LMS-Based Time Delay Estimation Algorithm (LMSTDE)

In this article, we provide a detailed explanation of the LMS-based Time Delay Estimation algorithm (LMSTDE). The LMSTDE algorithm employs an adaptive filtering approach, typically using the LMS criterion to minimize the mean square error between reference and delayed signals. This method is commonly applied for estimating network latency and is frequently utilized in network congestion control mechanisms. The core implementation involves iterative weight updates using the formula: w(n+1) = w(n) + μ·e(n)·x(n), where μ represents the step size, e(n) denotes the error signal, and x(n) is the input vector. However, our analysis reveals that the standard LMSTDE algorithm exhibits certain limitations, particularly in convergence speed and stability under dynamic network conditions. To address these issues, we have developed an enhanced version—the ETDE (Enhanced Time Delay Estimation) algorithm. This improved algorithm incorporates modified adaptation mechanisms and better error correction features, overcoming the drawbacks of LMSTDE while delivering superior performance in terms of estimation accuracy and computational efficiency. The ETDE implementation includes optimized step-size control and enhanced tracking capabilities for time-varying delays. We will upload the complete ETDE algorithm implementation, including MATLAB/Python code samples and performance comparisons, at a later time for community use and reference.