Abstract
A novel modification is proposed to the Kalman filter for the case of non-Gaussian measurement noise. We model the non-Gaussian data as outliers. Measurement data is robustly discriminated between Gaussian (valid data) and outliers by Robust Sequential Estimator (RSE). The measurement update is carried out for the valid data only. The modified algorithm proceeds as follows. Initially, the robust parameter and scale estimates of the measurement data are obtained for a sample of data using maximum likelihood estimates for a t-distribution error model through Iteratively Reweighted Least Squares (IRLS). The sample is dynamically updated with each new observation. Sequential classification of each new measurement is decided through a weighting scheme determined by RSE. State updates are carried out for the valid data only. Simulations provide satisfactory results and a significant improvement in mean square error with the proposed scheme.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hawkins, D.: Identification of outliers. Chapman and Hall, Boca Raton (1980)
Lange, K.L., Little, R.J.A., Taylor, J.M.G.: Robust Statistical Modeling Using the t Distribution. Journal of the American Statistical Association 84(408), 881–896 (1989)
Hewer, G.A., Martin, R.D., Zeh, J.: Robust Preprocessing of Kalman Filtering of Glint Noise. IEEE Trans. Aerosp. Electron. Syst., AES 23, 120–128 (1987)
Bilik, I., Tabrikian, J.: Target Tracking in Glint Noise Environment Using Nonlinear Non-Gaussian Kalman Filter. In: 2006 IEEE National Radar Conference Proceedings, art. no. 1631813, pp. 282–287 (2006)
Sorrenson, H.W., Stubberud, A.R.: Nonlinear filtering by approximation of the a posteriori density. Int. J. Control 18, 33–51 (1968)
Sorrenson, H.W., Alspach, D.I.: Recursive Bayesian Estimation using Gaussian Sums. Automatica 18, 456–476 (1971)
Masreliez, C.J.: Approximate non-Gaussian filtering with linear state and observation relations. IEEE Tran. Automat. Contr. 18 (AC-20), 107–110 (1975)
Wen-Rong, W., Amlan, K.: Kalman filtering in non-Gaussian environment using efficient score function approximation. In: Proc. of IEEE International Conference on Circuits and Systems, pp. 403-410 (1989)
Maryak, J.L., Spall, J.C., Heydon, B.D.: Use of the Kalman Filter for Inference in State-Space Models With Unknown Noise Distributions. IEEE Trans. Automat. Contr. 49(1), 87–90 (2004)
Boyer, K.L., Mirza, M.J., Ganguly, G.: Robust Sequential Estimator: A General Approach and its Application to Surface Organization in Range Data. IEEE Trans. Pattern Anal. Machine Intel. 16(10), 987–1001 (1994)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mirza, M.J. (2011). A Modified Kalman Filter for Non-gaussian Measurement Noise. In: Ma, M. (eds) Communication Systems and Information Technology. Lecture Notes in Electrical Engineering, vol 100. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21762-3_52
Download citation
DOI: https://doi.org/10.1007/978-3-642-21762-3_52
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21761-6
Online ISBN: 978-3-642-21762-3
eBook Packages: EngineeringEngineering (R0)