Analytical calculation for probability of detection given time dependent search parameters

Melvin H. Friedman, Joseph Reynolds, David Wilson, Ronald Driggers

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations


The problem solved in this paper is easily stated: given search parameters (P, τ) that are known functions of time, calculate how the probability a single observer acquires a target grows with time. This problem has been solved analytically. In this paper we describe the analytical solution and provide derivations of the results. Comparison with perception experiments will be reported in a future publication and hopefully will support the results presented here. The provided solution is applicable to any scenario where the search parameters are changing with time and are specified. In particular, the solution can be used to estimate the probability of target acquisition as a function of time: (1) when the sensor-target range is changing, (2) for a slewed sensor where the target is alternately in and out of the field of view, and (3) for a sensor that switches between wide and narrow fields of view.

Original languageEnglish (US)
Title of host publicationInfrared Imaging Systems
Subtitle of host publicationDesign, Analysis, Modeling, and Testing XXII
StatePublished - 2011
Externally publishedYes
EventInfrared Imaging Systems: Design, Analysis, Modeling, and Testing XXII - Orlando, FL, United States
Duration: Apr 26 2011Apr 28 2011

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X


ConferenceInfrared Imaging Systems: Design, Analysis, Modeling, and Testing XXII
Country/TerritoryUnited States
CityOrlando, FL


  • Detection
  • Moving sensor
  • Moving target
  • Search
  • Search parameters
  • Time dependent

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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