1 Haug, AJ. Bayesian Estimation and Tracking: A Practical Guide. New York: John Wiley %26 Sons
2 Ito, K, Xiong, K. Gaussian filters for nonlinear filtering problems. IEEE Trans Automat Contr 2000, 45: 910–927.
3 Quine, B, Uhlmann, JK, Durrant‐Whyte, HF. Implicit Jacobians for linearized state estimation in nonlinear systems. Proceedings of the American Control Conference, vol. 10, 1995, 1645–1646.
4 Julier, SJ, Uhlmann, JK, Durrant‐Whyte, HF. A new approach for filtering nonlinear systems. Proceedings of the American Control Conference, vol. 10, 1995, 1628–1632.
5 Julier, SJ. The spherical simplex unscented transformation. Proceedings of the American Control Conference, vol. 3, 2003, 2430–2433.
6 Wilf, HS. Mathematics for the Physical Sciences. New York: John Wiley %26 Sons
7 Ball, JS. Orthogonal polynomials, Gaussian quadratures and PDEs. Comput Sci Eng 1999: 92–95.
8 Press, WH, Teukolsky, SA, Vetterling, WT, Flannery, BP. Numerical Recipes in C. Cambridge, UK: Cambridge University Press
9 McNamee, J, Stenger, F. Construction of fully symmetric numerical integration formulas. Numerische Mathematik 1967, 10: 327–344.
10 Cool, R, Mysovskikh, IP, Schmid, HJ. Cubature formulae and orthogonal polynomials. J Comput Appl Math 2001, 127: 121–152.
11 Cool, R. Advances in multidimensional integration. J Comput Appl Math 2002, 149: 1–12.
12 Lu, J, Darmonfal, DL. Higher‐dimensional integration with Gaussian weight for application in probabilistic design. Siam J Sci Comput 2004, 26: 613–624.
13 Haug, AJ. Bayesian estimation for target tracking, part I: general concepts. WIREs Comput Stat 2012. doi:10.1002/wics.1211.
14 Evans, M, Swartz, T. Approximating Integrals via Monte Carlo and Deterministic Methods. Oxford Statistical Science Series, no. 20. New York, NY: Oxford University Press
15 Gelb, A. Applied Optimal Estimation. Cambridge, MA: The MIT Press
16 Wu, Y, Hu, D, Wu, M, Hu, X. A numerical integration perspective on Gaussian filters. IEEE Trans Signal Process 2006, 54: 2910–2921.
17 Stroud, AK. Approximate Calculations of Multiple Integrals. Englewood Cliffs, NJ: Prentice‐Hall
18 Davis, PJ, Rabinowitz, P. Methods of Numerical Integration. Mineola, NY: Dover Publications
19 Candy, JV. Bayesian Signal Processing: Classical, Modern, and Particle Filter Methods. New York, NY: John Wiley %26 Sons
20 Lerner, UN. Hybrid Bayesian Networks for Reasoning about Complex Systems
, PhD thesis, Stanford University, Stanford, CA; 2002.
21 Julier, SJ, Uhlmann, JK. A general method for approximating nonlinear transformations of probability distributions. Technical Report of Robotics Research Group, Department of Engineering Science, University of Oxford, Oxford, UK; 1996.
22 Julier, SJ. Process Models for the Navigation of High Speed Land Vehicles
, PhD thesis, Wadham College, Oxford, UK; 1997.
23 Julier, SJ, Uhlmann, JK, Durrant‐Whyte, HF. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Automat Contr 2000, 45: 477–482.
24 Lefebvre, T, Bruyninckx, H, DeSchutter, J. Comments on “a new method for the nonlinear transformation of means and covariances in filters and estimators.” IEEE Trans Automat Contr 2002, 47: 1406–1408.
25 Wan, EA, van der Merwe, R. The unscented Kalman filter for nonlinear estimation. Adaptive Systems for Signal Processing, Communications and Control Symposium, 2000, 153–158.
26 van der Merwe, R, Wan, EA. The square‐root unscented Kalman filter for state and parameter estimation. ICASSP 01, vol. 6, 2001, 3461–3464.
27 van Zandt, J. A more robust unscented transform. Proceedings of SPIE, vol. 4473, 2001, 371–379.
28 Julier, SJ. The scaled unscented transform. Proceedings of the American Control Conference, vol. 6, 2002, 4555–4559.
29 Tenne, D, Singh, T. The higher order unscented filter. Proceedings of the American Control Conference, vol. 3, 2003, 2441–2446.
30 Briers, M, Maskell, SR, Wright, R. A Rao‐Blackwellised unscented Kalman filter. Sixth International Conference on Information Fusion
, vol. 1, 2003, 55–61.
31 Banani, SA, Nasnadi‐Shirazi, MA. A new version of unscented Kalman filter. Proc World Acad Sci Eng Technol 2010, 20: 269–324.
32 van de Merwe, R. Sigma‐point Kalman Filters for Probabilistic Inference in Dynamic State‐space Models
, PhD thesis, Oregon Health and Science University, Portland, OR; 2004.
33 Julier, SJ, Uhlmann, JK. Unscented filtering and nonlinear estimation. Proc IEEE 2004, 92: 401–422.
34 Haug, AJ. A tutorial on Bayesian estimation and tracking techniques applicable to nonlinear and non‐Gaussian processes. MITRE Technical Report MTR 05W0000004, MITRE, McLean, VA; 2005.
35 Schei, TS. A finite‐difference approach to linearization in nonlinear estimation algorithms. Proceedings of the American Control Conference, vol. 1, 1995, 114–118.
36 Schei, TS. A finite‐difference approach to linearization in nonlinear estimation algorithms. Automatica 1997, 33: 2053–2058.
37 Norgaard, M, Poulsen, NK, Ravn, O. Advances in derivative‐free state estimation for nonlinear systems. Technical Report of IMM‐REP‐1998‐15, Department of Automation, Technical University of Denmark, Lyngby, Denmark; 2000.