A Novel Family of Adaptive Filtering Algorithms Based on The Logarithmic Cost

We introduce a novel family of adaptive filtering algorithms based on a relative logarithmic cost. The new family intrinsically combines the higher and lower order measures of the error into a single continuous update based on the error amount. We introduce important members of this family of algorithms such as the least mean logarithmic square (LMLS) and least logarithmic absolute difference (LLAD) algorithms that improve the convergence performance of the conventional algorithms. However, our approach and analysis are generic such that they cover other well-known cost functions as described in the paper. The LMLS algorithm achieves comparable convergence performance with the least mean fourth (LMF) algorithm and extends the stability bound on the step size. The LLAD and least mean square (LMS) algorithms demonstrate similar convergence performance in impulse-free noise environments while the LLAD algorithm is robust against impulsive interferences and outperforms the sign algorithm (SA). We analyze the transient, steady state and tracking performance of the introduced algorithms and demonstrate the match of the theoretical analyzes and simulation results. We show the extended stability bound of the LMLS algorithm and analyze the robustness of the LLAD algorithm against impulsive interferences. Finally, we demonstrate the performance of our algorithms in different scenarios through numerical examples.Comment: Submitted to IEEE Transactions on Signal Processin

A Recursive Least M-Estimate Algorithm for Robust Adaptive Filtering in Impulsive Noise: Fast Algorithm and Convergence Performance Analysis

This paper studies the problem of robust adaptive filtering in impulsive noise environment using a recursive least M-estimate algorithm (RLM). The RLM algorithm minimizes a robust M-estimator-based cost function instead of the conventional mean square error function (MSE). Previous work has showed that the RLM algorithm offers improved robustness to impulses over conventional recursive least squares (RLS) algorithm. In this paper, the mean and mean square convergence behaviors of the RLM algorithm under the contaminated Gaussian impulsive noise model is analyzed. A lattice structure-based fast RLM algorithm, called the Huber Prior Error Feedback-Least Squares Lattice (H-PEF-LSL) algorithm1 is derived. It has an order O(N) arithmetic complexity, where N is the length of the adaptive filter, and can be viewed as a fast implementation of the RLM algorithm based on the modified Huber M-estimate function and the conventional PEF-LSL adaptive filtering algorithm. Simulation results show that the transversal RLM and the H-PEF-LSL algorithms have better performance than the conventional RLS and other RLS-like robust adaptive algorithms tested when the desired and input signals are corrupted by impulsive noise. Furthermore, the theoretical and simulation results on the convergence behaviors agree very well with each other.published_or_final_versio

A Huber recursive least squares adaptive lattice filter for impulse noise suppression

This paper proposes a new adaptive filtering algorithm called the Huber Prior Error-Feedback Least Squares Lattice (H-PEF-LSL) algorithm for robust adaptive filtering in impulse noise environment. It minimizes a modified Huber M-estimator based cost function, instead of the least squares cost function. In addition, the simple modified Huber M-estimate cost function also allows us to perform the time and order recursive updates in the conventional PEF-LSL algorithm so that the complexity can be significantly reduced to O(M), where M is the length of the adaptive filter. The new algorithm can also be viewed as an efficient implementation of the recursive least M-estimate (RLM) algorithm recently proposed by the authors [1], which has a complexity of O(M 2). Simulation results show that the proposed H-PEF-LSL algorithm is more robust than the conventional PEF-LSL algorithm in suppressing the adverse influence of the impulses at the input and desired signals with small additional computational cost.published_or_final_versio

A robust quasi-newton adaptive filtering algorithm for impulse noise suppression

This paper studies the problem of robust adaptive filtering in impulse noise environment using the Quasi-Newton (QN) adaptive filtering algorithm. An M-estimate based cost function is minimized instead of the commonly used mean square error (MSE) to suppress the adverse effect of the impulse noise on the filter coefficients. In particular, a new robust quasi-Newton (R-QN) algorithm using the self-scaling variable metric (SSV) method for unconstrained optimization is studied in details. Simulation results show that the R-QN algorithm is more robust to impulse noise in the desired signal than the RLS algorithm and other QN algorithm considered. Its initial convergence speed and tracking ability to sudden system change are also superior to those of the quasi-Newton algorithm proposed in [1].published_or_final_versio

A robust M-estimate adaptive filter for impulse noise suppression

In this paper, a robust M-estimate adaptive filter for impulse noise suppression is proposed. The objective function used is based on a robust M-estimate. It has the ability to ignore or down weight large signal error when certain thresholds are exceeded. A systematic method for estimating such thresholds is also proposed. An advantage of the proposed method is that its solution is governed by a system of linear equations. Therefore, fast adaptation algorithms for traditional linear adaptive filters can be applied. In particular, a M-estimate recursive least square (M-RLS) adaptive algorithm is studied in detail. Simulation results show that it is more robust against individual and consecutive impulse noise than the MN-LMS and the N-RLS algorithms. It also has fast convergence speed and a low steady state error similar to its RLS counterpart.published_or_final_versio

Delay Estimator and Improved Proportionate Multi-Delay Adaptive Filtering Algorithm

This paper pertains to speech and acoustic signal processing, and particularly to a determination of echo path delay and operation of echo cancellers. To cancel long echoes, the number of weights in a conventional adaptive filter must be large. The length of the adaptive filter will directly affect both the degree of accuracy and the convergence speed of the adaptation process. We present a new adaptive structure which is capable to deal with multiple dispersive echo paths. An adaptive filter according to the present invention includes means for storing an impulse response in a memory, the impulse response being indicative of the characteristics of a transmission line. It also includes a delay estimator for detecting ranges of samples within the impulse response having relatively large distribution of echo energy. These ranges of samples are being indicative of echoes on the transmission line. An adaptive filter has a plurality of weighted taps, each of the weighted taps having an associated tap weight value. A tap allocation/control circuit establishes the tap weight values in response to said detecting means so that only taps within the regions of relatively large distributions of echo energy are turned on. Thus, the convergence speed and the degree of estimation in the adaptation process can be improved