Thresholding the ambiguity function

In this paper we propose a new method for estimating the ambiguity function (AF) of a random process with limited spreading support. The observed process is modelled as the aggregation of a non-stationary signal of interest and noise. As the AF has limited spreading, thresholding is a suitable estimation procedure. Some key stochastic properties of the empirical ambiguity function are derived to obtain a suitable threshold. Based on a median absolute deviation estimator for the variance, we derive a suitable threshold, which forms the basis for our proposed estimator. The estimator is tested on both artificial and real signals, and our results demonstrate a remarkably high resolution and reduced variance.