Optimal pinging frequencies in the search for an immobile beacon

Abstract

ABSTRACT We consider a search for an immobile object that can only be detected if the searcher is within a given range of the object during one of a finite number of instantaneous detection opportunities; i.e., “pings.” More specifically, motivated by naval searches for battery-powered flight data recorders of missing aircraft, we consider the trade-off between the frequency of pings for an underwater locator beacon and the duration of the search. First, assuming that the search speed is known, we formulate a mathematical model to determine the pinging period that maximizes the probability that the searcher detects the beacon before it stops pinging. Next, we consider generalizations to discrete search speed distributions under a uniform beacon location distribution. Lastly, we present a case study based on the search for Malaysia Airlines Flight 370 that suggests that the industry-standard beacon pinging period—roughly 1 second between pings—is too short.