Resolution Limits of 20 Questions Search Strategies for Moving Targets

TL;DR

This paper investigates the fundamental limits of tracking a moving target using 20 questions strategies with noisy, query-dependent measurements, providing asymptotic bounds on the minimal achievable resolution.

Contribution

It introduces a framework for analyzing the resolution limits of non-adaptive search strategies for moving targets under measurement-dependent noise.

Findings

Derived second-order asymptotic bounds on minimal resolution

Established fundamental limits for non-adaptive search procedures

Analyzed the impact of measurement-dependent noise on search performance

Abstract

We establish fundamental limits of tracking a moving target over the unit cube under the framework of 20 questions with measurement-dependent noise. In this problem, there is an oracle who knows the instantaneous location of a target. Our task is to query the oracle as few times as possible to accurately estimate the trajectory of the moving target, whose initial location and velocity is \emph{unknown}. We study the case where the oracle's answer to each query is corrupted by random noise with query-dependent discrete distribution. In our formulation, the performance criterion is the resolution, which is defined as the maximal absolute value between the true location and estimated location at each discrete time during the searching process. We are interested in the minimal resolution of any non-adaptive searching procedure with a finite number of queries and derive approximations to this optimal resolution via the second-order asymptotic analysis.