A Neural Approach to the Underdetermined-Order Recursive Least-Squares Adaptive Filtering

Area of Science:

• Signal Processing
• Machine Learning
• Adaptive Filtering

Background:

• Adaptive filtering is crucial in many signal processing applications.
• Traditional algorithms like Normalized Least Mean Square and Recursive Least Squares have limitations.
• Digital implementations can suffer from error propagation and ill-conditioned matrix inversions.

Purpose of the Study:

• To reformulate the Underdetermined-Order Recursive Least-Squares (URLS) algorithm using a neural architecture.
• To explore the advantages of a neural network approach for adaptive filtering.
• To compare the performance and characteristics of the neural network with the algorithmic URLS approach.

Main Methods:

• Development of a neural network architecture to implement the URLS algorithm.
• Analysis of the neural network's response compared to the established URLS algorithm.
• Evaluation of numerical properties, circuit realization, and flexibility for prediction order alteration.

Main Results:

• The neural network's response was found to be identical to the algorithmic URLS approach.
• The neural network avoids drawbacks of digital computation, such as error propagation and ill-conditioned matrix inversion.
• The neural network offers simpler circuit realization and flexible alteration of the prediction order.

Conclusions:

• Neural network reformulation of the URLS algorithm is a viable and advantageous alternative to digital implementations.
• This approach simplifies circuit design and enhances numerical stability in adaptive filtering.
• The neural network provides flexibility in prediction order, crucial for various applications, and integrates easily into digital systems.