Abstract
In this paper, modeling and estimation of a class of dynamic multiscale system subject to colored state equation noise is proposed. The colored state noise vector is augmented in the system state variables, the state space projection equation is used to link the scales, and then a new system model is built. The new model is in a form suitable for the application of the Kalman filter equations. Haar-wavelet-based model and estimation algorithm are given. Monte Carlo simulation results demonstrate that the proposed algorithm is effective and powerful in this kind of multiscale estimation problem.
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Basseville, M., Benveniste, A., Chou, K., Golden, S., Nikoukhah, R., Willsky, A.S.: Modeling and Estimation of Multiresolution Stochastic Processes. IEEE Trans. Information Theory 38, 766–784 (1992)
Chou, K., Willsky, A.S., Benveniste, A.: Multiscale Recursive Estimation, Data Fusion, and Regularization. IEEE Trans. Automatic Control 39, 464–478 (1994)
Chou, K., Willsky, A.S., Nikoukhah, R.: Multiscale Systems, Kalman Filters, and Riccati Equations. IEEE Trans. on Automatic Control 39, 479–492 (1994)
Daoudi, K., Frakt, A., Willsky, A.S.: Multiscale Autoregressive Models and Wavelets. IEEE Trans. Information Theory 45, 828–845 (1999)
Luettgen, M., Karl, W., Willsky, A.S., Tenney, R.: Multiscale Representations of Markov Random Fields. IEEE Trans. on Signal Processing 41, 3377–3396 (1993)
Frakt, A.: Internal Multiscale Autoregressive Processes, Stochastic Realization, and Covariance Extension. PhD thesis, Massachusetts Institute of Technology (1999)
Hong, L.: Centralized and Distributed Kalman Filtering in Multi-coordinate Systems with Uncertainties. In: Proceedings of the IEEE Aerospace and Electronics Conference, pp. 389–394 (1990)
Hong, L., Chen, G., Chui, C.K.: A Filter-Bank Based Kalman Filtering Technique for Wavelet Estimation and Decomposition of Random Signals. IEEE Trans. on Circuits and Systems II 45(2), 237–241 (1998)
Hong, L.: Multiresolutional Filtering using Wavelet Transform. IEEE Trans. on Aerospace and Electronic Systems 29(4), 1244–1251 (1993)
Hong, L.: Distributed Filtering using Set Models. IEEE Trans. on Aerospace and Electronic Systems 28(4), 1144–1153 (1992)
Hong, L.: Adaptive Distributed Filtering in Multicoordinated Systems. IEEE Trans. on Aerospace and Electronic systems 27(4), 715–724 (1991)
Hong, L.: An Optimal Reduced-Order Stochastic Observer-Estimator. IEEE transactions on Aerospace and Electronic systems 28(2), 453–461 (1992)
Hong, L.: Optimal Multiresolutional Distributed Filtering. In: Proceedings of the 31th Conference on Decision and Control, pp. 3105–3110 (1992)
Hong, L., Werthmann, J.R., Bierman, G.S., Wood, R.A.: Real-Time Multiresolution Target Tracking. In: Signal and Data Processing of Small Target, Orlando, FL, pp. 233–244 (1993)
Hong, L.: Multiresolutional Distributed Filtering. IEEE Trans. on Automatic Control 39(4), 853–856 (1994)
Zhang, L.: The Optimal Estimation of a Class of Dynamic Multiscale Systems. PhD Thesis, Northwestern Polytechnic University, Xi’an, PRC (2001)
Anderson, B.D.O., Moore, J.B.: Optimal Filtering. Prentice- Hall, Inc., Englewood Cliffs (1979)
Chen, C.T.: Linear System Theory and Design. Holt, Rinehart and Winston, New York (1970)
Daubechies, I.: Ten Lectures on Wavelets. CBMS-NSF Series in Appl. Math. SIAM, Philadelphia (1992)
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Cui, P., Pan, Q., Wang, G., Cui, J. (2005). Multiresolutional Filtering of a Class of Dynamic Multiscale System Subject to Colored State Equation Noise. In: Prasanna, V.K., Iyengar, S.S., Spirakis, P.G., Welsh, M. (eds) Distributed Computing in Sensor Systems. DCOSS 2005. Lecture Notes in Computer Science, vol 3560. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11502593_18
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DOI: https://doi.org/10.1007/11502593_18
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