Abstract
Nonlinear filtering is of great importance in many applied areas. As a typical nonlinear filtering algorithm, the unscented Kalman filter (UKF) has the merits such as simplicity in realization, high filtering precision, and good convergence. However, its filtering performance is very sensitive to system model error. To overcome this limitation, this paper presents a new UKF for state estimation in nonlinear systems. This algorithm integrates model prediction into the process of the traditional UKF to improve the filtering robustness. This algorithm incorporates system driving noise in system state by increasing the state space dimension to expand the input of system state information to the system. The system model error is constructed by model prediction to rectify the system estimation from the traditional UKF. Simulation and experimental analyses have been conducted, showing that the proposed filtering algorithm is superior to the existing nonlinear filtering algorithms such as the EKF and traditional UKF in terms of accuracy.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Boutayeb, M., & Aubry, D. (1999). A strong tracking extended Kalman observer for nonlinear discrete-time systems. IEEE Transactions on Automatic Control, 44(8), 1550–1556.
Crassidis, J. L., & Markley, F. L. (1997). Predictive filtering for nonlinear systems. Journal of Guidance Control and Dynamics, 20(3), 566–572.
Ding, W., Wang, J., & Rizos, C. (2007). Improving adaptive Kalman estimation in GPS/INS integration. Journal of Navigation, 60(3), 517–529.
Doucet, A. On sequential simulation-based methods for Bayesian filtering, Technical Report 310. (1998). Department of Engineering, Cambridge University.
Doucet, A., de Freitas, J. F. G., & Gordon, N. J. (2001). An introduction to sequential Monte Carlo methods, sequential Monte Carlo methods in practice. In A. Doucet, J. F. G. de Freitas & N. J. Gordon (Eds.). New York: Springer.
Einicke, G. A. (2012). Smoothing, filtering and prediction - estimating the past, present and future. Rijeka, Croatia: InTech.
Fang, J., & Gong, X. (2010). Predictive iterated Kalman filter for INS/GPS integration and its application to SAR motion compensation. IEEE Transactions on Instrumentation and Measurement, 59(4), 909–915.
Gao, S., Zhong, Y., & Li, W. (2011). Robust adaptive filtering method for SINS/SAR integrated navigation system. Aerospace Science and Technology, 15(6), 425–430.
Gao, S., Hu, G., & Zhong, Y. (2015). Windowing and random weighting-based adaptive unscented Kalman filter. International Journal of Adaptive Control and Signal Processing, 29(2), 201–223.
Goldenstein, S. (2004). A gentle introduction to predictive filters. Revista de Informática Teórica e Aplicada (RITA), XI (1), 61–89.
Huang, R., Patwardhan, S. C., & Biegler, L. T. (2013). Robust stability of nonlinear model predictive control with extended Kalman filter and target setting. International Journal of Robust and Nonlinear Control, 23(11), 1240–1264.
Julier, S. (1998). A skewed approach to filtering. Proceedings of SPIE, 3373, 271–282.
Julier, S. J, & Uhlmann, J. K. (1997). A new extension of the Kalman filter to nonlinear systems. Proceedings of SPIE, 3068, 182–193.
Julier, S. J., & Uhlmann, J. K. (2004). Unscented filtering and nonlinear estimation. Proceedings of The IEEE, 92(3), 401–422.
Julier, S. J., Uhlmann, J. K., & Durrant-Whyte, H. F. (1995). A new approach for filtering nonlinear systems. In: The Proceedings of the American Control Conference (pp. 1628–1632). Seattle, Washington.
Jwo, D. J., & Lai, S. Y. (2009). Navigation integration using the fuzzy strong tracking unscented Kalman filter. Journal of Navigation, 62(2), 303–322.
Oppenheim, G., Philippe, A., & de Rigal, J. (2008). The particle filters and their applications. Chemometrics and Intelligent Laboratory Systems, 91(1), 87–93.
Pan, Q., Yang, F., Ye, L., Liang, Y., & Cheng, Y. (2005). Survey of a kind of nonlinear filters - UKF. Control and Decision, 20(5), 481–489.
Sayed, A. H., & Rupp, M. (2010). Robust issues in adaptive filtering. In V. K. Madisetti (Ed.), Digital signal processing fundamentals (Vol. 20, pp. 1–20). Boca Raton, FL: Taylor & Francis.
Van der Merwe, R., Doucet, A., De Freitas, N., & Wan, E. (2000). The unscented particle filter. In: Advances in neural information processing systems (Vol. 4, pp. 351–357).
Wang, L. (2006). Fixed parameter estimation method using Gaussian particle filter. Lecture Notes in Computer Science, 4115/2006, 121–129.
Yang, Y., & Cui, X. (2008). Adaptively robust filter with multi adaptive factors. Survey Review, 40(309), 260–270.
Yang, Y., & Gao, W. (2006). An optimal adaptive Kalman filter. Journal of Geodesy, 80(4), 177–183.
Yang, W. B., & Li, S. Y. (2011). Autonomous navigation filtering algorithm for spacecraft based on strong tracking UKF. Systems Engineering and Electronics, 33(11), 2485–2491.
Yang, Y., He, H.-B., & Xu, G. (2001). Adaptively robust filtering for kinematic geodetic positioning. Journal of Geodesy, 75(2–3), 109–116.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Gao, S., Zhao, Y., Zhong, Y., Subic, A., Jazar, R. (2016). Nonlinear Filtering Based on Model Prediction. In: Jazar, R., Dai, L. (eds) Nonlinear Approaches in Engineering Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-27055-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-27055-5_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-27053-1
Online ISBN: 978-3-319-27055-5
eBook Packages: EngineeringEngineering (R0)