Trackability with Imprecise Localization

TL;DR

This paper investigates the fundamental limits of tracking a moving target in Euclidean space using noisy localization sensors, providing bounds on tracking performance under various conditions including obstacles and error models.

Contribution

It introduces a framework for analyzing tracking performance with imprecise localization, deriving bounds and strategies in worst-case scenarios.

Findings

Established upper and lower bounds for tracking accuracy under noise.

Analyzed the impact of obstacles on tracking performance.

Provided strategies for maintaining target proximity with noisy sensors.

Abstract

Imagine a tracking agent $P$ who wants to follow a moving target $Q$ in $d$-dimensional Euclidean space. The tracker has access to a noisy location sensor that reports an estimate $\tilde{Q}(t)$ of the target's true location $Q(t)$ at time $t$, where $||Q(T) - \tilde{Q}(T)||$ represents the sensor's localization error. We study the limits of tracking performance under this kind of sensing imprecision. In particular, we investigate (1) what is $P$'s best strategy to follow $Q$ if both $P$ and $Q$ can move with equal speed, (2) at what rate does the distance $||Q(t) - P(t)||$ grow under worst-case localization noise, (3) if $P$ wants to keep $Q$ within a prescribed distance $L$, how much faster does it need to move, and (4) what is the effect of obstacles on the tracking performance, etc. Under a relative error model of noise, we are able to give upper and lower bounds for the worst-case tracking performance, both with or without obstacles.