Estimation of Ambiguity Functions With Limited Spread

Abstract

This paper proposes a new estimation procedure for the ambiguity function of a non-stationary time series. The stochastic properties of the empirical ambiguity function calculated from a single sample in time are derived. Different thresholding procedures are introduced for the estimation of the ambiguity function. Such estimation methods are suitable if the ambiguity function is only non-negligible in a limited region of the ambiguity plane. The thresholds of the procedures are formally derived for each point in the plane, and methods for the estimation of nuisance parameters that the thresholds depend on are proposed. The estimation method is tested on several signals, and reductions in mean square error when estimating the ambiguity function by factors of over a hundred are obtained. An estimator of the spread of the ambiguity function is proposed.