Adaptive Robust Least-Squares Smoothing Algorithm

Abstract

The Kalman smoothing algorithm is widely use d in offline data processing in GNSS to improve filter calcu lation accuracy. When there are measurement outliers or b iased random models, the adaptive Kalman smoothing algo rithm can reduce their impact on the smoothing results to a certain extent. Nevertheless, the adaptive Kalman smoothi ng algorithm usually has difficulty obtaining optimal estim ation in a complex observation environment due to the inhe rent defects of the algorithm itself. Therefore, we propose a n adaptive robust least-squares smoothing algorithm. The row and column transformation of the least-square smooth noise covariance matrix is realized by constructing an orth ogonal space transformation matrix, and the noise covaria nce estimation problem of the Kalman filter is transformed into the problem of solving the variance covariance compo nent elements under a specific matrix structure. In additio n, by selecting the observation value with the largest stand ardized residual to determine whether it is gross error, we avoid the gross error misjudgment problem caused by the t wo-factor robust estimation method under least-square sm oothing, and further improve the smoothing accuracy. Fina lly, two experiments are studied to compare the performan ce of the new algorithm and the state-of-the-art algorithms. The proposed algorithm has demonstrated better perform ance in terms of robustness and estimation accuracy.