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CLC number: TP73

On-line Access: 2018-11-11

Received: 2018-04-07

Revision Accepted: 2018-09-24

Crosschecked: 2018-09-25

Cited: 0

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Citations:  Bibtex RefMan EndNote GB/T7714


Zhi-hua Lu


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Frontiers of Information Technology & Electronic Engineering  2018 Vol.19 No.9 P.1151-1165


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

Author(s):  Zhi-hua Lu, Meng-yao Zhu, Qing-wei Ye, Yu Zhou

Affiliation(s):  College of Information Science and Engineering, Ningbo University, Ningbo 315211, China; more

Corresponding email(s):   luzhihua@nbu.edu.cn, zhumengyao@shu.edu.cn, yeqingwei@nbu.edu.cn, zhouyu@nbu.edu.cn

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

Zhi-hua Lu, Meng-yao Zhu, Qing-wei Ye, Yu Zhou. Performance analysis of two EM-based measurement bias estimation processes for tracking systems[J]. Frontiers of Information Technology & Electronic Engineering, 2018, 19(9): 1151-1165.

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A1 - Zhi-hua Lu
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A1 - Yu Zhou
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DOI - 10.1631/FITEE.1800214

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.




Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Blackman S, Popoli R, 1999. Design and Analysis of Modern Tracking Systems. Artech House, Boston, USA.

[2]Bugallo MF, Lu T, Djuric PM, 2007. Bearings-only tracking with biased measurements. Proc 2nd IEEE Int Workshop on Computational Advances in Multi-sensor Adaptive Processing, p.265-268.

[3]Fortunati S, Farina A, Gini F, et al., 2011. Least squares estimation and Cramér-Rao type lower bounds for relative sensor registration process. IEEE Trans Signal Process, 59(3):1075-1087.

[4]Gustafsson F, Gunnarsson F, 2005. Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements. IEEE Signal Process Mag, 22(4):41-53.

[5]Hammes U, Zoubir AM, 2010. Robust mobile terminal tracking in NLOS environments based on data association. IEEE Trans Signal Process, 58(11):5872-5882.

[6]Haykin S, 2001. Kalman Filtering and Neural Networks. Wiley, New York, USA.

[7]Hernandez ML, Farina A, Ristic B, 2006. PCRLB for tracking in cluttered environments: measurement sequence conditioning approach. IEEE Trans Aerosp Electron Syst, 42(2):680-704.

[8]Huang DL, Leung H, 2010. An EM-IMM method for simultaneous registration and fusion of multiple radars and ESM sensors. In: Mukhopadhyay SC, Leung H (Eds.), Advances in Wireless Sensors and Sensor Networks. Springer Berlin Heidelberg, p.101-124.

[9]Karunaratne BS, Morelande MR, Moran B, 2012. Target tracking in a multipath environment. Proc IET Int Conf on Radar Systems, p.1-6.

[10]Li TC, Ekpenyong A, Huang YF, 2006. Source localization and tracking using distributed asynchronous sensors. IEEE Trans Signal Process, 54(10):3991-4003.

[11]Li TC, Su JY, Liu W, et al., 2017. Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond. Front Inform Technol Electron Eng, 18(12):1913-1939.

[12]Li W, Leung H, Zhou YF, 2004. Space-time registration of radar and ESM using unscented Kalman filter. IEEE Trans Aerosp Electron Syst, 40(3):824-836.

[13]Li XR, Jilkov VP, 2003. Survey of maneuvering target tracking. Part I. Dynamic models. IEEE Trans Aerosp Electron Syst, 39(4):1333-1364.

[14]Li ZH, Chen SY, Leung H, et al., 2004. Joint data association, registration, and fusion using EM-KF. IEEE Trans Aerosp Electron Syst, 46(2):496-507.

[15]Lian F, Han C, Liu W, et al., 2011. Joint spatial registration and multi-target tracking using an extended probability hypothesis density filter. IET Radar Sonar Navig, 5(4): 441-448.

[16]Lin XD, Bar-Shalom Y, Kirubarajan T, 2004. Exact multisensor dynamic bias estimation with local tracks. IEEE Trans Aerosp Electron Syst, 40(2):576-590.

[17]Matisko P, Havlena V, 2012. Cramér-Rao bounds for estimation of linear system noise covariances. J Mech Eng Autom, 2(2):6-11.

[18]Moon TK, 1996. The expectation-maximization algorithm. IEEE Signal Process Mag, 13(6):47-60.

[19]Okello NN, Challa S, 2004. Joint sensor registration and track-to-track fusion for distributed trackers. IEEE Trans Aerosp Electron Syst, 40(3):808-823.

[20]Okello NN, Ristic B, 2003. Maximum likelihood registration for multiple dissimilar sensors. IEEE Trans Aerosp Electron Syst, 39(3):1074-1083.

[21]Särkkä S, 2013. Bayesian Filtering and Smoothing. Cambridge University Press, Cambridge, UK.

[22]Savic V, Wymeersch H, Larsson E, 2016. Target tracking in confined environments with uncertain sensor positions. IEEE Trans Veh Technol, 65(2):870-882.

[23]Sayed AH, Tarighat A, Khajehnouri N, 2005. Network-based wireless location: challenges faced in developing techniques for accurate wireless location information. IEEE Signal Process Mag, 22(4):24-40.

[24]Shumway RH, Stoffer DS, 1982. An approach to time series smoothing and forecasting using the EM algorithm. J Time Ser Anal, 3(4):253-264.

[25]Stinco P, Greco MS, Gini F, et al., 2013. Posterior Cramér-Rao lower bounds for passive bistatic radar tracking with uncertain target measurements. Signal Process, 93(12):3528-3540.

[26]Tzikas DG, Likas CL, Galatsanos NP, 2008. The variational approximation for Bayesian inference. IEEE Signal Process Mag, 25(6):131-146.

[27]Zhou L, Liu XX, Hu ZT, et al., 2017. Joint estimation of state and system biases in non-linear system. IET Signal Process, 11(1):10-16.

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