A Newton-Raphson solution to the exponentially weighted least M-estimate formulation for acoustic system identification

The formulation of the exponentially weighted least M-estimate has shown significant promise in addressing acoustic system identification amidst non-Gaussian noise. A common approach to this formulation is the recursive least M-estimate algorithm. However, due to its derivation from nonlinear normal equations, resulting in a slow approximate solution, this algorithm tends to exhibit poor convergence performance. In this paper, we present a Newton-Raphson solution, where the cost function is expanded using the second-order Taylor series to establish the adaptive algorithm. This approach bypasses the nonlinear normal equations, yielding a robust solution that more dynamically reflects changes in the cost function, ultimately leading to improved convergence and tracking performance.