Improved Maximum Likelihood Filter Based on UD Decomposition Algorithm and its Application in Transfer Alignment

For the problem that the statistical characteristics of noise is difficult to accurately determine, and meantime the accumulation of calculation error will cause the state estimation covariance matrix to lose positive definiteness in the process of transfer alignment(TA), this paper proposes an improved maximum likelihood adaptive Kalman filter(AKF) based on UD decomposition algorithm. Firstly, real-time estimators of system noise and measurement noise according to the maximum likelihood criterion are constructed, and the observation information is used to update and correct the statistical characteristics of the noise in real time; Secondly, the UD decomposition algorithm is performed on the one-step prediction error covariance matrix, and the decomposed matrixes are updated with time to ensure the symmetric positive definiteness of the covariance matrix. The improved algorithm is applied to TA and compared with the traditional maximum likelihood filter. The simulation results show that the improved algorithm can maintain the noise adaptive ability. At the same time, when the prior state covariance matrix is unknown, the numerical stability of the filtering process can be effectively improved and the fast TA can be achieved.