the effectiveness of the proposed NEUIF method for tackling various uncertainties in complicated dynamic systems.