Lagrangian relaxation approaches to closed loop scheduling of track updates

Many modern agile sensor systems are capable of being adaptively tasked in response to an evolving environment. This paper describes an algorithm developed in the framework of previous work by Casta~non, Wintenby and Krishnamurthy. The goal is to schedule the time and dwell time for updates of targets under track using a phased array radar. This problem is addressed using Lagrangian relaxation, decoupling the joint optimisation into a series of single target problems. After discretising the single target decision state (i.e., the covariance matrix), these single target problems are solved as Markov decision processes. An example of a method for selecting the state space discretisation is outlined and the results used to generate a closed loop schedule for a set of track states.