Sensor selection and placement in adversarial environment

We study the problem of sensor placement, when the set of sensors are interrogated sequentially to detect a target employing evading actions. We model the sensor management problem as a two stage game between the observer and the target: in the first stage sensor locations are chosen by the observer, in the second stage the observer and the target choose open-loop control strategies to optimize error exponent for the probability of mis-detection with opposing interests. Therefore the observer chooses the sensor locations to optimize the value function of the game played in the second stage. We propose a computationally efficient gradient descent method to iteratively refine the sensor locations for maximizing the value function using the envelope theorem.