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.