The key to deriving Eq. (8-6) or (8-7) in Chapter 8 is the creation of nonnested confidence levels for each sensor as was illustrated in Figure 8.3. Nonnested confidence levels allow a unique value to be selected for the inherent sensor detection probability when different signal-to-interference ratios are postulated and implemented at each confidence level. In fact, the ability to specify and then implement unique detection probabilities for each confidence level is one of the considerations that make this voting fusion technique practical.
Alternatively, a Venn diagram such as the one in Figure B.1 with nested confidence levels implies that the detection probabilities at each confidence level are not independent. Here, the confidence levels A1, A2, and A3 of Sensor A, and the confidence levels in the other sensors are not independent of each other. Confidence level A3 is a subset of level A2, which is a subset of level A1. Discriminants other than signal-to-interference ratio are used in this case to differentiate among the confidence levels. For example, target-like features that are present in the signal can be exploited by algorithms to increase the confidence that the signal belongs to a bona fide target. This model is more restrictive and may not depict the way the sensors are actually operating in a particular application.