Calculation of the Detection Probability for a Statistically Located Target

This paper presents a method of computing the cumulative probability of detection of a statistically located target. The method is completely analytic and is based on a very simple model. The curve which relates the single scan probability of detection to the target-interceptor range is replaced by the function which is 1.0 up to some critical range and 0 thereafter. The critical range is that value which results in equal areas under the two curves. A factor AR is calculated which depends on scan angle, closing velocity and scan time, and which approximates the decrease in effective range due to nonzero scan time and closing velocity. Finally, a cumulative probability of detection is calculated using an assumed target distribution. An "exact" evaluation via a digital computer takes into account the actual single scan detection probability (as a function of range), the effect of multiple scans, flyback time, scan time variation with angle, and closing velocity as well as the target distribution. A comparison of the results obtained by the two methods show the simple analytical model to be sufficiently accurate for all but the most exacting analyses.