  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.
