Adaptive square-root unscented Kalman filter algorithm

By combining the classical square root uncented Kalman filter (SRUKF) with Gaussian process regression, we derive a filter algorithm for an uncertain system model with inaccurate noise covariance. The new algorithm includes a learning stage and an estimation stage. In the first stage, Gaussian process regression is applied to learn the training data to obtain the regression model and the noise covariance of the dynamic system. In the second stage, state equations and observation equations are substituted by their regression models, respectively; the noise covariance is adaptively adjusted by using the Gaussian kernel function real-time. Thus, the problem of uncertain system model and inaccurate noise covariance in the classical filters are solved. Simulation results show the new algorithm is effective.