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.