Analysis and Design of Sliding m-of-n Detectors
Abstract
Quickest detection of the onset of a signal is a common problem in many applications. For example, consider the detection of a sonar contact as it enters the sonar's detection range. While Page's test is known to optimally provide the lowest average delay before detection (i.e., bar-over-D or detection latency) for a constrained average time between false alarms, it does not necessarily maximize the probability of detecting (Pd) an ephemeral signal (e.g., a sonar contact passing through a convergence zone). In such cases a common alternative is the sliding m-of-n detector where a detection is declared when m successes are observed within n of the most recent trials (e.g., 3 detections during the 5 most recent pings). Techniques for evaluating or approximating the performance measures of the sliding m-of-n detector are developed and used to optimally design the detector. As expected, Page's test outperforms the sliding m-of-n detector with respect to bar-over-D , except under certain cases of significant mismatch between the assumed and actual single-trial success probability. However, for finite-duration signals, the sliding m-of-n detector outperforms Page's test with respect to Pd or robustness in false-alarm rate to mismatch in design assumptions. Unfortunately, optimization requires different (m, n) pairs as a function of signal length. Thus, while Page's test remains the most desirable detector to minimize bar-over-D or if the signal length is unknown, the gains in Pd achievable by a properly designed sliding m-of-n detector make it the best choice for finite-duration signals of known length.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 10, 2011
- Accession Number
- ADA565377
Entities
People
- Douglas A. Abraham