A New Adaptive Square-Root Unscented Kalman Filter for Nonlinear Systems with Additive Noise

The Kalman filter (KF), extended KF, and unscented KF all lack a self-adaptive capacity to deal with system noise. This paper describes a new adaptive filtering approach for nonlinear systems with additive noise. Based on the square-root unscented KF (SRUKF), traditional Maybeck’s estimator is modified and extended to nonlinear systems. The square root of the process noise covariance matrix Q or that of the measurement noise covariance matrix R is estimated straightforwardly. Because positive semidefiniteness of Q or R is guaranteed, several shortcomings of traditional Maybeck’s algorithm are overcome. Thus, the stability and accuracy of the filter are greatly improved. In addition, based on three different nonlinear systems, a new adaptive filtering technique is described in detail. Specifically, simulation results are presented, where the new filter was applied to a highly nonlinear model (i.e., the univariate nonstationary growth model (UNGM)). The UNGM is compared with the standard SRUKF to demonstrate its superior filtering performance. The adaptive SRUKF (ASRUKF) algorithm can complete direct recursion and calculate the square roots of the variance matrixes of the system state and noise, which ensures the symmetry and nonnegative definiteness of the matrixes and greatly improves the accuracy, stability, and self-adaptability of the filter.