A signal depending on two a priori unknown parameters is considered. Estimation of one of the parameters from statistics that are invariant to changes of the other parameter is considered. The problem of determination of such statistics is solved. The proposed approach is illustrated by considering the radar problem of estimating the arrival time for a chirp signal when the Doppler frequency shift is a nuisance parameter. It is shown that, upon suppression of the Fisher information on the Doppler shift, the ridge of the ambiguity function in the space of invariant descriptors becomes strictly perpendicular to the time axis.
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