Optimal estimation of sensor biases for asynchronous multi-sensor data fusion

Wenqiang Pu, Ya Feng Liu, Junkun Yan, Hongwei Liu, Zhi Quan Luo

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


An important step in a multi-sensor surveillance system is to estimate sensor biases from their noisy asynchronous measurements. This estimation problem is computationally challenging due to the highly nonlinear transformation between the global and local coordinate systems as well as the measurement asynchrony from different sensors. In this paper, we propose a novel nonlinear least squares formulation for the problem by assuming the existence of a reference target moving with an (unknown) constant velocity. We also propose an efficient block coordinate decent (BCD) optimization algorithm, with a judicious initialization, to solve the problem. The proposed BCD algorithm alternately updates the range and azimuth bias estimates by solving linear least squares problems and semidefinite programs. In the absence of measurement noise, the proposed algorithm is guaranteed to find the global solution of the problem and the true biases. Simulation results show that the proposed algorithm significantly outperforms the existing approaches in terms of the root mean square error.

Original languageEnglish (US)
Pages (from-to)357-386
Number of pages30
JournalMathematical Programming
Issue number1
StatePublished - Jul 1 2018

Bibliographical note

Funding Information:
This work was performed at the Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen. It is funded in part by a National Natural Science Foundation of China (NSFC) Key Project Grant 61731018, by NSFC Grants 11331012, 11631013, and 61601340, and in part by the China National Funds for Distinguished Young Scientists Grant 61525105.

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.


  • Block coordinate decent algorithm
  • Nonlinear least squares
  • Sensor registration problem
  • Tightness of semidefinite relaxation


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