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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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Keywords:
- satellite clock error /
- Kalman filter /
- noise estimation
[1] Yang Y, He H, Xu G 2001 J. Geodesy 75 109
[2] Yang Y, Gao W 2005 J. Navigation 58 471
[3] Yang Y, Gao W 2006 J. Geodesy 80 177
[4] Yang Y, Cui X 2008 Survey Rev. 40 260
[5] Hauschild A, Montenbruck O 2009 GPS Solut. 13 173
[6] Liu Y Y, Lian B W, Zhao H W, Liu Y Q 2014 Acta Phys. Sin. 63 228402 (in Chinese) [刘洋洋, 廉保旺, 赵宏伟, 刘亚擎 2014 63 228402]
[7] Chen W D, Liu Y L, Zhu Q G, Chen Y 2013 Acta Phys. Sin. 62 170506 (in Chinese) [陈卫东, 刘要龙, 朱奇光, 陈颖 2013 62 170506]
[8] Zhao L 2012 Acta Phys. Sin. 61 104301 (in Chinese) [赵龙 2012 61 104301]
[9] Shmaliy Y S 2006 IEEE Trans. Ultrason. Ferr. 53 862
[10] Contreras-Gonzalez J, Ibarra-Manzano O, Shmaliy Y S 2013 Measurement 46 476
[11] Huang G W, Yang Y X, Zhang Q 2011 Acta Geodaet. Cartograph. Sin. 40 15 (in Chinese) [黄观文, 杨元喜, 张勤 2011 测绘学报 40 15]
[12] Guo H R, Yang Y X, He H B, Xu T H 2010 Acta Geodaet. Cartograph. Sin. 39 146 (in Chinese) [郭海荣, 杨元喜, 何海波, 徐天河 2010 测绘学报 39 146]
[13] Huang G, Zhang Q 2012 GPS Solut. 16 531
[14] Guo H R 2006 Ph. D. Dissertation (Zhengzhou: Information Engineering University) (in Chinese) [郭海荣 2006 博士学位论文 (郑州:信息工程大学)]
[15] Kwon W H, Kim P S, Han S H 2002 Automatic 38 545
[16] Rajamani M R, Rawlings J B 2009 Automatic 45 142
[17] Odelson B J, Rajamani M R, Rawlings J B 2006 Automatic 42 303
[18] Luo Z C, Lin X, Zhou B Y 2012 Geomat. Inform. Sci. Wuhan Univ. 37 1164 (in Chinese) [罗志才, 林旭, 周波阳 2012 武汉大学学报: 信息科学版 37 1164]
[19] International GNSS Service ftp://igscb.jpl.nasa.gov/[2014.10.20.]
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[1] Yang Y, He H, Xu G 2001 J. Geodesy 75 109
[2] Yang Y, Gao W 2005 J. Navigation 58 471
[3] Yang Y, Gao W 2006 J. Geodesy 80 177
[4] Yang Y, Cui X 2008 Survey Rev. 40 260
[5] Hauschild A, Montenbruck O 2009 GPS Solut. 13 173
[6] Liu Y Y, Lian B W, Zhao H W, Liu Y Q 2014 Acta Phys. Sin. 63 228402 (in Chinese) [刘洋洋, 廉保旺, 赵宏伟, 刘亚擎 2014 63 228402]
[7] Chen W D, Liu Y L, Zhu Q G, Chen Y 2013 Acta Phys. Sin. 62 170506 (in Chinese) [陈卫东, 刘要龙, 朱奇光, 陈颖 2013 62 170506]
[8] Zhao L 2012 Acta Phys. Sin. 61 104301 (in Chinese) [赵龙 2012 61 104301]
[9] Shmaliy Y S 2006 IEEE Trans. Ultrason. Ferr. 53 862
[10] Contreras-Gonzalez J, Ibarra-Manzano O, Shmaliy Y S 2013 Measurement 46 476
[11] Huang G W, Yang Y X, Zhang Q 2011 Acta Geodaet. Cartograph. Sin. 40 15 (in Chinese) [黄观文, 杨元喜, 张勤 2011 测绘学报 40 15]
[12] Guo H R, Yang Y X, He H B, Xu T H 2010 Acta Geodaet. Cartograph. Sin. 39 146 (in Chinese) [郭海荣, 杨元喜, 何海波, 徐天河 2010 测绘学报 39 146]
[13] Huang G, Zhang Q 2012 GPS Solut. 16 531
[14] Guo H R 2006 Ph. D. Dissertation (Zhengzhou: Information Engineering University) (in Chinese) [郭海荣 2006 博士学位论文 (郑州:信息工程大学)]
[15] Kwon W H, Kim P S, Han S H 2002 Automatic 38 545
[16] Rajamani M R, Rawlings J B 2009 Automatic 45 142
[17] Odelson B J, Rajamani M R, Rawlings J B 2006 Automatic 42 303
[18] Luo Z C, Lin X, Zhou B Y 2012 Geomat. Inform. Sci. Wuhan Univ. 37 1164 (in Chinese) [罗志才, 林旭, 周波阳 2012 武汉大学学报: 信息科学版 37 1164]
[19] International GNSS Service ftp://igscb.jpl.nasa.gov/[2014.10.20.]
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