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

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