Trackability with Imprecise Localization
This addresses fundamental limits in robotics and surveillance for scenarios with noisy sensors, though it appears incremental in extending tracking theory.
The paper tackles the problem of tracking a moving target with imprecise localization, deriving worst-case bounds on tracking performance under relative error noise and obstacles.
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.