In this chapter Bayes decision rules are developed for optimizing the detection of multiple targets. We show that the strategy consists of an independent threshold test at each expected time of arrival for all targets in the radar field of view. This separable test strategy is shown to be optimum for the limiting cases of large and small signal-to-noise ratios; however, a different threshold level is required, in general, for large signal detection and for small signal detection. The separable test strategy is compared to the averaging solution, which is obtained from a Bayes strategy with cost assignments that are independent of parameters. The averaging approach is shown to be unsuitable for most radars when echo arrival times are unknown.

Chapter Contents:

• 17.1 Introduction
• 17.2 Approach to the Problem
• 17.3 Detection of Two Known Targets
• 17.4 Interpretation of Two-Target Detection Strategy for Small Signal-to-Noise Ratios
• 17.5 Interpretation of Two-Target Detection Strategy for Large Signal-to-Noise Ratios
• 17.6 Bayes Strategy for N Exactly Known Signals
• 17.7 Bayes Detection Strategy for N Targets with Unknown Times of Arrival
• 17.8 Existence of a Single Target with Unknown Times of Arrival
• 17.9 Approximation of Bayes Receiver
• 17.10 Extension of Bayes Receiver to Angle and Doppler
• 17.11 Difficulties with the Theory
• Problems
• References

Inspec keywords: echo; Bayes methods; time-of-arrival estimation; radar detection

Other keywords: independent threshold test; Bayes strategy; signal-to-noise ratio; signal detection; Bayes decision rules; threshold level; echo arrival times; radar detection; multiple-target detection; separable test strategy; cost assignments

Subjects: Signal detection; Radar theory; Other topics in statistics