Efficient Algorithms for Identifying an Unknown FIR System in Noisy Adaptive Filtering

Abstract

Adaptive filters have been used in a wide variety of applications such as noise cancellation, system identification, and prediction. However, it is well established that noisy inputs cause bias in the estimates obtained by common adaptive filtering algorithms. Furthermore, the performances of the adaptive filtering algorithms, accuracy or convergence rate of the estimation, are severely degraded by outliers such as an impulsive noise. To overcome these problems, there have been proposed several algorithms but there still exists room for improvement on performance and efficiency. Therefore, this dissertation presents some adaptive filtering algorithms working with noisy input or impulsive noisy output and having improved performance and reduced computational complexity.At first, a bias-compensated normalized least mean square (NLMS) algorithm with a noisy input is presented. The algorithm produces unbiased estimate and overcomes the drawbacks of the consistent NLMS algorithm, a former work of this subject. The algorithm is obtained from an approximated cost function based on the statistical properties of the input noise and involves a condition checking constraint to decide whether the weight coefficient vector must be updated.At second, an efficient unbiased recursive least squares (RLS) filtering algorithm with noisy input is proposed. The unbiased estimate is obtained without knowing any a priori information via a new cost. Furthermore, to reduce computational complexity, the estimate is updated along the current input-vector direction and the corresponding gain is efficiently computed. In addition, to increase a convergence rate, the algorithm is extended to update the estimate along not only current but also past input-vector directions.At third, a fast RLS algorithm for impulsive noisy adaptive filtering is presented. An outlier identifier is designed to recognize measurements corrupted by impulsive noises and used to produce the robust RLS algorithm using a new cost with the outlier identifier. To find its fast version, the stochastic line search method is used. The detection and reinitialization procedure for sudden system changes is also included to enhance tracking performance. The algorithm achieves a small steady-state error and a good tracking performance simultaneously while dramatically reducing computational complexity.Lastly, an efficient algorithm that is developed to handle both noisy input and impulsive noisy output is presented by combining the above algorithms.