The overall question is the following:
Which actions have to perform the sensing agents to find the lost target?
Without taking into account the time, we can simplify the question to:
Which actions have to perform the sensing agents to maximize the probability of detecting the target?
Or its inverse question:
Which actions have to perform the sensing agents to minimize the probability of non-detecting the target?
From the probabilistic reasoning point of view, this question is formally defined as:
The problem as a joint probability distribution is then stated as:
The question depends on the estimation of the target location , the sensing platform states and the sensor model
1. Assuming no uncertainty within the agents movements that is it exist a deterministic function that makes agent go from state by applying the action to state unequivocally, we can avoid the using of .
2. Assuming that the sensing platforms while they are searching, the measurements obtained by the sensors are always not detection
3. Assuming that the platforms counts with a prior information of the possible location of the target .
4. Assuming that the observations made by the agents are independent (i.e. only depends on the phenomenon and not on the rest of the sensors)
The final question is the following: