WSEAS Transactions on Mathematics

Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018

Double-Parameter Ridge-Type Kalman Filter Based on Signal-to-Noise Ratio Test

AUTHORS: Hao Li, Yongwei Gu, Shumei Guo, Guochao Zhang

Download as PDF

ABSTRACT: In this paper, the ill-conditioning diagnosis and processing of Kalman filter are combined. First, the ill-conditioning of Kalman filter and the disadvantage of ridge-type Kalman filter are analyzed. Then t he signal-to-noise ratio(SNR) statistic is introduced to measure how much each parameter suffers from the ill-conditioning. Accordingly, all parameters are divided into two parts, named involved parameters and n on-involved parameters respectively. Then, the two parts of parameters are corrected with two ridge para meters of different size. This method is named double-parameter ridge-type Kalman filter and can reduce the bias introduced in ridge-type Kalman filter while reducing the variance of the state parameter estimati on. Combined with the idea of generalized ridge estimation, the selection method of two ridge parameters are given. Finally, the example illustrates the new algorithm can effectively overcome the influence of th e ill-condition on Kalman filter and the reduce the bias in ridge-type Kalman filter, which improves the a ccuracy of the estimates of parameters.

KEYWORDS: Kalman filter; ill-conditioning; double-parameter ridge estimation; signal-to-noise ratio


[1] Y. Y. Qin and H. Y. Zhang and S. H. Wang, Theory of Kalman Filter and Integrated Navigation Principles, Northwestern Polytechnical University Press, 2012.

[2] D. E. Catlin, Estimation, Control, and the Discrete Kalman Filter, Springer, 1989.

[3] C. X. Zhang and J. J Yue, Application of an improved adaptive chaos prediction model in aero-engine performance parameters, WSEAS Trans-actions on Mathematics. Vol.11, 2012, pp. 114-124.

[4] A. A. Keller, pl -Norm Minimization Method for Solving Nonlinear Systems of Equations, WSEAS Transactions on Mathematics. Vol.13, 2014, pp. 654-665.

[5] N. A. Nechval and G. Berzins and M. Pur-gailis, Improved Estimation of State of Stochas-tic Systems via Invariant Embedding Technique, WSEAS Transactionson Mathematics. Vol.7,2008, pp. 141-159.

[6] Kaipio J and Somersalo E, Nonstationary Inverse Problems and State Estimation, Journal of Inverse Ill-Posed Problems, Vol.7, 1998, pp. 273-282.

[7] Baroudi D and Kaipio J and somersalo E, Dynamical Electric Wire Tomography: Time Series Approach. Inverse Problems, Vol.14, 1998, pp. 799-813.

[8] Tan Jiajia and Li Dan and Zhang Jianqing, Biased Kalman Filter, International Conference on Sensing Technology, Palmerson North, 2011.

[9] Ou Jikun and Ding Wenwu and Liu Jihua, An Improved Algorithm for Autonomous Orbit Determination of Navigation Satellite Constellation, Survey Review, Vol.43, 2011, pp.361-369.

[10] Han Song-hui and DU Lan and Gui Qing-ming and GU Yong-wei, Characteristics of Diagnostic Complex Multicollinearity and Its Application in GEO Orbit Determination, Acta Metallurgica Sinica, Vol.1, 2013, pp.19-26.

[11] Li Yongming and Gui Qingming and Gu Yongwei, Ridge-Type Kalman Filter and Its Algorithm,WSEAS Transactions on Mathematics, Vol. 13, 2014, pp. 852-862.

[12] Yang Yuanxi, Adaptive Navigation and Kinematic Positioning, Surveying and Mapping Press , 2006.

[13] Gu Yongwei, Regularization methods based on multicollinearity diagnosis and their applications to geodesy , Information Engineering University, 2010.

[14] Han Songhui and Gui Qingming and Li Jianwen, Ridge—Type EKF of Distributed Autonomous Orbit Determination, Geomatics and Information Science of Wuhan University, Vol. 38, 2013, pp. 399-402.

[15] Hoerl AE and Kennard R W, Ridge Regression: Applications to Non-Orthogonal Problems, Technometrics, Vol. 12, 1970, pp. 69-82.

[16] Han Songhui and Du Lan and Gui Qingming, Characteristics Analysis Approach for Multicollinearity Diagnosis and Its Applications in Orbit Determination of GEO Satellites, Acta Geodaetica et Cartographica Sinica, Vol. 42,2013, pp.19-26.

[17] Wang Songgui, The Theory of Linear Model and Its Application, Anhui Education Press, 1987.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #21, pp. 162-169

Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

Bulletin Board


The editorial board is accepting papers.

WSEAS Main Site