LMS Adaptive Time Delay Estimation Algorithm

The LMS adaptive time delay estimation algorithm enables precise calculation of time delays in signal processing systems. Specifically, this method utilizes the Least Mean Squares (LMS) algorithm to estimate temporal delays introduced when audio signals propagate through transmission channels. During signal transmission through multiple nodes, signals often experience varying interference patterns and path delays, resulting in dynamic time delay variations. To address this challenge, the LMS algorithm adaptively adjusts filter coefficients to minimize the mean square error between reference and delayed signals, effectively tracking delay changes. The core implementation involves initializing an adaptive FIR filter with adjustable tap weights, computing the error signal between actual and estimated outputs, and iteratively updating weights using the gradient descent method with μ (mu) as the step-size parameter. This approach ensures robust delay estimation for optimized data transmission and processing, particularly in real-time applications where delay compensation is critical for signal synchronization.