Looking for the boxes.
I asked a friend who does analysis for various people to look at the problem of how to find the boxes and received the following reply:
For these sorts of searches, the best possible search pattern is to just "mow the lawn." If that's the case then the probability of detection is just the ratio of the area searched to the area to be searched. Generally, though that estimate is excessively optimistic. In practice few searchers actually conform to that plan for a myriad of reasons. Generally what actually happens is that they just randomly churn around places they haven't looked before until finally they find something. Statistically, the worst you can do is just by random chance. Is given by the cumulative exponential distribution.
Pd = 1 - exp(2*R*v*t/A)
where
Pd = the probability of detection
R = is the sensor range
v = the searcher speed
t = search time
A = size of the area to be searched.