  Gradient-descent based iterative algorithms pervade a variety of problems in
estimation, prediction, learning, control, and optimization. Recently iterative
algorithms based on higher-order information have been explored in an attempt
to lead to accelerated learning. In this paper, we explore a specific a
high-order tuner that has been shown to result in stability with time-varying
regressors in linearly parametrized systems, and accelerated convergence with
constant regressors. We show that this tuner continues to provide bounded
parameter estimates even if the gradients are corrupted by noise. Additionally,
we also show that the parameter estimates converge exponentially to a compact
set whose size is dependent on noise statistics. As the HT algorithms can be
applied to a wide range of problems in estimation, filtering, control, and
machine learning, the result obtained in this paper represents an important
extension to the topic of real-time and fast decision making.
