A novel adaptive unscented Kalman filter for nonlinear estimation

The normal unscented Kalman filter (UKF) suffers from performance degradation and even divergence while mismatch between the noise distribution assumed to be known as a priori by UKF and the true ones in a real system. In this paper, a novel adaptive UKF (AUKF) is developed and applied to nonlinear joint estimation of both time-varying states and parameters. A cost function is built based on the error between the covariance matrices of innovation and their corresponding estimations. An adaptive algorithm is then designed to online update the covariance of the process noise by minimizing the cost function. The updated covariance is further fed back into the normal UKF. As a result of using such an adaptive mechanism, the robustness of conventional UKF is substantially improved with respect to the uncertain and time-varying noise covariance in the real system. To illustrate this mechanism, simulations are conducted on the dynamics of an unmanned helicopter by jointly estimating both the states and model errors. The improvements of the proposed AUKF are demonstrated by comparing the results with and without the adaptive mechanism.