  Consider a target moving at a constant velocity on a unit-circumference
circle, starting at an arbitrary location. To acquire the target, any region of
the circle can be probed to obtain a noisy measurement of the target's
presence, where the noise level increases with the size of the probed region.
We are interested in the expected time required to find the target to within
some given resolution and error probability. For a known velocity, we
characterize the optimal tradeoff between time and resolution, and show that in
contrast to the well studied case of constant measurement noise, measurement
dependent noise incurs a multiplicative gap in the targeting rate between
adaptive and non-adaptive search strategies. Moreover, our adaptive strategy
attains the optimal rate-reliability tradeoff. We further show that for optimal
non-adaptive search, accounting for an unknown velocity incurs a factor of at
least two in the targeting rate.
