Cramér-Rao bounds for polynomial signal estimation using sensors with AR(1) drift

Swarnendu Kar, Pramod K. Varshney, Marimuthu Palaniswami

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We seek to characterize the estimation performance of a sensor network where the individual sensors exhibit the phenomenon of drift, i.e., a gradual change of the bias. Though estimation in the presence of random errors has been extensively studied in the literature, the loss of estimation performance due to systematic errors like drift have rarely been looked into. In this paper, we derive closed-form Fisher Information Matrix and subsequently Cramér-Rao bounds (up to reasonable approximation) for the estimation accuracy of drift-corrupted signals. We assume a polynomial time-series as the representative signal and an autoregressive process model for the drift. When the Markov parameter for drift p < 1 we show that the first-order effect of drift is asymptotically equivalent to scaling the measurement noise by an appropriate factor. For p = 1 i.e., when the drift is nonstationary, we show that the constant part of a signal can only be estimated inconsistently (non-zero asymptotic variance). Practical usage of the results are demonstrated through the analysis of 1) networks with multiple sensors and 2) bandwidth limited networks communicating only quantized observations.

Original languageEnglish (US)
Article number6218789
Pages (from-to)5494-5507
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume60
Issue number10
DOIs
StatePublished - Sep 26 2012

Keywords

  • Autoregressive process
  • Distributed estimation
  • Polynomial regression
  • Sensor networks
  • Systematic errors

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

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