Institute for Systems Research
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Item Multi-Sensor Correlation and Quantization in Distributed Detection Systems(1991) Chau, Yawgeng A.; Geraniotis, Evaggelos A.; ISRQuantization and fusion schemes are derived for multi-sensor correlation in distributed K- sensor systems that are used for the detection of weak signals or general signal discrimination from dependent observations. The dependence in the observations across time and sensors is modeled via stationary m - dependent, f - mixing, or r - mixing processes. The observation sequences of the various sensors have identical individual statistics and identical pairwise statistics (symmetric conditions). Each sensor observation is passed through a memoryless non-linearity or quantizer (the same one for all sensors) to form the sensor test statistic; the decision statistics of the various sensors are then passed to the fusion center in an unquantized or binary quantized manner to form the final decision statistic of the fusion center. Based on a common large sample size for each sensor that is necessary for achieving high-quality performance, an asymptotic analysis is applied for the error probabilities of the fusion center. This provides design criteria for the optimal memoryless nonlinearity and quantizer. Optimization of these design criteria yields the optimal nonlinearity or quantizer as solutions to linear integral equations involving the first - and second-order pdfs of the sensor observations describing the individual and pairwise dependence. the analytical results obtained are valid for any number of sensors K. Numerical results based on the simulation of the performance of our schemes with different number of sensors are presented. The performance of the optimal nonlinearities and quantizers is shown to outperform that of nonlinearities or quantizers obtained by ignoring the dependence in sensor observations and to improve as the number of sensors increases.Item Quantization and Fusion for Multi-Sensor Discrimination from Dependent Observations(1991) Chau, Yawgeng A.; Geraniotis, Evaggelos A.; ISRSchemes 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.Item Optimal Quantization and Fusion In Multi-Sensor Systems for the Detection of Weak Signals in Dependent Noise.(1989) Chau, Yawgeng A.; Geraniotis, Evaggelos A.; ISRTwo problems of memoryless quantization and data fusion for the detection of a weak signal in stationary dependent noise are addressed: (i) fusion from sensors with mutually independent observations across sensors but dependent across time and (ii) fusion from sensors with correlated observations across time and sensors. For each problem, we consider four distinct schemes (a) fusing the test statistics formed by the sensors without previous quantization (b) quantizing suboptimally each observation and then fusing, (c) quantizing optimally each observation and then fusing, and (d) quantizing optimally each test statistic of the sensors and then fusing the observation sequence of each sensor consists of a common weak signal disturbed by an additive stationary m-dependent, f-mixing or p-mixing noise process. To guarantee high-quality performance, a common large sample size is employed by each sensor. Design criteria are developed from the Neyman-Pearson test in the fusion center for the optimal memoryless sensor test statistics and the sensor quantizer parameters (quantization levels and breakpoints); these design criteria are shown to involve an extension of the asymptotic relative efficiency used in single-sensor detection and quantization. Numerical results in support of the analysis are given for the case of dependent p=mixing Cauchy noise.Item Distributed Detection From Multiple Sensors with Correlated Observations.(1989) Chau, Yawgeng A.; Geraniotis, Evaggelos A.; ISRWe address two problems of memoryless distributed dependent observations across time and sensors. In the first problem, the observation sequence of each sensor consists of common weak signal in additive dependent noise with stationary univariate and second-order joint densities; here the objective of the sensors is to cooperatively detect the presence of a weak signal. In the second problem, the observation sequence of each sensor is characterized by its stationary univariate and second-order pint densities; here the objective of the sensors is to cooperatively discriminate between two arbitrary such sequences of observations. For both problems, the analysis and design are based on a common large sample size. The dependence acms time and sensors is modeled by m-dependent, f-mixing, or p-mixing processes. The performance of the two-sensor configuration for each problem is measured by an average cost, which couples the decisions of the sensors. The design criteria for the test statistics of the sensors, which consist of sums of memoryless nonlinearities, are established by using two-dimensional Chemoff bounds on the associated error probabilities involved in the average cost. The optimal nonlinearities are obtain as the solutions of linear coupled or uncoupled integral equations. Numerical results for specific cases of practical interest show that the performance of the proposed scheme is superior to the one that ignores the dependence across time and/or sensors for each of the two problems.Item Distributed Estimation of a Location Parameter in Dependent Noise.(1989) Chau, Yawgeng A.; Geraniotis, Evaggelos A.; ISRWe address the problem of distributed estimation from dependent observations involving two sensors that collect observations of the same nonrandom location parameter THETA in additive noise. We consider two cases of interest, the case of independent observations across sensors and the case of correlated observations across sensors. The estimation schemes of the sensors are chosen so as to minimize a common cost function consisting of the weighted sum of the mean square errors of the estimates from the two sensors and the mean square of their difference. The observations of the two sensors are modeled as two MU - dependent or PHI mixing sequences. The correlation between the two observation sequences is also characterized by an p-dependent or PHI mixing sequence. Because high-order statistics of dependent observations are generally difficult to characterize, maximum-likehood estimates may be impossible to derive or implement; instead, suboptimal estimates which use memoryless nonlinearities g_k (DOT) (i.e. nonlinear functions of observations,) for k = 1,2, are employed by the two sensors. With this structure in each sensor, minimizing the above cost function with respect to the estimates is equivalent to minimizing it with respect to the nonlinearities g_k (DOT), which results in linear integral equations. If we solve these integral equations, we obtain optimal nonlinearities within this suboptimal scheme. Examples for m - dependent Cauchy noise are provided in support of our analysis.Item Distributed Detection of Weak Signals from Multiple Sensors with Correlated Observations.(1988) Geraniotis, Evaggelos A.; Chau, Yawgeng A.; ISRWe address two problems of distributed detection of a weak signal from dependent observations. In the first problem, two detectors must decide on the basis of their observations whether a weak signal is present or not. The observations of the two detectors consist of a common weak signal disturbed by two independent additive m-dependent or hi-mixing noise processes. Fixed-sample- size (block) detection is employed. The decisions are coupled through a common cost function, which consists of the sum of the error probabilities under the two hypotheses. In the second problem, the observations of each individual detector still consist of a common weak signal disturbed by an additive m- dependent or hi-mixing noise process, but the noise processes of the two detectors are now correlated. The cost function has a structure similar to that of the first problem. In both cases, the detectors employ suboptimal decision tests based on memoryless nonlinearities. Since the signal is weak, large sample sizes are necessary to guarantee high quality tests and the asymptotic performance is of interest. To determine the optimal nonlinearities for the two detectors, we identify new performance measures based on twodimensional Chernoff bounds, which correspond to the asymptotic relative efficiency (ARE) used for single-detector problems, and whose maximization implies the minimization of the aforementioned average cost function. This optimization results in integral equations whose solution provides the optimal nonlinearities. Numerical results based on simulation of the performance of the proposed two-sensor schemes are provided to support the analysis.Item On Minimax Robust Data Fusion.(1988) Geraniotis, Evaggelos A.; Chau, Yawgeng A.; ISRIn this paper, minimax robust data fusion schemes based on discrete-time observations with statistical uncertainty are considered. The observations are assumed to be i.i.d and the decisions of all sensors independent when conditioned on the either of two hypotheses. The statistics of the observations are only known to belong to uncertainty classes determined by 2- alternating Choquet capacities. Both cases of fixed sample-size (block) data fusion and sequential data fusion are examined. For specific performance measures, three robust fusion rules: suboptimal, optimal and asymptotically optimal - as the number of sensors increases - are derived for the block data fusion case, and an asymptotically robust fusion rule is derived for the sequential data fusion case; these fusion rules are optimal in the class of rules employing likelihood ratio tests. In all situations the robust fusion rule makes use of likelihood ratios and thresholds which depend on the least-faborable probability distributions in the uncertainty class. In the limit of a large number of sensors, it is shown that the same threshold can be used by all sensors, which in turn simplifies the overall computation.Item On Robust Continuous-Time Discrimination.(1987) Geraniotis, Evaggelos A.; Chau, Yawgeng A.; ISRContinuous-time discrimination problems characterized by observations which are the output of stochastic dynamical systems driven by colored Gaussian noise are considered. The parameters of the dynamical systems belong to one of the following distinct uncertainty classes: (i) classes determined by 2-alternating capacities and (ii) classes with minimal or maximal elements. Discrimination tests with a fixed observation interval and sequential tests are derived whose likelihood ratios depend on the least-favorable pairs of parameters in the aforementioned uncertainty classes and are shown to have an acceptable level of performance despite the uncertainty. For tests with a fixed observation interval the performance measures considered are the actual error probabilities and the Chernoff upper bounds on them; the latter are shown to preserve their desirable asymptotic properties in the presence of the uncertainties. For sequential tests the performance measures are the error probabilities and the average required length of the observation interval under each hypothesis.