AUTHORS: Yongming Li, Qingming Gui, Songhui Han, Yongwei Gu

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ABSTRACT: Kalman filter is one of the most common ways to deal with dynamic data and has been widely used in project fields. However, the accuracy of Kalman filter for discrete dynamic system is poor when the observation matrix is ill-conditioned. Therefore, the method for overcoming the harmful effect caused by ill-conditioned observation matrix in discrete dynamic system is studied in this paper. Firstly, Tikhonov regularized Kalman filter (TRKF) and its algorithm are proposed by combining Tikhonov regularization method and Kalman filter. Meanwhile, some excellent properties of TRKF are proved. Secondly, the methods of choosing regularization parameter and regularization matrix in TRKF are given. Thirdly, simulated examples are designed to evaluate the performance of TRKF and comparisons between TRKF and Ordinary Ridge-type Kalman Filter (ORKF) are given. Finally, TRKF is applied in autonomous orbit determination of BeiDou Navigation Satellite System (BDS) with cross-link ranging observations and ground tracking observations so as to prevent filter divergent which is caused by ill-conditioned observation matrix. Simulations and applications illustrate that TRKF can overcome the harmful effect caused by ill-conditioned observation matrix in discrete dynamic system and the accuracy is improved effectively.

KEYWORDS: Discrete dynamic system, Kalman filter, Ill-conditioning, Tikhonov regularization, Regularization parameter, Regularization matrix, Autonomous orbit determination

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