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A new noise covariance matrix estimation method of Kalman filter for satellite clock errors

Lin Xu Luo Zhi-Cai

A new noise covariance matrix estimation method of Kalman filter for satellite clock errors

Lin Xu, Luo Zhi-Cai
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  • Received Date:  21 October 2014
  • Accepted Date:  27 November 2014
  • Published Online:  05 April 2015

A new noise covariance matrix estimation method of Kalman filter for satellite clock errors

  • 1. School of Geodesy and Geomatics, Wuhan University, Wuhan 430079, China;
  • 2. Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, Wuhan University, Wuhan 430079, China;
  • 3. State Key Laboratory of Information Engineering in Surveying, Mapping and Remote Sensing, Wuhan 430079, China
Fund Project:  Project supported by the National Basic Research Program of China (Grant No. 2013CB733302), the National Natural Science Foundation of China (Grant Nos. 41174062, 41131067), the Fundamental Research Funds for the Central Universities, China (Grant No. 2012214020206), and the Open Research Fund Program of the Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, China (Grant No. 12-02-09).

Abstract: The satellite clock plays a key role in the global navigation satellite system (GNSS). The accuracy of GNSS and its applications depend on the quality of the satellite clock. Therefore, precisely estimating and predicting the satellite clock is an important issue in the fields of GNSS and its application. As an optimal estimation algorithm, Kalman filter has been used to estimate and predict the satellite clock. However, in a conventional Kalman filter algorithm, the noise covariance matrices of satellite clock need to be predetermined, which restricts its further applications since the noise covariance matrices, especially the process noise covariance matrix, are usually unknown in the real cases. With inappropriate noise covariance matrices, the state estimation of conventional Kalman filter is suboptimal. To cope with this problem, a new noise covariance matrix estimation method of Kalman filter is proposed, and then we apply it to the problem of satellite clock estimation and prediction. Considering the fact that the process noise covariance matrix depends on the unknown noise parameters, the problem of estimating process noise covariance matrix can be solved by estimating the unknown noise parameters. First, the correlation between the Kalman innovations is used to establish a linear relationship with the unknown noise parameters. Then the unknown parameters can be estimated by least-squares estimation. Finally, the satellite clock can be estimated and predicted with the estimated noise parameters. In the new method, no prior information about the noise parameters is needed. Even with some extreme prior noise parameters, the new method can also work very well and has good convergence properties. For comparison, we conduct two experiments using the new method and the adaptively robust Kalman filter with classified adaptive factors based on opening windows separately, both results are consistent with each other very well, which verifies the correctness and effectiveness of this new method.

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