Counting

In this case, the total number of targets, $n$ , is unknown. For determining $n$ , the lower and upper bounds on each shadow at $t = t_0$ are set as $l_i = 0, u_i = +\infty$ . As new component or FOV events are observed by the robots moving in the environment, the previous procedure is run to keep refining the initial bounds. Once we have $l_i = u_i$ for each initial condition, $n$ has been determined. Note that if the free space is not completely explored, then the upper bound remains at infinity. Another instance of counting is knowing $n$ . For example, in a wild animal preserve, it may be required that the total number of a species is verified periodically. This reduces to the problem of being given $n$ and wanting to account for all of them. To verify the count, we can keep track of the lower bounds on the total number of targets, and if the number agrees with $n$ , then the task has been accomplished.