Adaptive CDKF Based on Gradient Descent with Momentum and its Application to POS

In Position and Orientation System (POS), the Global Navigation Satellite System (GNSS) is susceptible to external severe weather and electromagnetic interference, which will cause the sudden or abnormal measurement noise of the GNSS and reduce the integration accuracy and stability of POS. To solve this problem, this paper proposes an adaptive center differential Kalman filter (CDKF) based on gradient descent with momentum (named as GDM-ACDKF). Firstly, the iterative theory of measurement noise covariance is introduced into CDKF, and the adaptive CDKF based on fixed sliding window factor (ACDKF) is achieved to adjust the measurement noise covariance matrix adaptively. Then, to further improve the tracking measurement noise ability of ACDKF, motivated by the idea of momentum gradient descent, the function between estimated error variance matrix and sliding window factor is established and the adaptive sliding window based on gradient descent with momentum is derived, so that the adaptive sliding window factor can be obtained with the minimum estimated error variance matrix. The adaptive sliding window factor, served as a variable weighting factor for adjusting the measurement noise covariance matrix, can determine the update difference of the measurement noise covariance matrix at the current moment by adjusting the proportion of the current innovation in the mean innovation in a real time, so as to realize the prediction and tracking effect of the measurement noise. The flight test results show that the proposed method has stronger measurement noise tracking ability and higher precision compared with CDKF, strong tracking CDKF and ACDKF.