Threshold optimization according to the restricted Bayes criterion in decentralized detection problems

In this paper, the restricted Bayes approach is studied in a decentralized detection problem. All decisions on which the hypothesis is true are made by local sensors through conditionally independent observations. Then these decisions are transmitted to the fusion center for the final decision. In the conventional approach, all thresholds of local sensors and the fusion center are considered as deterministic variables and optimized according to the given criterion for given test statistics of local sensors and the fusion center. In this paper, it is shown that setting thresholds as random variables instead of deterministic ones can improve the performance according to the restricted Bayes criterion. It is proved that optimal random thresholds are dependent on each other, and the probability density function of each one consists of at most two point masses. Two methods for the implementation of this scheme are proposed. A necessary and sufficient condition for improvability of the conventional approach through replacing optimal deterministic thresholds by optimal random ones is derived. Finally, theoretical results are investigated through simulations.

PDF

___

[1] Tenney RR, Sandell NR. Detection with distributed sensors. IEEE Transactions on Aerospace and Electronic Systems 1981; 17: 501-510.
[2] Chamberland JF, Veeravalli VV. Decentralized detection in sensor networks. IEEE Transactions on Signal Processing 2003; 51: 407-416.
[3] Duman TM, Salehi M. Decentralized detection over multiple-access channels. IEEE Transactions on Aerospace and Electronic Systems 1998; 34: 469-476.
[4] Xiou JJ, Luo ZQ. Universal decentralized detection in a bandwidth-constrained sensor network. IEEE Transactions on Signal Processing 2005; 53: 2617-2624.
[5] Rago C, Willett P, Bar-Shalom Y. Censoring sensors: a low-communication-rate scheme for distributed detection. IEEE Transactions on Aerospace and Electronic Systems 1996; 32: 554-568.
[6] Appadwedula S, Veeravalli VV, Jones DL. Decentralized detection with censoring sensors. IEEE Transactions on Signal Processing 2008; 56: 1362-1373.
[7] Wimalajeewa T, Varshney P. Collaborative human decision making with random local thresholds. IEEE Transactions on Signal Processing 2013; 61: 2975-2989.
[8] Papastavrou J, Athans M. The team roc curve in a binary hypothesis testing environment. IEEE Transactions on Aerospace and Electronic Systems 1995; 31: 96-105.
[9] Hodges JL, Lehmann EL. The use of previous experience in reaching statistical decisions. The Annals of Mathematical Statistics 1952; 23: 396-407.
[10] Lehmann EL. Testing Statistical Hypotheses. 2nd ed. New York, NY, USA: Chapman & Hall, 1986.
[11] Viswanathan R, Varshney P. Distributed detection with multiple sensors I. fundamentals. Proceedings of the IEEE 1997; 85: 54-63.
[12] Bayram S, Gezici S. On the restricted Neyman-Pearson approach for composite hypothesis-testing in presence of prior distribution uncertainty. IEEE Transactions on Signal Processing 2011; 59: 5056-5065.
[13] Bayram S, Vanli ND, Dulek B, Sezer I, Gezici S. Optimum power allocation for average power constrained jammers in the presence of non-gaussian noise. IEEE Communications Letters 2012; 16: 1153-1156.
[14] Bayram S, Gezici S. Stochastic resonance in binary composite hypothesis-testing problems in the Neyman-Pearson framework. Digital Signal Processing 2012; 22: 391-406.