Variants of Cubature Kalman Filter

  • Kumar Pakki Bharani Chandra
  • Da-Wei GuEmail author


Cubature Kalman filter (CKF) discussed in the last chapter deals with nonlinear systems with single set of sensors and with Gaussian noise. In this chapter, variants of CKF, namely the cubature information filter (CIF), cubature \(\mathcal{H}_{\infty }\) filter (C\(\mathcal{H}_{\infty }\)F) and cubature \(\mathcal{H}_{\infty }\) information filter (C\(\mathcal{H}_{\infty }\)IF), and their square-root versions, will be explored. Each of these filters is suitable for particular applications. For example, the CIF is suitable for state estimation of nonlinear systems with multiple sensors in the presence of Gaussian noise; the C\(\mathcal{H}_{\infty }\)F is suitable for nonlinear systems with Gaussian or non-Gaussian noises; and finally, the C\(\mathcal{H}_{\infty }\)IF is useful for estimating the states of nonlinear systems with multiple sensors in the presence of Gaussian or non-Gaussian noise.


  1. Anderson BDO, Moore JB (1979) Optimal filtering, vol 21. Prentice-Hall, Englewood Cliffs, pp 22–95zbMATHGoogle Scholar
  2. Arasaratnam I, Haykin S (2009) Cubature kalman filters. IEEE Trans Autom control 54(6):1254–1269MathSciNetCrossRefGoogle Scholar
  3. Bar-Shalom Y, Li XR, Kirubarajan T (2004) Estimation with applications to tracking and navigation: theory algorithms and software. Wiley, New YorkGoogle Scholar
  4. Chandra KB, Gu DW, Postlethwaite I (2013) Square root cubature information filter. IEEE SensJ 13(2):750–758CrossRefGoogle Scholar
  5. Chandra KPB, Gu D-W, Postlethwaite I (2014) A cubature \(H_{\infty }\) filter and its square-root version. Int J Control 87(4):764–776MathSciNetCrossRefGoogle Scholar
  6. Chandra KPB, Gu D-W, Postlethwaite I (2016) Cubature \(H_{\infty }\) information filter and its extensions. Eur J Control 29:17–32MathSciNetCrossRefGoogle Scholar
  7. Eustice RM, Singh H, Leonard JJ, Walter MR (2006) Visually mapping the rms titanic: conservative covariance estimates for slam information filters. Int J Robot Res 25(12):1223–1242CrossRefGoogle Scholar
  8. Grewal M, Andrews A (2001) Kalman filtering: theory and practice using matlabGoogle Scholar
  9. Grewal MS, Andrews AP (2010) Applications of kalman filtering in aerospace 1960 to the present [historical perspectives]. IEEE Control Syst Mag 30(3):69–78MathSciNetCrossRefGoogle Scholar
  10. Hassibi B, Kailath T, Sayed AH (2000) Array algorithms for h/sup/spl infin//estimation. IEEE Trans Autom Control 45(4):702–706CrossRefGoogle Scholar
  11. Ishihara J, Macchiavello B, Terra M (2006) H8 estimation and array algorithms for discrete-time descriptor systems. In: 2006 45th IEEE conference on decision and control. IEEE, pp 4740–4745Google Scholar
  12. Kailath T, Sayed AH, Hassibi B (2000) Linear estimation, vol 1. Prentice Hall, Upper Saddle RiverzbMATHGoogle Scholar
  13. Kurtz MJ, Henson MA (1995) Nonlinear output feedback control of chemical reactors. In: Proceedings of the 1995 American control conference, vol 4 IEEE, pp 2667–2671Google Scholar
  14. Lee D-J (2008) Nonlinear estimation and multiple sensor fusion using unscented information filtering. IEEE Signal Process Lett 15:861–864CrossRefGoogle Scholar
  15. Li W, Jia Y (2010) H-infinity filtering for a class of nonlinear discrete-time systems based on unscented transform. Signal Process 90(12):3301–3307CrossRefGoogle Scholar
  16. Mutambara AG (1998) Decentralized estimation and control for multisensor systems. CRC Press, Boca RatonzbMATHGoogle Scholar
  17. Park P, Kailath T (1995) New square-root algorithms for kalman filtering. IEEE Trans Autom Control 40(5):895–899MathSciNetCrossRefGoogle Scholar
  18. Raol J, Girija G (2002) Sensor data fusion algorithms using square-root information filtering. IEE Proc-Radar Sonar Navig 149(2):89–96CrossRefGoogle Scholar
  19. Rigatos GG (2009) Particle filtering for state estimation in nonlinear industrial systems. IEEE Trans Instrum Meas. 58(11):3885–3900CrossRefGoogle Scholar
  20. Shen X-M, Deng L (1997) Game theory approach to discrete \(h_\infty \) filter design. IEEE Trans Signal Process 45(4):1092–1095CrossRefGoogle Scholar
  21. Sibley G, Sukhatme GS, Matthies LH (2006) The iterated sigma point kalman filter with applications to long range stereo. Robot: Sci Syst 8:235–244Google Scholar
  22. Simon D (2006) Optimal state estimation: Kalman, H infinity, and nonlinear approaches. Wiley, New YorkCrossRefGoogle Scholar
  23. Terra MH, Ishihara JY, Jesus G (2009) Fast array algorithms for \(h_\infty \) information estimation of rectangular discrete-time descriptor systems. In: 2009 IEEE control applications, (CCA) & intelligent control, (ISIC). IEEE, pp 637–642Google Scholar
  24. Tsyganova J, Kulikova M (2013) State sensitivity evaluation within ud based array covariance filters. IEEE Trans Autom Control 58(11):2944–2950MathSciNetCrossRefGoogle Scholar
  25. Uppal A, Ray W, Poore A (1974) On the dynamic behavior of continuous stirred tank reactors. Chem Eng Sci 29(4):967–985CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.GMR Institute of TechnologyRajamIndia
  2. 2.Department of EngineeringUniversity of LeicesterLeicesterUK

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