Square-Root Sigma-Point Kalman Filters: Standard vs. Spherical Simplex Forms

Juan G. Castrejón-Lozano; Alejandro Dzul; Victor Santibáñez; Pedro Castillo

doi:10.15866/irea.v4i3.10510

Square-Root Sigma-Point Kalman Filters: Standard vs. Spherical Simplex Forms

Juan G. Castrejón-Lozano^(1*), Alejandro Dzul⁽²⁾, Victor Santibáñez⁽³⁾, Pedro Castillo⁽⁴⁾

^(*) Corresponding author

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Abstract

There exists a growing use of Sigma-Point Kalman filters (SPKF) in fields where historically has dominated the Extended Kalman Filter (EKF). The SPKF are superiors to EKF in accuracy estimation and simplicity of implementation. However, their major drawback is due to the relatively poor execution speed compared with respect to the EKF. In order to reduce this problem, a new criterion for selecting a minimum set of sigma points has been proposed. This approach is known as Spherical Simplex Sigma-Points. Despite the relevance of achieving this goal for real-time applications, this approach is practically not discussed in literature. In this paper, we analyse the performance of two variants of classic SPKF with respect to two variants of Spherical Simplex Sigma-Points, all versions have been applied to the three-dimensional position estimation of a mini-helicopter. The results of the comparative analysis are shown through simulations.
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Keywords

Inertial Navigation; Mobile Robots; Nonlinear Filtering; Sigma-Point Kalman Filters

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References

Rudy Negenborn, Robot Localization and Kalman Filters, M.S. dissertation, Utrecht University, Netherlands, 2003.
http://dx.doi.org/10.15420/aer.2015.29.2

Rudolph Van der Merwe, Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models, Ph.D. dissertation, OGI School of Science & Engineering at Oregon Health & Science University, USA, 2004.
http://dx.doi.org/10.1109/icassp.2003.1201778

X. Rong Li, Vesselin P. Jilkov, A Survey of Maneuvering Target Tracking: Approximation Techniques for Nonlinear Filtering, In Proceedings of SPIE Conference on Signal and Data Processing of Small Targets, San Diego, CA, USA, 2004.
http://dx.doi.org/10.1117/12.553357

S. J. Julier, J. Uhlmann, H. Durrant-Whyte, A new approach for filtering nonlinear systems, In Proceedings of the American Control Conference, Seattle, WA, USA, 1995.
http://dx.doi.org/10.1109/acc.1995.529783

S. J. Julier , J. Uhlmann, A New Extension of the Kalman Filter to Nonlinear Systems, In Proc. SPIE - INt. Soc. Opt. Eng, Orlando, FL, USA, 1997.
http://dx.doi.org/10.1117/12.280797

S. J. Julier , J. K. Uhlmann, Reduced Sigma Point Filters for the Propagation of Means and Covariances Through Nonlinear Transformations, In Proc. American Control Conference, 2002.
http://dx.doi.org/10.1109/acc.2002.1023128

Simon J. Julier, The Spherical Simplex Unscented Transformation, in Proceedings of the American Control Conference, Denver, Colorado, USA, June 4-6, 2003.
http://dx.doi.org/10.1109/acc.2003.1243439

Simon Haykin, Kalman Filtering and Neural Networks, (Wiley Inter-Science, New York, 2001).
http://dx.doi.org/10.1002/0471221546

Rudolph van der Merwe, Eric Wan, The Square–Root Unscented Kalman Filter for State and Parameter Estimation, In Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, Salt Lake City, USA, 2001.
http://dx.doi.org/10.1109/icassp.2001.940586

S. J. Julier, J. K. Uhlmann, The Scaled Unscented Transformation, In Proceedings of the American Control Conference, pp. 4555–4559, Anchorage, Alaska, USA, May 8-10, 2002.
http://dx.doi.org/10.1109/acc.2002.1025369

S. J. Julier, J. K. Uhlmann, Unscented Filtering and Nonlinear Estimation, In Proceedings of the IEEE, vol. 92, n. 3, 2004.
http://dx.doi.org/10.1109/jproc.2003.823141

D. Titterton, J. Weston, Strapdown Inertial Navigation Technology, second edition (Ed. Institution of Electrical Engineers, USA, 2004).
http://dx.doi.org/10.1049/pbra017e

R. M. Rogers, J. A. Schetz, Applied Mathematics in Integrated Navigation Systems, second edition (AIAA Education Series, 2003).
http://dx.doi.org/10.2514/4.861598

Crassidis J.L., Sigma-Point Kalman Filtering for Integrated GPS and Inertial Navigation, In AIAA Guidance, Navigation, and Control Conference, San Francisco, CA, USA, 2005.
http://dx.doi.org/10.2514/6.2005-6052

Castillo P., Dzul A., Lozano R., Real-Time Stabilization and Tracking of a Four-Rotor Mini Rotorcraft, IEEE Transactions on Control Systems Technology, vol. 12, n. 4, pp. 510-516, 2004.
http://dx.doi.org/10.1109/tcst.2004.825052

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