Efficient convex relaxation methods for robust target localization by a sensor network using time differences of arrivals

Kehu Yang, Gang Wang, Zhi Quan Luo

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217 Scopus citations


We consider the problem of target localization by a network of passive sensors. When an unknown target emits an acoustic or a radio signal, its position can be localized with multiple sensors using the time difference of arrival (TDOA) information. In this paper, we consider the maximum likelihood formulation of this target localization problem and provide efficient convex relaxations for this nonconvex optimization problem. We also propose a formulation for robust target localization in the presence of sensor location errors. Two Cramer-Rao bounds are derived corresponding to situations with and without sensor node location errors. Simulation results confirm the efficiency and superior performance of the convex relaxation approach as compared to the existing least squares based approach when large sensor node location errors are present.

Original languageEnglish (US)
Pages (from-to)2775-2784
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number7
StatePublished - 2009

Bibliographical note

Funding Information:
Manuscript received February 28, 2008; accepted January 24, 2009. First published March 10, 2009; current version published June 17, 2009. The associate editor coordinating the review of this paper and approving it for publication was Dr. Zhi Tian. Part of this work was presented at the 2008 IEEE Radar Conference, Rome, Italy, May 26–30, 2008. The work of K. Yang and G. Wang was supported in part by the National Natural Science Foundation of China (NSFC) under Grant 60672127, by the 111 Project under Grant B08038, and by the Special Fund for Key Laboratories under Grant ISN02080004. The work of Z.-Q. Luo was supported in part by the National Science Foundation under Grant DMS-0610037 and by the USDOD ARMY under Grant W911NF-05-1-0567.


  • Convex optimization
  • Sensor networks
  • Target localization


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