Dynamic Filter Length Reduction in NLMS for System Identification

Adaptive filtering techniques are fundamental in system identification, enabling the estimation and modeling of unknown systems from observed input-output data. Among these methods, the Normalized Least Mean Squares (NLMS) algorithm holds paramount importance due to its versatility and widespread application in real-time adaptive signal processing. In system identification, NLMS algorithms serve as robust tools for approximating unknown systems by continuously adjusting the impulse response of adaptive filters based on incoming data. Conventional implementations of the NLMS algorithm assume a fixed filter length, creating challenges in scenarios where the length of the filter to be identified is unknown, thus hindering accurate system modeling, often leading to "overmodeling" and ineffective use of computational resources. This paper introduces an adaptation in the NLMS algorithm to dynamically modify the length of the adaptive filter, enhancing its computational resource efficiency. The proposed methodology addresses the challenge of accurately approximating unknown filters while decreasing the computational complexity. Simulation results demonstrate the efficacy of the proposed adaptive length modification technique, showcasing reduced computational overhead compared to traditional fixed-length NLMS methods, while still obtaining good misalignment values.