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Studies of Numerically Stable Estimation for Multi-Channel Systems with Multiplicative Noises

Author: ChenMeng
Tutor: ZuoDongSheng
School: Ocean University of China
Course: Signal and Information Processing
Keywords: Multi-channel with multiplicative noise Singular value decomposition (SVD) Linear minimum variance Optimal Estimation
Type: Master's thesis
Year: 2004
Downloads: 112
Quote: 13
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State with multiplicative noise system optimal estimation theory has important applications in oil seismic exploration, underwater target detection, speech processing, and many other fields. Made in this area in recent years, a series of new theoretical and applied research results, breaking the multiplicative noise limit of the one-dimensional random sequence, the development of the multi-channel optimal estimation algorithm with multiplicative noise under, and in turn, the development of a series of research results to a multi-sensor information fusion technology and two-dimensional with multiplicative noise system optimal estimation. The meaning of these algorithms are linear minimum variance is optimal. During the practical application of these algorithms may appear numerical instability in the recursive calculation of long numerical instability will affect the calculation accuracy of the algorithm divergence serious cause the algorithm fails completely. Therefore, these algorithms Numerical stability method is necessary. In this paper, the more universal significance of multi-channel state with multiplicative noise system optimal estimation theory, linear minimum variance sense optimal while numerical stability as: First, this article recalled with multiplicative noise systems development and current status of optimal estimation theory, and numerical stability research in this field and describes the development of the status quo. Second, in a multi-channel observation models with multiplicative noise system, multiplicative noise is no longer the traditional one-dimensional random sequence, but in the form of random matrices, the first is a random diagonal matrix, and then extended to the general random matrix. First observation channel multiplicative noise random diagonal matrix systems, the use of the singular value decomposition (SVD) as a tool for the given channel characteristics not related to the numerical stability of the optimal state filtering algorithm, and the application of this method to multiplicative noise to a general random matrix system, given the same complex numerical stability of the multi-channel with multiplicative noise system algorithm. Both filtering algorithms are kept linear minimum variance sense optimality. With multiplicative noise system for multi-channel, in the optimal state filtering algorithm based on first derive a the Optimal Fixed case of a diagonal matrix directly smoothing algorithm multiplicative noise is random, and then using the singular value decomposition ( SVD) method to decompose the error covariance matrix of the smoothing algorithm, given its numerical stability of the algorithm, and thus the use of filtering and smoothing optimal estimation results, given the fixed domain deconvolution algorithm. Turn the above algorithm is then extended to the multiplicative noise is generally random array of circumstances, given the complex case of multi-channel direct fixed domain smoothing algorithm, deconvolution algorithms and numerical stability of the algorithm. Fourth, simulation examples verify the effectiveness of each algorithm.

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CLC: > Industrial Technology > General industrial technology > Acoustic engineering > Vibration, noise and its control
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