High Dynamic Weak Signal Tracking Algorithm of a Beidou Vector Receiver Based on an Adaptive Square Root Cubature Kalman Filter

Compared with a scalar tracking receiver, the Beidou vector tracking receiver has the advantages of smaller tracking errors, fast loss-of-lock reacquisition, and high stability. However, in extremely challenging conditions, such as highly dynamic and weak signals, the loop will exhibit a high degree of nonlinearity, and observations with gross errors and large deviations will reduce the positioning accuracy and stability. In view of this situation, based on the concepts of cubature Kalman filtering and square root filtering, a square root cubature Kalman filtering (SRCKF) algorithm is given. Then, combining this algorithm with the concept of covariance matching based on an innovation sequence, an adaptive square root cubature Kalman filter (ASRCKF) algorithm is proposed. The algorithm was verified, and the tracking performance of the vector locking loop (VLL) realized by the algorithm was compared with the SRCKF VLL and the ASRCKF scalar locking loop (SLL). The simulation results show that, regardless of whether in a highly dynamic weak signal environment or in a general situation where the signal-to-noise ratio is higher than the tracking threshold, the tracking accuracy and stability of the ASRCKF VLL are higher than those of the SRCKF VLL and the ASRCKF SLL, the three-dimensional position error of the ASRCKF VLL does not exceed 36 m, and the three-dimensional velocity error does not exceed 3.5 m/s.