Autocovariance Least-Squares Estimation for Colored Noise

Abstract

Abstract:

Conventional Autocovariance Least-Squares (ALS) mothed is limited to estimate the covariance of white noise. In order to overcome the deficiency, a new method based on ALS is proposed to estimate the covariance of colored noise, and the noise estimation models are given with regard to colored state noise, or colored observation noise and both of them. Numerical simulation results show the correctness and validity of the method.

Key words: Autocovariance Least-Squares method, state noise, observation noise, noise estimation, colored noise, Kalman filter

CLC Number:

P207

References

[1] YANG Yuanxi, HE Haibo, XU Tianhe. Adaptive Robust Filtering for Kinematic GPS Positioning[J]. Acta Geodaetica et Cartographica Sinica, 2001,30(4):293-298. (杨元喜．何海波，徐天河．论动态自适应滤波[J]．测绘学报，2001，30(4)：293-298.)
[2] YANG Yuanxi. Properties of the Adaptive Filtering for Kinematic Positioning[J]. Acta Geodaetica et Cartographica Sinica, 2003,32(3):189-192.(杨元喜. 动态定位自适应滤波解的性质[J]. 测绘学报，2003，32(3)：189-192.)
[3] YANG Yuanxi. Model Error Influence on Kalman Filtering[J]. Science of Surveying and Mapping, 2006,31(1):17-18.(杨元喜．动态Kalman滤波模型误差的影响[J]．测绘科学，2006，31(1)：17-18.)
[4] FU Mengyin, DENG Zhihong, ZHANG Jiwei. The Applications of Kalman Filtering Theory on the Navigation Systems[M]. Beijing: Scinece Press, 2003. 58-61,108-111. (付梦印，邓志红，闫莉萍．Kalman滤波理论及其在导航系统中的应用[M]．北京：科学出版社，2010. 108-111.)
[5] HE Zhengbin, WU Fumei,NIE Jianliang. Error Influences of Prior Covariance Matrices on Dynamic Kalman Filtering[J]. Geomatics and Information Science of Wuhan University, 2011,36(1):34-38. (何正斌，吴富梅，聂建亮. 先验协方差阵误差对动态Kalman滤波解的影响[J]. 武汉大学学报(信息科学版)，2011,36(1):34-38.)
[6] Shumway R H, Stoffer D S. Time Series Analysis and its Application[M]. Springer-Verlag New York Inc., New York, 2000.
[7] Raghavan H, Tangirala A K, Gopaluni R B, et al. Identification of Chemical Processes with Irregular Output Sampling[J]. Control Eng. Pract. 2006,14:467-480.
[8] HU Guorong, OU Jikun. The Improved Method of Adaptive Kalman Filtering for GPS High Kinematic Positioning[J]. Acta Geodaetica et Cartographica Sinica, 1999, 28(4):290-294. (胡国荣，欧吉坤. 改进的高动态GPS定位自适应卡尔曼滤波方法[J]. 测绘学报, 1999, 28(4):290-294.)
[9] Mohamed A H, Schwarz K P. Adaptive Kalman Filtering for INS/GPS. Journal of Geodesy, 1999, 73(4):193-203.
[10] YANG Yuanxi, XU Tianhe. An Adaptive Kalman Filter Combining Variance Component Estimation with Covariance Matrix Estimation Based on Moving Window[J]. Geomatics and Information Science of Wuhan University, 2003, 28(6):714-718. (杨元喜，徐天河. 基于移动开窗法协方差估计和方差分量估计的自适应滤波[J]. 武汉大学学报(信息科学版), 2003, 28(6):714-718.)
[11] GAO Weiguang, YANG Yuanxi, CUI Xianqiang, et al. Application of Adaptive Kalman Filtering Algorithm in IMU/GPS Integrated Navigation System[J]. Geomatics and Information Science of Wuhan University, 2006, 31(5):466-469. (高为广, 杨元喜, 崔先强, 等. IMU/GPS组合导航系统自适应Kalman滤波算法[J]. 武汉大学学报(信息科学版), 2006, 31(5):466-469.)
[12] Mehra R. On-line identification of linear dynamic systems with applications to Kalman filtering[J]. IEEE Trans on Automatic Control, 1971,16(1):12-21.
[13] Mehra R. Approachies to adaptive filtering[J]. IEEE Trans on Automatic Control, 1972,17(5):693-698.
[14] Carrew B, Bellanger P. Identification of optimum filter steady state gain for system with unknown noise parameters[J]. IEEE Trans Automatic Control, 1973,18(60)：582-587.
[15] Odelson B J, Rajamani M R, Rawlings J B. A new autocovariance least-squares method for estimating noise covariances[J]. Automatica, 2006,42(2):303-308.
[16] Odelson B J, Lutz A, Rawlings J B. The autocovariance least-squares method for estimating covariances: application to model-based control of chemical reactors[J]. IEEE Transactions on Control Systems Technology, 2006,14(3):532-540.
[17] Rajamani M R, Rawlings J B. Estimation of the disturbance structure from data using semidefinite programming and optimal weighting[J]. Automatica, 2009,45(1):142-148.
[18] Akesson B M, Jorgensen J B, Poulsen N K, et al. A generalized autocovariance least-square method for Kalman filter tuning[J]. Journal of Process Control, 2008,18:769-779.
[19] YANG Yuanxi, CUI Xianqiang. Influence Functions of Colored Noises on Kinematic Positioning—Taking the AR Model of First Class as an Example[J]. Acta Geodaetica et Cartographica Sinica, 2003,32(1):6-10. (杨元喜，崔先强．动态定位有色噪声影响函数——以一阶AR模型为例[J]. 测绘学报，2003，32(1)：6-10.)
[20] CUI Xianqiang, YANG Yuanxi, GAO Weiguang. Comparison of Adaptive Filter Arithmetics in Controlling Influence of Colored Noises[J]. Geomatics and Information Science of Wuhan University, 2006,31(8):731-735. (崔先强，杨元喜，高为广. 多种有色噪声自适应滤波算法的比较[J]. 武汉大学学报(信息科学版)，2006，31(8)：731-735