Correlational inference-based adaptive unscented Kalman filter with application in GNSS/IMU-integrated navigation

A generalized Kalman filtering estimator with nonlinear models is derived based on correlational inference, in which a new target function with constraint equation is established. Hence, a new unscented Kalman filter (UKF) expression is deduced from this target function. In this new expression, the state estimator is directly related to the predicted states vector, predicted residuals vector, and their covariance matrices as well as their cross-covariance matrix. Furthermore, a new estimator, called adaptive unscented Kalman filter (AUKF), is extended directly from the derived target function to reduce the impact of disturbances of dynamic model and system noise. Simulation and a field test have been conducted to compare the performance of AUKF and conventional UKF, as well as the innovation-based adaptive estimation (IAE) method. The simulation proves that the AUKF outperforms the conventional UKF regarding positioning and velocity estimates. Similarly, the field test also proves the superiority of the AUKF against the conventional UKF. This test also shows that the adaptive factor-based AUKF has similar performance with IAE-based AUKF, but requires less computation time.