Asymptotic Optimality Theory for Decentralized Sequential Multihypothesis Testing Problems

作者：Wang Yan^*; Mei Yajun

来源：IEEE Transactions on Information Theory, 2011, 57(10): 7068-7083.

DOI：10.1109/TIT.2011.2165808

• Asymptotic optimality
• maximin quantizer
• multihypotheses testing
• sequential detection
• two-stage tests
• unambiguous likelihood quantizer (ULQ)

The Bayesian formulation of sequentially testing M >= 3 hypotheses is studied in the context of a decentralized sensor network system. In such a system, local sensors observe raw observations and send quantized sensor messages to a fusion center which makes a final decision when stopping taking observations. Asymptotically optimal decentralized sequential tests are developed from a class of "two-stage" tests that allows the sensor network system to make a preliminary decision in the first stage and then optimize each local sensor quantizer accordingly in the second stage. It is shown that the optimal local quantizer at each local sensor in the second stage can be defined as a maximin quantizer which turns out to be a randomization of at most M-1 unambiguous likelihood quantizers (ULQ). We first present in detail our results for the system with a single sensor and binary sensor messages, and then extend to more general cases involving any finite alphabet sensormessages, multiple sensors, or composite hypotheses.

• 出版日期2011-10