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On the fluctuations of the ambiguity function in radar and sonar

The ambiguity function is useful for describing the behavior of a radar or a sonar signal. This function was introduced to radar theory by Woodward, it appears to be a good tool to select good signals for the range and Doppler estimation. In this context, the signal of interest is supposed to be a deterministic function corrupted by an additive Gaussian white noise. Extensions to stochastic narrow band signals exist. The object of this paper is not to discuss about each estimator's accuracy, but simply to show the effect of a colored noise and a fluctuating target on the ambiguity function in one hand, and to present a process which will limit their influence. The statistical behavior of the ambiguity function is studied, and we show how the ambiguity function can be separated into two quantities: a deterministic one, and a stochastic one. Then, a process to minimize the stochastic part is proposed. Finally, an application to a moving target localisation is presented.