A simple and robust sequential detector commonly used in remote sensing applications declares a signal is present the first time M successes are observed in any N consecutive measurements. In scenarios where N is fixed by stationarity restrictions, the sliding M-of-N detector is designed by varying M. This provides coarse control of the false alarm rate (FAR), which decreases as M is increased from one to N. In this report, the value of M is randomized to allow precise control of the FAR, which can reduce the average delay before detection (i.e., latency) compared to using the smallest fixed value of M that meets or exceeds the FAR specification. The cost of using a randomized sliding M-of-N detector is an increase in the standard deviation of the number of measurements required to make a decision relative to its mean. Approximations to the detection performance measures for standard sliding M-of-N detectors are reviewed and employed to design and analyze the randomized sliding M-of-N detector. Precise control of the false alarm performance is then exploited to compare approaches for controlling FAR in a two-stage detection algorithm when the first-stage background is dominated by false-alarm-inducing clutter and the second stage employs a sliding M-of-N detector. Throttling the first stage to maintain a constant single-measurement probability of false alarm was seen to have a minor advantage in detection latency at very high signal-to-noise power ratio (SNR), compared with passing the clutter-induced false alarms to a randomized sliding M-of-N detector in the second stage. At moderate SNR with heavy clutter or at low SNR, however, throttling reduces the single-measurement probability of detection to the point where there is a significant increase in latency relative to using the randomized sliding M-of-N detector to control FAR. This analysis supports the commonly encountered engineering design approach where the first-stage single-measurement detector is run "hot" and the second-stage multiple-measurement detector cleans up the excessive false alarms, while providing a means for precise control of the FAR and adding the nuance of the high-SNR result.

Acknowledgments

This report was sponsored by the Office of Naval Research, Code 32, Undersea Signal Processing, through Naval Sea Systems Command contract N00024-21-D-6400 under task orders N00024-22-F- 8714 and N00024-25-F-8703.