Robust Suboptimal Local Basis Function Algorithms for Identification of Nonstationary FIR Systems in Impulsive Noise Environments

TL;DR

The paper tackles the challenge of identifying time-varying FIR systems when measurement noise is impulsive. It extends the local basis function (LBF) approach by (i) optimizing the number and shape of basis functions using prior parameter-variation statistics, and (ii) introducing a noncausal, sequential trimming scheme to robustify tracking against outliers, with an adaptive version that updates noise and parameter-change statistics online. A parallel, leave-one-out cross-validation strategy guides trimming level selection, and computational considerations are addressed via efficient matrix updates and potential Toeplitz structure exploitation. Simulation results in a self-interference underwater acoustic (UWA) channel demonstrate that the proposed adaptive trimmed LBF method achieves robustness comparable to the more expensive LAD approach while significantly reducing computational load. Overall, the work provides a practical, robust, and online-capable framework for nonstationary FIR identification in impulsive-noise environments, with direct relevance to FDUWA and mobile communications.

Abstract

While local basis function (LBF) estimation algorithms, commonly used for identifying/tracking systems with time-varying parameters, demonstrate good performance under the assumption of normally distributed measurement noise, the estimation results may significantly deviate from satisfactory when the noise distribution is impulsive in nature, for example, corrupted by outliers. This paper introduces a computationally efficient method to make the LBF estimator robust, enhancing its resistance to impulsive noise. First, the choice of basis functions is optimized based on the knowledge of parameter variation statistics. Then, the parameter tracking algorithm is made robust using the sequential data trimming technique. Finally, it is demonstrated that the proposed algorithm can undergo online tuning through parallel estimation and leave-one-out cross-validation.

Figures (8)

• Figure 1: Comparison of the mean squared parameter tracking errors for three algorithms operating in the presence of $\epsilon$-contaminated measurement noise: the unmodified LBF algorithm (${\rm LBF}_1$), adaptive trimmed LBF algorithm (A), and adaptive LAD algorithm. Results obtained for the unmodified LBF algorithm operating in the absence of impulsive disturbances (${\rm LBF}_2$) are provided as a reference.
• Figure 2: Comparison of the mean squared parameter tracking errors for three algorithms operating in the presence of $\epsilon$-contaminated measurement noise: the unmodified LBF algorithm (${\rm LBF}_1$), adaptive trimmed LBF algorithm (A), and adaptive LAD algorithm. Results obtained for the unmodified LBF algorithm operating in the absence of impulsive disturbances (${\rm LBF}_2$) are provided as a reference.
• Figure 3: Left: typical realizations, displayed in the range [-10, 10], of $\epsilon$-contaminated noise for different values of $\epsilon$. Right: estimates (thin red lines) of system parameter ${\rm Re}[\theta_3(t)]$ (thick black lines) obtained for $\epsilon=0.1$ and $K=301$.
• Figure 4: Dependence of the optimal number of basis functions $m_{\rm opt}$ on the width of the analysis interval $K$ in the outlier-free case ($\epsilon=0$).
• Figure 5: Comparison of the mean squared parameter tracking errors for three algorithms operating in the presence of $\alpha$-stable measurement noise: the unmodified LBF algorithm (LBF), adaptive trimmed LBF algorithm (A), and adaptive LAD algorithm.