A fast algorithm for AR parameter estimation using a novel noise-constrained least-squares method.

Area of Science:

• Signal Processing
• Statistical Signal Processing
• Machine Learning

Background:

• Online autoregressive (AR) parameter estimation is crucial for time-series analysis.
• Blind Gaussian noise environments pose challenges for traditional estimation methods.
• Existing methods like least-squares (LS) and generalized least absolute deviation (GLAD) have limitations in accuracy and computational efficiency.

Purpose of the Study:

• To develop a novel noise-constrained least-squares (NCLS) method for online AR parameter estimation.
• To propose a discrete-time learning algorithm with fixed step length for robust estimation.
• To evaluate the performance of the proposed algorithm against conventional methods.

Main Methods:

• Development of a noise-constrained least-squares (NCLS) cost function.
• Design of a discrete-time learning algorithm with a fixed step length.
• Minimization of a quadratic convex function for online estimation.

Main Results:

• The proposed learning algorithm achieves global convergence to an optimal autoregressive (AR) estimate.
• The NCLS method yields robust estimates with a smaller mean-square error (MSE) compared to conventional LS and higher-order statistical methods.
• The algorithm demonstrates faster convergence and higher accuracy than GLAD-based methods.

Conclusions:

• The developed NCLS method and its associated learning algorithm provide a robust and efficient solution for online AR parameter estimation in blind Gaussian noise.
• The algorithm's ability to minimize a quadratic convex function makes it well-suited for real-time applications.
• Simulation results validate the superior performance in terms of accuracy and convergence speed.