Calculation of Radar Probability of Detection in K-Distributed Sea Clutter and Noise

Abstract : The detection performance of maritime radars is usually limited by sea clutter. The K-distribution is a well established statistical model of sea clutter which is widely used in performance calculations. There is no closed form solution for the probability of detection in K-distributed clutter, so numerical methods are required. The K-distribution is a compound model which consists of Gaussian speckle modulated by a slowly varying mean level, this local mean being gamma distributed. A series solution for the probability of detection in Gaussian noise is integrated over the gamma distribution for the local clutter power. Gauss-Laguerre quadrature is used for the integration, with the nodes and weights calculated using matrix methods, so that a general purpose numerical integration routine is not required. The method is implemented in Matlab and compared with an approximate solution based on lookup tables. The solution described here is slower, but more accurate and more flexible in that it allows for a wider range of target fluctuation models.