A stochastic total least squares solution of adaptive filtering problem.

Area of Science:

• Signal Processing
• Adaptive Filtering
• Numerical Analysis

Background:

• Adaptive filtering is crucial for signal processing applications.
• Existing methods like LMS and NLMS struggle with noise in both input and output signals.
• Total Least Squares (TLS) offers a more robust solution when both signal sets are noisy.

Purpose of the Study:

• To develop an efficient and computationally linear algorithm for the total least squares solution of adaptive filtering problems.
• To introduce a novel algorithm, Total Least Mean Squares (TLMS), for adaptive filtering under dual noise conditions.
• To analyze the convergence properties and performance of the proposed TLMS algorithm.

Main Methods:

• Derivation of a computationally linear algorithm for adaptive total least squares.
• Recursive computation of an optimal solution by minimizing a weighted cost function.
• Convergence analysis to demonstrate global convergence under specific parameter choices.

Main Results:

• The proposed TLMS algorithm is computationally simpler than existing TLS algorithms.
• TLMS demonstrates superior performance compared to Least Mean Squares (LMS) and Normalized Least Mean Squares (NLMS) algorithms.
• The algorithm achieves minimum mean square deviation and better convergence in misalignment for system identification.

Conclusions:

• The TLMS algorithm provides an efficient and effective solution for adaptive filtering problems with noisy input and output signals.
• The algorithm exhibits improved performance and convergence characteristics over traditional methods.
• TLMS is a valuable tool for unknown system identification in the presence of significant noise.