Source Detection and Localization Using a Multi-Mode Detector A Bayesian Approach

This paper considers a class of detection/localization problems in which the detector offers multiple operating modes. The modes differ in their detection performance and geographical coverage: "focused " modes offer higher detection performance

SOURCE DETECTION AND LOCALIZATION USING A MULTI-MODE DETECTOR: A BAYESIAN APPROACH Douglas Cochran, Dana Sinno, and Axel Clausen Arizona State University, Tempe, AZ 85287-7206, U.S.A. This paper considers a class of detection/localization problems in which the detector o ers multiple operating modes. The modes di er in their detection performance and geographical coverage:\focused" modes o er higher detection performance but less coverage area than\broad search" modes. It is assumed that a signal source is to be detected and localized using a sequence of tests, each possibly employing a di erent mode. The goal is to determine a strategy for mode selection in the sequence of tests that will yield optimal payo in terms of a pre-established criterion. A mathematical model capturing the key characteristics of this situation is proposed and used to develop optimal mode selection strategies.

ABSTRACT

moment, the pilot can test the entire area of interest with the long-range radar with the expense of either low probability of detection or many false alarms; alternatively a small sub-region can be examined with higher probability of detection and lower false alarm rate, but limited time on station generally prevents the entire region from being searched in this mode. The ideas formulated in this paper generalize to detectors having more than two modes in a straightforward way{ provided, of course, that the modes are satisfactorily modeled as described in the following sections.

2. MATHEMATICAL FORMULATION A useful mathematical description of the situation introduced in the previous section must account for differences in the detector's operating modes, both in detection performance and geographical coverage. In the case of only two operating modes, as in the motivating application, an idealized model for the geographical coverage is obtained by considering the entire region of interest S to be partitioned into N disjoint\cells" C1;:::; CN . Operating in the broad search mode (Mode A), the detector tests for the presence of a signal source in S . In the focused mode (Mode B), however, the test may be applied to exactly one cell Cn . To account for di erence in detector performance in the two operating modes, detector performance is modeled as arising from the problem of detecting of a known signal in white gaussian noise of known variance. This model provides a well understood solution (i.e., the matched lter) in each test, admits several straightforward generalizations, and allows detection performance in Mode B to be distinguished from that in Mode A by simply raising the signal-to-noise ratio (SNR). More speci cally, in each mode of operation the detector encounters a problem of the form H0: X= N (1) H1: X= S+ N (2) where S is a known signal M -vector with energy jjS jj2= 1 and N is a zero-mean white gaussian M -vector hav-

1. INTRODUCTION Recent advances in microprocessor and other technologies have greatly enhanced the capabilities an

d practicality of tunable, deployable, and con gurable sensors in a wide variety of applications. Building upon pioneering work that considered optimal measurement map selection in estimating the state of certain classes of stochastic dynamical systems 1, 2, 7], research explicitly addressing the development of strategies to effectively control the con guration of a sensor system in order to estimate parameters of the process being measured has begun to emerge over the past few years 4, 5, 9, 10]. This paper considers a situation in which a detector is con gurable in such a way as to provide multiple modes of operation that di er in their detection performance and geographical coverage. The development that follows focuses on the case of a detector with two operating modes: a\broad search" mode that provides wide coverage and a\focused" mode that provides better detection performance but covers less area. This is indeed the case in the actual application that motivated this research, in which an aircraft is to search for a target using long-range and short-range radar systems that cannot be operated simultaneously. At any given

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