# Naval Operations Analysis, Additional Problems for Chapter 5

1. An aircraft flies directly toward an air-search radar at 600 knots.  The radar glimpses the aircraft once per minute.  The radar’s capability to detect the aircraft is modeled by: (1) a time process representing mean signal, (2) a (l, s) process representing deviation from the mean signal, and (3) a level that the signal excess must exceed for detection to occur.  Suppose λ= 10 jumps per hour, σ = 5 dB, and the signal excess must exceed 0.0 dB for detection to occur.

a.       Suppose the mean signal at range 150 nm is determined to be –2.0 dB.  Find the single glimpse detection probability for this range.

b.      Suppose that it has been determined that single-glimpse detection probabilities for various ranges are as follows.

 range (nm) 100 110 120 130 140 150 single-glimpse detection probability 0.9 0.8 0.65 0.45 0.15 0

What is the probability that the aircraft will be detected at a range of 120 nm or greater?  Do NOT assume independence.

2. A submarine passes a line of 5 sonobuoys in such a way that the probability of detection by each of the sonobuoys is 0.1, 0.3, 0.6, 0.4, and 0.2, respectively.  What is the probability that the submarine will be detected by at least one of the sonobuoys?  Assume independence of the sonobuoys’ detection.