Keywords
Kalman filter
wavelet denoising
multiresolution analysis
Procesamiento de señales
filtro de Kalman
eliminación de ruido con onditas
análisis de multirresolución
How to Cite
Abstract
Under the analysis of signals disturbed by noise, in this paper we propose a working methodology aimed to seize the best estimate of combining Kalman filtering with the characterization that is achieved by applying a multiresolution analysis (MRA) using wavelets. From the standpoint of Kalman filtering this combined procedure is quasi-optimal, but the change to be made allows the simultaneous implementation of a scheme of wavelet denoising; with this decreases the computational cost of applying both procedures separately. Our proposal is to process the signal by successive non-overlapping intervals, combining the process for calculating the optimal filter with a MRA using the Haar wavelet. The method takes advantage of the combined use of both tools (Kalman-Haar) and is free from edge problems related to the signal segmentation.
References
D’Attellis, C.E. (1981) Estimadores Óptimos y sus Aplicaciones. CONICET, Argentina.
Hirchoren, G.A.; D’Attellis, C.E. (1998) “Estimation of fractal signals using wavelets and filter banks”, IEEE Trans. on Signal Processing 46(6): 1624–1630.
Hirchoren, G.A.; D’attellis, C.E. (1999) “Estimation of fractional brownian motion with multiresolution Kalman filter banks”, IEEE Trans. on Signal Processing 47(5): 1431–1434.
Kalman, R.E. (1960) “A new approach to linear filtering and prediction problems”, Trans. ASME-Journal of Basic Engineering 82:35–45.
Kalman, R.E.; Bucy, R.S. (1961) “New results in linear filtering and prediction theory”, Trans. ASME-Journal of Basic Engineering: 95– 108.
Postalcioglu, S.; Erkan, K.; Bolat, E.D. (2005) “Comparison of Kalman filter and wavelet filter for denoising”, en: IEEE Conference Proceedings International Conference on Neural Network and Brain, Vol 2, Beijing, China: 951–954.
Renaud, O.; Starck, J.; Murtagh, F. (2005) “Wavelet-based combined signal filtering and prediction”, IEEE Trans. on Sytems, Man, and Cybernetics, Part B: Cybernetics 35(6): 1241–1251.
Walmut, D.F. (2002) An Introduction to Wavelet Analysis. Birkhaüser, Boston.
Zhao, J.; Ma, H.; You, Z.; Umeda, M. (2001) Lecture Notes in Computer Science: Multiscale Kalman filtering of fractal signals using wavelet transform, Springer-Verlag Berlin, Heidelberg: 305–313.