On statistical properties of the detection range of a moving target

The detection range of a moving target at which an approaching target is first detected by a radar according to some criterion is analyzed. Because of the effect of random factors (noise, fluctuations of the target’s echo signal, etc.), the detection range of a moving target is a random quantity. The probability density function of the detection range is calculated. It is shown that the most probable value of the detection range of a moving target may differ substantially from the traditional maximum detection range with specified probabilities of correct detection and false alarms. It is found that the detection range of a moving target depends substantially of the target velocity and its statistical spread is rather large as compared to the mean value of this range.