A filter-bank-based Kalman filtering technique for waveletestimation and decomposition of random signals

摘要

In this work an effective algorithm is derived for optimalnestimation and multiresolutional decomposition of noisy random signals.nThis algorithm performs the estimation and decomposition simultaneously,nusing the discrete wavelet transform implemented by a filter bank. Thenalgorithm is developed based on the standard Kalman filtering scheme,nand hence preserves the merits of the Kalman filter for random signalnestimation in the sense that it produces an optimal (linear, unbiased,nand minimum error variance) estimate of the unknown signal in anrecursive manner. A set of Monte Carlo simulations was performed, andnthe statistical performance tests showed that the proposed estimationnand decomposition approach outperforms the Kalman filter