Measure-Transformed Recursive Least Squares

This paper deals with robust system identification in the presence of impulsive noise. To this end, we present a new robust variant of the recursive-least-squares (RLS) estimator, called measure-transformed (MT)-RLS. The MT-RLS is an exact recursive counterpart to the recently developed MT least-squares estimator (MT-LSE), which operates by applying a transform to the probability measure of the data. This stands in contrast to other robust RLS variants that only approximate robust batch estimators. The considered measure transform is generated by a non-negative data-weighting function, called the MT-function. We have previously shown that a properly chosen MT-function can significantly mitigate the influence of outliers arising from impulsive noise, thereby substantially enhancing the estimation accuracy of the MT-LSE. Consequently, as an exact recursive extension, the MT-RLS fully inherits the robustness of MT-LSE. The MT-RLS is illustrated in simulations, underscoring its advantage over RLS and other robust extensions in both stationary and non-stationary environments.