Bounds on the number of identifiable outliers in source localization by linear programming

Joseph S. Picard, Anthony J. Weiss

Research output: Contribution to journalArticlepeer-review

Abstract

Precise localization have attracted considerable interest in the engineering literature. Most publications consider small measurement errors. In this work we discuss localization in the presence of outliers, where several measurements are severely corrupted while sufficient other measurements are reasonably precise. It is known that maximum likelihood or least squares provide poor results under these conditions. On the other hand, robust regression can successfully handle up to 50% outliers but is associated with high complexity. Using the l1 norm as the penalty function provides some immunity from outliers and can be solved efficiently with linear programming methods. We use linear equations to describe the localization problem and then we apply the l1 norm and linear programming to detect the outliers and avoid the wild measurements in the final solution. Our main contribution is an exploitation of recent results in the field of sparse representation to obtain bounds on the number of detectable outliers. The theory is corroborated by simulations and by real data.

Original languageEnglish
Article number5395681
Pages (from-to)2884-2895
Number of pages12
JournalIEEE Transactions on Signal Processing
Volume58
Issue number5
DOIs
StatePublished - May 2010

Keywords

  • Angle of arrival (AOA)
  • L norm
  • Linear programming
  • Localization
  • Outliers
  • Received signal strength (RSS)
  • Time difference of arrival (TDOA)
  • Time of arrival (TOA)

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