Performance analysis of two EM-based measurement bias estimation processes for tracking systems

  • Zhi-hua LuEmail author
  • Meng-yao Zhu
  • Qing-wei Ye
  • Yu Zhou


In target tracking, the measurements collected by sensors can be biased in some real scenarios, e.g., due to systematic error. To accurately estimate the target trajectory, it is essential that the measurement bias be identified in the first place. We investigate the iterative bias estimation process based on the expectation-maximization (EM) algorithm, for cases where sufficiently large numbers of measurements are at hand. With the assistance of extended Kalman filtering and smoothing, we derive two EM estimation processes to estimate the measurement bias which is formulated as a random variable in one state-space model and a constant value in another. More importantly, we theoretically derive the global convergence result of the EM-based measurement bias estimation and reveal the link between the two proposed EM estimation processes in the respective state-space models. It is found that the bias estimate in the second state-space model is more accurate and of less complexity. Furthermore, the EM-based iterative estimation converges faster in the second state-space model than in the first one. As a byproduct, the target trajectory can be simultaneously estimated with the measurement bias, after processing a batch of measurements. These results are confirmed by our simulations.

Key words

Non-linear state-space model Measurement bias Extended Kalman filter Extended Kalman smoothing Expectation-maximization (EM) algorithm 

CLC number



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Copyright information

© Zhejiang University and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.College of Information Science and EngineeringNingbo UniversityNingboChina
  2. 2.School of Communication and Information EngineeringShanghai UniversityShanghaiChina

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