Multiple Ranging Fusion Positioning Model Based on Total Least Squares

During the flight of a spacecraft, ranging measurement data are a very important data source for realizing high-accuracy trajectory and achieving the characteristics of fewer error sources and high measurement accuracy. According to the GPS pseudo-range measuring element of multiple satellites with similar observation intervals, in this paper, we proposed a fusion positioning method based on the total least squares algorithm, linearized the observation equation, established the augmented matrix of the coefficient matrix error and observation vector, and obtained the trajectory fusion positioning results based on singular value decomposition theory. In contrast to the least squares algorithm, the proposed algorithm considers both the measurement information error and coefficient matrix error without necessitating the execution of iterations and providing a precise trajectory as the input. In addition, the validity estimation model of the proposed algorithm was established. The positioning difference between the positioning result obtained using the proposed algorithm and that obtained using the traditional LS algorithm is within 10 meters, and at the time of object maneuvering, the position random error improved from 1–2 meters to 0.5 meters. The first- and second- order validities of the estimation fusion model are greater than 0.9. The trajectory positioning result obtained using the proposed algorithm is more reliable, and the precision accords with the processing requirements.