Performance bounds for the rate-constrained universal decentralized estimators

Jin Jun Xiao, Zhi Quan Luo, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

19 Scopus citations

Abstract

We consider decentralized estimation of a noise-corrupted deterministic parameter using a bandwidth-constrained sensor network with a fusion center (FC). Each sensor's noise is additive, zero mean, and independent across sensors. A decentralized estimator is said to be universal if the local sensor quantization rules and the final fusion rule at the FC are independent of sensor noise pdf. Assuming that information rate from each sensor to the FC is constrained to one bit per sample, we derive a Cramér-Rao lower bound (CRLB) on the mean-squared error (MSE) performance of a class of rate-constrained universal decentralized estimators. Our results show that if sensor observation noise has finite range in [-U,U], then the minimum MSE performance of any one-bit rate-constrained universal decentralized estimator is at least U2/(4K), where K is the total number sensors. This bound implies that the recently proposed universal decentralized estimators are optimal up to a constant factor of 4.

Original languageEnglish (US)
Pages (from-to)47-50
Number of pages4
JournalIEEE Signal Processing Letters
Volume14
Issue number1
DOIs
StatePublished - Jan 1 2007

Keywords

  • Cramér-Rao bound
  • Distributed estimation
  • Quantization
  • Sensor network

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