Radar detection probabilities and their calculation

Most radar targets are complex objects and produce a wide variety of reflections. Different targets often require different models to characterize the varied statistical nature of these responses. Several commonly used statistical models and extensions to them are considered here along with techniques for reliably calculating the resulting probabilities of detection. Marcum (1960) and Swerling (1960, 1965, 1970) have provided us with expressions for constant and some fluctuating targets, respectively. Expressions for the probability of detection for cell-averaging constant false alarm rate (CFAR) have been given by Mitchell and Walker (1971), but only for clutter cells whose input to the receiver was assumed to be zero mean Gaussian clutter. These CFAR results have been generalized here for non-zero mean clutter. We have replaced the chi-square distribution for clutter with a noncentral chi-square distribution allowing for a non-zero mean. Other fluctuation models, such as log-normal, Weibull, and Ricean models, are considered for both target and clutter fluctuations. Methods for false alarm calculations are also given. Reliable algorithms for the computations of these detection probabilities are determined for the various models. Though reliability is primary, efficiency, generality and accuracy are also issues of concern