Passive Acoustic Detection Model
A detection by a single sensor (e.g. hull sonar) occurs when the signal excess, SE, is greater than or equal to zero.
SE is periodically computed until a detection occurs. The sampling rate is set to the integration time of the acoustic processor.
Probability that an acoustic sensor detects a target, p , is the probability that a normal random variable with mean, , and standard deviation, ?, is greater than zero.
where ?(?) is the Cumulative Normal Distribution Function.
The probability that a sonobuoy pattern detects a target is the average of detection probability when sonobuoy detections are assumed independent and the probability when sonobuoy detections are assumed to be dependent.
where pk is the detection probability of the kth sonobuoy