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Network theoretic analysis of maximum a posteriori detectors for optimal input detection

Anguluri, R. and Katewa, V. and Roy, S. and Pasqualetti, F. (2022) Network theoretic analysis of maximum a posteriori detectors for optimal input detection. In: Automatica, 141 .

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Official URL: http://10.1016/j.automatica.2022.110277

Abstract

We study maximum-a-posteriori detectors to detect changes in the constant mean vector and the covariance matrix of a Gaussian stationary stochastic input driving a few nodes in a network, using remotely located sensor measurements. We show that the detectors’ performance can be analyzed using specific input-to-output gain of the network system's transfer function matrix and the input statistics and sensor noise in the asymptotic measurement regime. Using this result, we study the detector's performance using node cutsets that separate the nodes containing inputs from a partitioned set of nodes not containing inputs. In the absence of noise, we show that the detectors’ performance is no better for sensors on a partitioned set than those on the cutset. Instead, in the presence of noise, we show that the detectors’ performance can be better for sensors on a partitioned set than those on the cutset for certain choices of edge weights. Our results quantify the extent to which input and sensor nodes’ distance modulates detection performance via separating cutsets, and have potential applications in sensor placement problems. Finally, we complement the theory with simulations. © 2022 Elsevier Ltd

Item Type: Journal Article
Publication: Automatica
Publisher: Elsevier Ltd
Additional Information: The copyright of this document belongs to the authors
Keywords: Sensor nodes; Statistical tests; Stochastic systems, Covariance detection; Cut sets; Detector performance; Maximum a posteriori detectors; Mean detection; Mean vector; Network systems; Sensor placement; Statistical hypothesis testing; Theoretic analysis, Covariance matrix
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 19 May 2022 07:29
Last Modified: 19 May 2022 07:29
URI: https://eprints.iisc.ac.in/id/eprint/71925

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