Information Fusion from the Point of View of Communication Theory; Fusing Information to Trade-Off the Resolution of Assessments Against the Probability of Mis-Assessment
Final rept. 1 Jun 2010-31 May 2013
COLORADO STATE UNIV FORT COLLINS DEPT OF MATHEMATICS AND STATISTICS
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In this final report, several questions in information fusion and compression are answered 1 The generalized likelihood ratio for fusing the several time series in a distributed array of sensors, to detect dependence, is a generalized Hadamard ratio under the null hypothesis of independence of Gaussian time series, the statistic is distributed as a product of independent beta random variables in the limit of long observation times, the statistic is a broadband coherence 2 the fusion and compression of noisy sensor measurements, for power-limited transmission over a noisy channel, consists of a transformation of measurements into canonical coordinates, scaling, and rotation there is a water-filling interpretation 3 the optimum design of a linear secondary channel of measurements to fuse with a primary linear channel of measurements maximizes a generalized Rayleigh quotient 4 the asymptotically optimum threshold setting at a local detector in a sensor array is determined by a one-dimensional search on a Receiver Operating Characteristic that maximizes a Kullback-Leibler distance the threshold setting that maximizes a mutual information is a useful approximation 5 Is there a greedy policy for compressing a sequence of vector-valued measurements into a sequence of scalar measurements that maximize information gain at each compression When the measurements are linear maps of an underlying Gaussian state, and the measurement noise is white, the policy selects compressors from pre-computed eigenvectors of a prior covariance, according to eigenvalues of a posterior covariance. Performance at a given number of scalar compressions is nearly as good as the performance of a globally optimum policy for many illustrative problems.
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