Asymptotically Optimal Truncated Multivariate Gaussian Hypothesis Testing with Application to Consensus Algorithms
In the interest of complexity reduction or to facilitate efficient distributed computation using consensus, truncated versions of the optimal hypothesis test are considered for a canonical multivariate Gaussian problem with L observations. The truncated tests employ 2k+1 < L correlation terms involving any given observation. The focus is on cases with a large L such that significant efficiency results with a truncation rule, k as a function of L, which increases very slowly with L. A key result provides sufficient conditions on truncation rules and sequences of hypothesis testing problems which provide no loss in deflection performance as L approaches infinity when compared to the optimal detector. The set of asymptotically optimal truncation rules satisfying these sufficient conditions varies with the scaling behavior of the difficulty of the hypothesis testing problem with L. Several popular classes of system and process models, including observations from wide-sense stationary limiting processes asL→ ∞ after the mean is subtracted, are used as illustrative classes of examples to demonstrate the sufficient conditions are not overly restrictive. In these examples, significant truncation can be employed even when the difficulty of the hypothesis testing problem scales in the least favorable manner, putting the most stringent conditions on the truncation rule. In all the cases considered, numerical results imply the fixed-false-alarm-rate detection probability of the truncated detector converges to the detection probability of the optimal detector for our asymptotically optimal truncation in terms of deflection.
J. Zhang and R. S. Blum, "Asymptotically Optimal Truncated Multivariate Gaussian Hypothesis Testing with Application to Consensus Algorithms," IEEE Transactions on Signal Processing, vol. 62, no. 2, pp. 431-442, Institute of Electrical and Electronics Engineers (IEEE), Jan 2014.
The definitive version is available at https://doi.org/10.1109/TSP.2013.2288673
Electrical and Computer Engineering
Keywords and Phrases
Consensus; Deflection; Large System; Multivariate Gaussian Hypothesis Test; Sensor Network; Truncated Detector
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2014