Optimal Sequential Detection of Signals with Unknown Appearance and
Disappearance Points in Time
- URL: http://arxiv.org/abs/2102.01310v1
- Date: Tue, 2 Feb 2021 04:58:57 GMT
- Title: Optimal Sequential Detection of Signals with Unknown Appearance and
Disappearance Points in Time
- Authors: Alexander G. Tartakovsky, Nikita R. Berenkov, Alexei E. Kolessa, and
Igor V. Nikiforov
- Abstract summary: The paper addresses a sequential changepoint detection problem, assuming that the duration of change may be finite and unknown.
We focus on a reliable maximin change detection criterion of maximizing the minimal probability of detection in a given time (or space) window.
The FMA algorithm is applied to detecting faint streaks of satellites in optical images.
- Score: 64.26593350748401
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The paper addresses a sequential changepoint detection problem, assuming that
the duration of change may be finite and unknown. This problem is of importance
for many applications, e.g., for signal and image processing where signals
appear and disappear at unknown points in time or space. In contrast to the
conventional optimality criterion in quickest change detection that requires
minimization of the expected delay to detection for a given average run length
to a false alarm, we focus on a reliable maximin change detection criterion of
maximizing the minimal probability of detection in a given time (or space)
window for a given local maximal probability of false alarm in the prescribed
window. We show that the optimal detection procedure is a modified CUSUM
procedure. We then compare operating characteristics of this optimal procedure
with popular in engineering the Finite Moving Average (FMA) detection algorithm
and the ordinary CUSUM procedure using Monte Carlo simulations, which show that
typically the later algorithms have almost the same performance as the optimal
one. At the same time, the FMA procedure has a substantial advantage --
independence to the intensity of the signal, which is usually unknown. Finally,
the FMA algorithm is applied to detecting faint streaks of satellites in
optical images.
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