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

Zhi-hua LU; Meng-yao ZHU; Qing-wei YE; Yu ZHOU

doi:10.1631/FITEE.1800214

Your Location：

Home >

Browse articles >

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

Regular Papers | Updated：2022-05-19

- Performance analysis of two EM-based measurement bias estimation processes for tracking systems
- 针对目标跟踪的两种基于最大期望算法测量值偏差估计过程的性能分析
- Frontiers of Information Technology & Electronic Engineering Vol. 19, Issue 9, Pages: 1151-1165(2018)
- Affiliations：
  
  College of Information Science and Engineering, Ningbo University, Ningbo 315211, China
  School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China
- Author bio：
  
  Zhi-hua LU, E-mail: luzhihua@nbu.edu.cn
  [ "Meng-yao ZHU, E-mail: zhumengyao@shu.edu.cn" ]
  [ "Qing-wei YE, E-mail: yeqingwei@nbu.edu.cn" ]
  [ "Yu ZHOU, E-mail: zhouyu@nbu.edu.cn" ]
- Funds：
- DOI：10.1631/FITEE.1800214
  CLC： TP73
- Received：07 April 2018，
  
  Revised：2018-;9-25，
  
  Published：2018-09
- Accepted：
Scan QR Code
Zhi-hua LU, Meng-yao ZHU, Qing-wei YE, et al. 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.
DOI：

Zhi-hua LU, Meng-yao ZHU, Qing-wei YE, et al. 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. DOI： 10.1631/FITEE.1800214.

摘要

在现实目标跟踪问题中，传感器采集的测量值，比如系统缺陷，可能存在一定程度偏差。为正确估计目标的运动轨迹，测量值偏差的识别与估计将成为首要任务。首先，提出两种状态空间模型，分别把测量值偏差视为随机变量和常数。其次，假设测量值样本数足够大，基于最大期望算法，利用扩展卡尔曼滤波和平滑，针对两种模型提出不同的循环迭代偏差估计过程。最后，分析这两种估计过程的全局收敛结果，揭示其内在联系。结果表明，第二种估计过程比第一种估计过程更简单准确，并且收敛速度更快。批量处理测量值样本后，可同时获得目标运动轨迹和测量值偏差的估计结果。

Abstract

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.

关键词

Keywords

references

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

MF Bugallo , , , T Lu , , , PM Djuric . . Bearings-only tracking with biased measurements . . Proc 2$^\rm nd$ IEEE Int Workshop on Computational Advances in Multi-sensor Adaptive Processing , , 2007 . . p.265 - - 268 . . DOI: 10.1109/CAMSAP.2007.4498016 http://doi.org/10.1109/CAMSAP.2007.4498016 . .

S Fortunati , , , A Farina , , , F Gini , , , 等 . . Least squares estimation and Cramér-Rao type lower bounds for relative sensor registration process . . IEEE Trans Signal Process , , 2011 . . 59 ( ( 3 ): ): 1075 - - 1087 . . DOI: 10.1109/TSP.2010.2097258 http://doi.org/10.1109/TSP.2010.2097258 . .

F Gustafsson , , , F Gunnarsson . . Mobile positioning using wireless networks: possibilities and fundamental limitations based on available wireless network measurements . . IEEE Signal Process Mag , , 2005 . . 22 ( ( 4 ): ): 41 - - 53 . . DOI: 10.1109/MSP.2005.1458284 http://doi.org/10.1109/MSP.2005.1458284 . .

U Hammes , , , AM Zoubir . . Robust mobile terminal tracking in NLOS environments based on data association . . IEEE Trans Signal Process , , 2010 . . 58 ( ( 11 ): ): 5872 - - 5882 . . DOI: 10.1109/TSP.2010.2063425 http://doi.org/10.1109/TSP.2010.2063425 . .

S Haykin . . Kalman Filtering and Neural Networks , , : : New York, USA Wiley , , 2001 . . .

ML Hernandez , , , A Farina , , , B Ristic . . PCRLB for tracking in cluttered environments: measurement sequence conditioning approach . . IEEE Trans Aerosp Electron Syst , , 2006 . . 42 ( ( 2 ): ): 680 - - 704 . . DOI: 10.1109/TAES.2006.1642582 http://doi.org/10.1109/TAES.2006.1642582 . .

DL Huang , , , H Leung . . 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 , , 2010 . . p.101 - - 124 . . . .

BS Karunaratne , , , MR Morelande , , , B Moran . . Target tracking in a multipath environment . . Proc IET Int Conf on Radar Systems , , 2012 . . p.1 - - 6 . . DOI: 10.1049/cp.2012.1645 http://doi.org/10.1049/cp.2012.1645 . .

TC Li , , , A Ekpenyong , , , YF Huang . . Source localization and tracking using distributed asynchronous sensors . . IEEE Trans Signal Process , , 2006 . . 54 ( ( 10 ): ): 3991 - - 4003 . . DOI: 10.1109/TSP.2006.880213 http://doi.org/10.1109/TSP.2006.880213 . .

TC Li , , , JY Su , , , W Liu , , , 等 . . Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond . . Front Inform Technol Electron Eng , , 2017 . . 18 ( ( 12 ): ): 1913 - - 1939 . . DOI: 10.1631/FITEE.1700379 http://doi.org/10.1631/FITEE.1700379 . .

W Li , , , H Leung , , , YF Zhou . . Space-time registration of radar and ESM using unscented Kalman filter . . IEEE Trans Aerosp Electron Syst , , 2004 . . 40 ( ( 3 ): ): 824 - - 836 . . DOI: 10.1109/TAES.2004.1337457 http://doi.org/10.1109/TAES.2004.1337457 . .

XR Li , , , VP Jilkov . . Survey of maneuvering target tracking . . Part Ⅰ. Dynamic models. IEEE Trans Aerosp Electron Syst , , 2003 . . 39 ( ( 4 ): ): 1333 - - 1364 . . DOI: 10.1109/TAES.2003.1261132 http://doi.org/10.1109/TAES.2003.1261132 . .

ZH Li , , , SY Chen , , , H Leung , , , 等 . . Joint data association, registration, and fusion using EM-KF . . IEEE Trans Aerosp Electron Syst , , 2004 . . 46 ( ( 2 ): ): 496 - - 507 . . DOI: 10.1109/TAES.2010.5461637 http://doi.org/10.1109/TAES.2010.5461637 . .

F Lian , , , C Han , , , W Liu , , , 等 . . Joint spatial registration and multi-target tracking using an extended probability hypothesis density filter . . IET Radar Sonar Navig , , 2011 . . 5 ( ( 4 ): ): 441 - - 448 . . DOI: 10.1049/iet-rsn.2010.0057 http://doi.org/10.1049/iet-rsn.2010.0057 . .

XD Lin , , , Y Bar-Shalom , , , T Kirubarajan . . Exact multisensor dynamic bias estimation with local tracks . . IEEE Trans Aerosp Electron Syst , , 2004 . . 40 ( ( 2 ): ): 576 - - 590 . . DOI: 10.1109/TAES.2004.1310006 http://doi.org/10.1109/TAES.2004.1310006 . .

P Matisko , , , V Havlena . . Cramér-Rao bounds for estimation of linear system noise covariances . . J Mech Eng Autom , , 2012 . . 2 ( ( 2 ): ): 6 - - 11 . . DOI: 10.5923/j.jmea.20120202.02 http://doi.org/10.5923/j.jmea.20120202.02 . .

TK Moon . . The expectation-maximization algorithm . . IEEE Signal Process Mag , , 1996 . . 13 ( ( 6 ): ): 47 - - 60 . . DOI: 10.1109/79.543975 http://doi.org/10.1109/79.543975 . .

NN Okello , , , S Challa . . Joint sensor registration and track-to-track fusion for distributed trackers . . IEEE Trans Aerosp Electron Syst , , 2004 . . 40 ( ( 3 ): ): 808 - - 823 . . DOI: 10.1109/TAES.2004.1337456 http://doi.org/10.1109/TAES.2004.1337456 . .

NN Okello , , , B Ristic . . Maximum likelihood registration for multiple dissimilar sensors . . IEEE Trans Aerosp Electron Syst , , 2003 . . 39 ( ( 3 ): ): 1074 - - 1083 . . DOI: 10.1109/TAES.2003.1238759 http://doi.org/10.1109/TAES.2003.1238759 . .

S Särkkä . . Bayesian Filtering and Smoothing , , : : Cambridge, UK Cambridge University Press , , 2013 . . .

V Savic , , , H Wymeersch , , , E Larsson . . Target tracking in confined environments with uncertain sensor positions . . IEEE Trans Veh Technol , , 2016 . . 65 ( ( 2 ): ): 870 - - 882 . . DOI: 10.1109/TVT.2015.2404132 http://doi.org/10.1109/TVT.2015.2404132 . .

AH Sayed , , , A Tarighat , , , N Khajehnouri . . Network-based wireless location: challenges faced in developing techniques for accurate wireless location information . . IEEE Signal Process Mag , , 2005 . . 22 ( ( 4 ): ): 24 - - 40 . . DOI: 10.1109/MSP.2005.1458275 http://doi.org/10.1109/MSP.2005.1458275 . .

RH Shumway , , , DS Stoffer . . An approach to time series smoothing and forecasting using the EM algorithm . . J Time Ser Anal , , 1982 . . 3 ( ( 4 ): ): 253 - - 264 . . DOI: 10.1111/j.1467-9892.1982.tb00349.x http://doi.org/10.1111/j.1467-9892.1982.tb00349.x . .

P Stinco , , , MS Greco , , , F Gini , , , 等 . . Posterior Cramér-Rao lower bounds for passive bistatic radar tracking with uncertain target measurements . . Signal Process , , 2013 . . 93 ( ( 12 ): ): 3528 - - 3540 . . DOI: 10.1016/j.sigpro.2013.02.021 http://doi.org/10.1016/j.sigpro.2013.02.021 . .

DG Tzikas , , , CL Likas , , , NP Galatsanos . . The variational approximation for Bayesian inference . . IEEE Signal Process Mag , , 2008 . . 25 ( ( 6 ): ): 131 - - 146 . . DOI: 10.1109/MSP.2008.929620 http://doi.org/10.1109/MSP.2008.929620 . .

L Zhou , , , XX Liu , , , ZT Hu , , , 等 . . Joint estimation of state and system biases in non-linear system . . IET Signal Process , , 2017 . . 11 ( ( 1 ): ): 10 - - 16 . . DOI: 10.1049/iet-spr.2015.0068 http://doi.org/10.1049/iet-spr.2015.0068 . .

Views

Downloads

CSCD

Alert me when the article has been cited

Submit

Tools

Publicity Resources

No data

Related Author

No data

Related Institution

No data

Chat

Address：Zhejiang University Press, 148 Tianmushan Road, Hangzhou, China Postal code：310028
Tel：+86-571-88273162 Email：fitee@zju.edu.cn
It is recommended to read the content of this site in Chrome&IE9+. Please switch to extreme mode in browser 360.
Cookies We use cookies to help provide and enhance our service and tailor content. By continuing, you agree to the use of cookies.

⁰