Information theoretic sensor management

Abstract

Sensor management may be defined as those stochastic control problems in which control values are selected to influence sensing parameters in order to maximize the utility of the resulting measurements for an underlying detection or estimation problem. While problems of this type can be formulated as a dynamic program, the state space of the program is in general infinite, and traditional solution techniques are inapplicable. Despite this fact, many authors have applied simple heuristics such as greedy or myopic controllers with great success. This thesis studies sensor management problems in which information theoretic quantities such as entropy are utilized to measure detection or estimation performance. The work has two emphases: Firstly, we seek performance bounds which guarantee performance of the greedy heuristic and derivatives thereof in certain classes of problems. Secondly, we seek to extend these basic heuristic controllers to nd algorithms that provide improved performance and are applicable in larger classes of problems for which the performance bounds do not apply. The primary problem of interest is multiple object tracking and identification; application areas include sensor network management and multifunction radar control.

(cont.) Utilizing the property of submodularity, as proposed for related problems by different authors, we show that the greedy heuristic applied to sequential selection problems with information theoretic objectives is guaranteed to achieve at least half of the optimal reward. Tighter guarantees are obtained for diffusive problems and for problems involving discounted rewards. Online computable guarantees also provide tighter bounds in specific problems. The basic result applies to open loop selections, where all decisions are made before any observation values are received; we also show that the closed loop greedy heuristic, which utilizes observations received in the interim in its subsequent decisions, possesses the same guarantee relative to the open loop optimal, and that no such guarantee exists relative to the optimal closed loop performance. The same mathematical property is utilized to obtain an algorithm that exploits the structure of selection problems involving multiple independent objects. The algorithm involves a sequence of integer programs which provide progressively tighter upper bounds to the true optimal reward. An auxiliary problem provides progressively tighter lower bounds, which can be used to terminate when a near-optimal solution has been found.

(cont.) The formulation involves an abstract resource consumption model, which allows observations that expend different amounts of available time. Finally, we present a heuristic approximation for an object tracking problem in a sensor network, which permits a direct trade-o between estimation performance and energy consumption. We approach the trade-o through a constrained optimization framework, seeking to either optimize estimation performance over a rolling horizon subject to a constraint on energy consumption, or to optimize energy consumption subject to a constraint on estimation performance. Lagrangian relaxation is used alongside a series of heuristic approximations to and a tractable solution that captures the essential structure in the problem.