Searching with Measurement Dependent Noise

TL;DR

This paper analyzes the problem of searching for a moving target on a circle with measurement noise that depends on the size of the probed region, characterizing optimal search strategies and tradeoffs.

Contribution

It introduces a framework for search with measurement-dependent noise, deriving optimal tradeoffs and demonstrating the benefits of adaptive strategies over non-adaptive ones.

Findings

Adaptive search achieves the optimal rate-reliability tradeoff.

Measurement-dependent noise causes a multiplicative gap between adaptive and non-adaptive search.

Unknown target velocity doubles the rate penalty in non-adaptive search.

Abstract

Consider a target moving with a constant velocity on a unit-circumference circle, starting from an arbitrary location. To acquire the target, any region of the circle can be probed for its presence, but the associated measurement noise increases with the size of the probed region. We are interested in the expected time required to find the target to within some given resolution and error probability. For a known velocity, we characterize the optimal tradeoff between time and resolution (i.e., maximal rate), and show that in contrast to the case of constant measurement noise, measurement dependent noise incurs a multiplicative gap between adaptive search and non-adaptive search. Moreover, our adaptive scheme attains the optimal rate-reliability tradeoff. We further show that for optimal non-adaptive search, accounting for an unknown velocity incurs a factor of two in rate.