Distributed Detection System Design Local sensors Fusion center D ata Local sensor i fu center Consider binary quantizers at the local sensors Requires the design of local detectors and the fusion rule jointly according to some optimization criterion NP-hard in general
Local Sensors Fusion Center Data fusion center u1 u2 uN ... Local Sensor i u0 yi ui • Consider binary quantizers at the local sensors. • Requires the design of local detectors and the fusion rule jointly according to some optimization criterion. • NP-hard, in general
Design of Decision Rules The crux of the distributed hypothesis testing problem is to derive decision rules of the form if detector i decides Ho Local decision rule can be defined 11 by the conditional probabilit if detector i decides H distribution function Plu l/v and at the fusion center: uo if ho is decided otherwise Fusion rule at the FC: logical function with n binary inputs and one binary output Number of fusion rules: 22
Design of Decision Rules The crux of the distributed hypothesis testing problem is to derive decision rules of the form and at the fusion center: u0 u0 = 0, if H0 is decided 1, otherwise 0, if detector i decides H0 1, if detector i decides H1 ui = Fusion rule at the FC: logical function with N binary inputs and one binary output Number of fusion rules: 22 N Local decision rule can be defined by the conditional probability distribution function P(ui=1|yi )
Possible Fusion rules for Two binary Input utput l4112 Iff2 4 fs fo f7 8j9j10j11J12j13J14J15 00 000000001111 11 010000111 1000 o11 100011001100110011 0101010101010101
Possible Fusion Rules for Two Binary Input Output u0 u 1 u 2 f 1 f 2 f 3 f 4 f 5 f 6 f 7 f 8 f 9 f 10 f 11 f 12 f 13 f 14 f 15 f 16 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 0 1 0 0 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 0 0 1 1 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
Decision criteria In the binary hypothesis testing problem, we know that either Ho or H, is true. Each time the experiment is conducted, one of the following can hal ppen 1. Ho true; choose Ho correct 2. Ho true choose H1 errol 3. Hi true choose Hi+correct 4. HI true; choose Ho errol
In the binary hypothesis testing problem, we know that either H0 or H1 is true. Each time the experiment is conducted, one of the following can happen:
Types of Errors in Detection Decide Decide Ho present T rue nu False alarm noise H I present ISS Detection (Signal+noise) MI-D
Decide H0 Decide H1 H0 present (noise) True Null PR=1-PF False alarm PF H1 present (signal+noise) Miss PM=1-PD Detection PD