Quantization and Fusion for Multi-Sensor Discrimination from Dependent Observations

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Schemes for quantization and fusion in multi-sensor systems used for discriminating between two sequences of dependent observations are introduced and analyzed. The observation sequences of each sensor under the two hypotheses are arbitrary stationary dependent sequences that can not be modeled as signal in additive noise; the objective of the fusion center is to discriminate between the two hypotheses. These observation models are well motivated by practical multi-sensor target discrimination problems. Two cases are considered: in the first, the observation sequences of the sensors are individually dependent but jointly mutually independent; in the second case, the observation sequences are dependent across both time and sensors. The dependence in the observations across time and/or sensors is modeled by m - dependent, j - mixing or r - mixing processes. The following four quantization/fusion schemes are considered: (a) forming test statistics at the sensors by passing the observations through memoryless nonlinearities, summing them up, and fusing these test statistics without previous quantization; (b) quantizing uniformally (with equidistant breakpoints) each sensor observation and then fusing; (c) quantizing optimally each sensor observation and then fusing; and (d) using the sensor test statistic of (a) to make binary decisions and then fusing the binary decisions. To guarantee high-quality performance, a common large sample size is employed by each sensor and an asymptotic analysis is pursued. Design criteria are developed from the bayesian cost of the fusion center for deriving the optimal memoryless nonlinearities of the sensor test statistics and the sensor quantizer parameters (quantization levels and breakpoints). These design criteria are shown to involve an extension of the generalized signal-to-noise ratio used in single-sensor detection and quantization. The optimal nonlinearities and quantizers are obtained as the solutions of linear coupled or uncoupled integral equations involving the univariate and bivariate probability densities of the sensor observations. Numerical results based on simulation are presented for specific cases of practical interest to compare the relative performance of the four quantization/fusion schemes described above and to establish their superiority to schemes that ignore the dependence across time and/or sensors in the observations.