Discrete-time unscented Kalman filter: Comprehensive study of stochastic stability

Abstract

The performance of the Unscented Kalman Filter (UKF) for a class of general nonlinear stochastic discretetime systems is investigated in this paper. It is proved that the estimation error of the UKF remains bounded provided a under certain conditions are satisfied. It is further shown that the estimation error remains bounded provided the system satisfies the nonlinear observability rank condition. Furthermore, it is shown that the design of noise covariance matrix plays an important role in improving the stability of the UKF algorithm. These results are verified by simulations for a given illustrative example of an inherently nonlinear plant.