Auto Regulated Recursive Non-Quadratic Algorithm.

The problem of non-stationary signals constitutes one of the most serious challenges in the context of adaptive filters, since it simultaneously demands high convergence speed, good tracking capability, and stability. However, several algorithms are developed based mainly on second-order statistics in strongly non-stationary scenarios or those subject to non-Gaussian perturbations. The temporal variability of the signal's statistical properties imposes the need for statistical detection and monitoring mechanisms for abrupt variations in the input signal, increasing the computational complexity of the algorithms. In this context, unlike basic adaptive filtering methods and approaches such as the Kalman filter algorithm, which presuppose second-order statistics, we present the Self-Regulated Non-Quadratic Recursive (RNQA) algorithm, using as a performance surface a sum of weighted even-power error functions and the dynamic adjustment of the correlation matrix normalized by the square of the error, which acts as a mechanism for continuous adaptation of the matrix, capable of responding effectively in non-stationary environments. In a system identification configuration, RNQA showed superior convergence to classical adaptive algorithms such as RNQ and the recursive Kalman filter.