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: