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Random weighting estimation for systematic error of observation model in dynamic vehicle navigation

  • Regular Papers
  • Control Theory and Applications
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Abstract

The Kalman filter requires kinematic and observation models not contain any systematic error. Otherwise, the resultant navigation solution will be biased or even divergent. In order to overcome this limitation, this paper presents a new random weighting method to estimate the systematic error of observation model in dynamic vehicle navigation. This method randomly weights the covariance matrices of observation residual vector, predicted residual vector and estimated state vector to control their magnitudes, thus governing the random weighting estimation for the covariance matrix of observation vector. Random weighting theories are established for estimations of the observation model’s systematic error and the covariance matrices of observation residual vector, predicted residual vector, observation vector and estimated state vector. Experiments and comparison analysis with the existing methods demonstrate that the proposed random weighting method can effectively resist the disturbance of the observation model’s systematic error on the state parameter estimation, leading to the improved accuracy for dynamic vehicle navigation.

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References

  1. S. Gao, Y. Gao, Y. Zhong, and W. Wei, “Random weighting estimation method for dynamic navigation positioning,” Chinese Journal of Aeronautics, vol. 24, no. 3, pp. 318–323, 2011. [click]

    Article  Google Scholar 

  2. M. S. Grewal and A. P. Andrews, Kalman Filtering: Theory and Practice using Matlab, John Wiley & Sons, New York, pp. 1–3, 2001.

    Google Scholar 

  3. Y. Geng and J. Wang, “Adaptive estimation of multiple fading factors in Kalman filter for navigation applications,” GPS Solutions, vol. 12, no. 4, pp. 273–279, 2008. [click]

    Article  Google Scholar 

  4. Y. Yang and S. Zhang, “Adaptive fitting of systematic errors in navigation,” Journal of Geodesy, vol. 79, no. 1-3, pp. 43–49, 2005. [click]

    Article  MATH  Google Scholar 

  5. D.-J. Jwo and T.-P. Weng, “An adaptive sensor fusion method with applications in integrated navigation,” The Journal of Navigation, vol. 61, no. 4, pp. 705–721, 2008. [click]

    Article  Google Scholar 

  6. K. H. Kim, G. I. Jee, and J. H. Song, “Carrier tracking loop using the adaptive two-stage Kalman filter for high dynamic situations,” International Journal of Control, Automation, and Systems, vol. 6, no. 6, pp. 948–953, 2008.

    Google Scholar 

  7. Y. J. Wang and K. K. Kubik, “Robust Kalman filter and its geodetic applications,” Manuscripta Geodaetica, vol. 18, pp. 349–354, 1993.

    Google Scholar 

  8. A. H. Jazwinski, Stochastic Processes and Filtering Theory, New York, Academic Press, pp. 281–286, 1970.

    MATH  Google Scholar 

  9. A. Schaffrin, “Generating robustified Kalman filters for the integration of GPS and INS,” Technical Report, no. 15, Institute of Geodesy, University of Stuttgart, pp. 31–36, 1991.

    Google Scholar 

  10. C. Tsai and L. Kurz, “An adaptive robustizing approach to Kalman filtering,” Automatica, vol. 19, no. 3, pp. 279–288, 1983. [click]

    Article  MATH  Google Scholar 

  11. A. H. Sayed and M. Rupp, “Robust issues in adaptive filtering,” Digital Signal Processing Fundamentals, V. K. Madisetti (ed.), Taylor & Francis, Boca Raton, FL, pp. 20-1–20-20, 2010.

    Google Scholar 

  12. M.-J. Yu, “INS/GPS integration system using adaptive filter for estimating measurement noise variance,” IEEE Transactions on Aerospace and Electronic Systems, vol. 48, no. 2, pp. 1786–1792, 2012. [click]

    Article  Google Scholar 

  13. Y. Zhong, S. Gao, and W. Li, “A Quaternion-based method for SINS/SAR integrated navigation system,” IEEE Transactions on Aerospace and Electronic Systems, vol. 48, no.1, pp. 514–524, 2012. [click]

    Article  Google Scholar 

  14. S. Gao, Y. Zhong, and W. Li, “Robust adaptive filtering method for SINS/SAR integrated navigation system,” Aerospace Science and Technology, vol. 15, no.6, pp. 425–430, 2011. [click]

    Article  Google Scholar 

  15. J. W. Lee and G. K. Lee, “Design of an adaptive filter with a dynamic structure for ECG signal processing,” International Journal of Control, Automation, and Systems, vol. 3, no.1, pp. 137–142, 2005.

    Google Scholar 

  16. H. Bian, Z. Jin, and W. Tian, “Study on GPS attitude determination system aided INS using adaptive Kalman filter,” Measurement Science and Technology, vol. 16, no. 10, pp. 2072–2079, 2005. [click]

    Article  Google Scholar 

  17. C. Hide, T. Moore, and M. Smith, “Adaptive Kalman filtering for low cost INS/GPS,” Journal of Navigation, vol. 56, no. 1, pp. 143–152, 2003. [click]

    Article  Google Scholar 

  18. K. H. Kim, G. I. Jee, C. G. Park, and J.-G. Lee, “The stability analysis of the adaptive fading extended Kalman filter using the innovation covariance,” International Journal of Control, Automation and Systems, vol. 7, no. 1, pp. 49–56, 2009. [click]

    Article  Google Scholar 

  19. Q. Xia, M. Rao, Y. Ying, and X. Shen, “Adaptive fading Kalman filter with an application,” Automatica, vol. 30, no. 8, pp. 1333–1338, 1994. [click]

    Article  MathSciNet  MATH  Google Scholar 

  20. T. S. Lee, “Theory and application of adaptive fading memory Kalman filters,” IEEE Transactions on Circuits and Systems, vol. 35, no. 4, pp. 474–477, 1988. [click]

    Article  MathSciNet  Google Scholar 

  21. S. C. Douglas, “Introduction to adaptive filters,” Digital Signal Processing Fundamentals, V. K. Madisetti (ed.), Taylor & Francis, Boca Raton, FL, pp. 18-1–18-18, 2010.

    Google Scholar 

  22. Y. Zhao, S. Gao, J. Zhang, and Q. Sun, “Robust predictive augmented unscented Kalman filter,” International Journal of Control, Automation and Systems, vol. 12, no. 5, pp. 996–1004, 2014. [click]

    Article  Google Scholar 

  23. Y. Yang, H. He, and G. Xu, “Adaptively robust filtering for kinematic geodetic positioning,” Journal of Geodesy, vol. 75, no. 2, pp. 109–116, 2001. [click]

    Article  MATH  Google Scholar 

  24. W. Ding, J. Wang, and C. Rizos, “Improving adaptive Kalman estimation in GPS/INS integration,” Journal of Navigation, vol. 60, no. 3, pp. 517–529, 2007. [click]

    Article  Google Scholar 

  25. K. Xiong, H. Zhang, and L. Liu, “Adaptive robust extended Kalman filter for nonlinear stochastic systems,” IET Control Theory & Applications, vol. 2, no. 3, pp. 239–250, 2008. [click]

    Article  MathSciNet  Google Scholar 

  26. S. Gao, G. Hu, and Y. Zhong, “Windowing and random weighting based adaptive unscented Kalman filter,” International Journal of Adaptive Control and Signal Processing, vol. 29, no. 2, pp. 201–223, 2015. [click]

    Article  MathSciNet  Google Scholar 

  27. Z. Zheng, “Random weighting method,” Acta Mathematicae Applicatae Sinica, vol. 10, no. 2, pp. 247–253, 1987.

    MathSciNet  MATH  Google Scholar 

  28. S. Gao and Y. Zhong, “Random weighting estimation of kernel density,” Journal of Statistical Planning and Inference, vol. 140, no. 9, pp. 2403–2407, 2010. [click]

    Article  MathSciNet  MATH  Google Scholar 

  29. S. Gao, Z. Feng, Y. Zhong, and B. Shirinzadeh, “Random weighting estimation of parameters in generalized Gaussian distribution,” Information Sciences, vol. 178, no. 9, pp. 2275–2281, 2008. [click]

    Article  MathSciNet  Google Scholar 

  30. S. Gao, J. Zhang, and T. Zhou, “Law of large number for sample mean of random weighting estimate,” Information Sciences, vol. 155, no. 1–2, pp. 151–156, 2003. [click]

    Article  MathSciNet  MATH  Google Scholar 

  31. S. Gao, Z. Zhang, and B. Yang, “The random weighting estimate of quantile process,” Information Sciences, vol. 164, no. 1–4, pp. 139–146, 2004. [click]

    Article  MathSciNet  MATH  Google Scholar 

  32. S. Gao, Y. Zhong, and B. Shirinzadeh, “Random weighting estimation for fusion of multi-dimensional position data,” Information Sciences, vol. 180, no. 24, pp. 4999–5007, 2010. [click]

    Article  MathSciNet  Google Scholar 

  33. S. Gao, Y. Zhong, and W. Li, “Random weighting method for multi-sensor data fusion,” IEEE Sensors Journal, vol. 11, no. 9, pp. 1955–1961, 2011. [click]

    Article  Google Scholar 

  34. S. Gao, Y. Zhong, and C. Gu, “Random weighting estimation of confidence intervals for quantiles,” Australian & New Zealand Journal of Statistics, vol. 55, no. 1, pp. 43–53, 2013. [click]

    Article  MathSciNet  Google Scholar 

  35. S. Gao, Y. Zhong, C. Sang, and B. Shirinzadeh, “Random weighting estimation for quantile processes and negatively associated samples,” Communications in Statistics–Theory and Methods, vol. 43, no. 3, pp. 656–662, 2014. [click]

    Article  MathSciNet  Google Scholar 

  36. G. Hu, S. Gao, Y. Zhong, and C. Gu, “Random weighting estimation of stable exponent,” METRIKA, pp. 1–18, 2013. [click]

    Google Scholar 

  37. G. Hu, S. Gao, Y. Zhong, and C. Gu, “Asymptotic properties of random weighted empirical distribution function,” Communications in Statistics-Theory and Methods, 2015. DOI: 10.1080/036 10926.2013.768669. [click]

    Google Scholar 

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Author information

Authors and Affiliations

  1. School of Automatics, Northwestern Polytechnical University, Xian, 710072, China

    Wenhui Wei & Shesheng Gao

  2. School of Engineering, RMIT University, Bundoora, 3083, Australia

    Yongmin Zhong & Chengfan Gu

  3. Swinburne Research & Development, Swinburne University of Technology, Hawthorn, VIC3122, Australia

    Aleksandar Subic

Authors
  1. Wenhui Wei
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  2. Shesheng Gao
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  3. Yongmin Zhong
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  4. Chengfan Gu
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  5. Aleksandar Subic
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Corresponding author

Correspondence to Shesheng Gao.

Additional information

Recommended by Associate Editor Wen-Hua Chen under the direction of Editor Hyouk Ryeol Choi. The work of this paper is supported by the National Natural Science Foundation of China (Project NO: 61174193).

Weihui Wei is a PhD student at the School of Automatics, Northwestern Polytechnical University, China. His research interests include control theory and engineering, navigation, guidance and control, and information fusion.

Shesheng Gao is a professor at the School of Automatics, Northwestern Polytechnical University, China. His research interests include control theory and engineering, navigation, guidance and control, and information fusion.

Yongmin Zhong is a senior lecturer within the School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Australia. His research interests include virtual reality and haptics, soft tissue modelling and surgery simulation, robotics, mechatronics, optimum estimation and control, and integrated navigation system.

Chengfan Gu is an ARC DECRA fellow within the School of Aerospace, Mechanical and Manufacturing Engineering, RMIT University, Australia. Her current research activity includes computational modelling, micro/nano manufacturing, fatigue and bio/nano mechanics, advanced materials characterization.

Aleksandar Subic is the Deputy Vice-Chancellor (R&D) at Swinburne University of Technology in Melbourne, Australia. Prior to this, he was the Dean of Engineering and Head of School of Aerospace, Mechanical and Manufacturing Engineering at RMIT University in Melbourne, Australia, which incorporates the Sir Lawrence Wackett Aerosapce Centre and the RMIT Advanced Manufacturing Precinct. Concurrent with his academic appointment he was also appointed to the positions of Director of the Society of Automotive Engineers Australasia (SAE-A), Director of the Australian Association of Aerospace and Aviation Industries (AAAI), Education Director of Cooperative Research Centre for Advanced Automotive Technologies (AutoCRC) and is an Executive Committee member of the Global Engineering Deans Council. He has around 25 years of educational and research experience at universities world wide. Professor Subic is the Editor-in-Chief of the International Journal of Sustainable Design and of Journal of Sports Technology (published by Routledge), Associate Editor of International Journal of Vehicle Design and is on a number of international Editorial Boards including European Journal of Engineering Education published by Taylor & Francis.

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Wei, W., Gao, S., Zhong, Y. et al. Random weighting estimation for systematic error of observation model in dynamic vehicle navigation. Int. J. Control Autom. Syst. 14, 514–523 (2016). https://doi.org/10.1007/s12555-014-0333-8

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  • DOI: https://doi.org/10.1007/s12555-014-0333-8

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