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 Q(t) of the target's true location Q(t) at time t, where ‖Q(t) - Q(t)‖ represents the sensor's localization error. We study the limits of tracking performance under this kind of sensing imprecision. In particular, (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 prove upper and lower bounds for the worst-case tracking performance, both with or without obstacles. We also provide simulation results on real and synthetic data to illustrate trackability under imprecise localization.
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