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C. Greco and M. Vasile
45. K. Murphy, S. Russell, Rao-Blackwellised particle filtering for dynamic Bayesian networks, in
Sequential Monte Carlo Methods in Practice (Springer, Berlin, 2001)
46. M.K. Pitt, N. Shephard, Filtering via simulation: auxiliary particle filters. J. Amer. Stat. Asso.
94(446), 590–599 (1999)
47. H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications, 2nd edn.
(Springer, Berlin, 1989)
48. B. Ristic, Particle Filters for Random Set Models (Springer, New York, 2013) https://doi.org/
10.1007/978-1-4614-6316-0
49. B. Ristic, S. Arulampalam, N. Gordon, Beyond the Kalman Filter: Particle Filters for Tracking
Applications (Artech House, Norwood, 2004)
50. T.P. Sapsis, G. Athanassoulis, New partial differential equations governing the responseexcitation joint probability distributions of nonlinear systems under general stochastic excitation. Probab. Eng. Mech. 23(2–3), 289–306 (2008). https://doi.org/10.1016/j.probengmech.
2007.12.028
51. S. Sarkka, Bayesian Filtering and Smoothing, 1st edn. (Cambridge University Press, New York,
2013)
52. F.H. Schlee, C.J. Standish, N.F. Toda, Divergence in the Kalman filter. AIAA J. 5(6), 1114–
1120 (1967)
53. S.N. Sharma, A Kolmogorov-Fokker-Planck approach for a stochastic Duffing-van der Pol
system. Differ. Equ. Dyn. Syst. 16(4), 351–377 (2008). https://doi.org/10.1007/s12591-0080019-x
54. A.N. Shiryaev, Probability, 2nd edn. (Springer, Berlin, 1996)
55. D. Simon, Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, 1st edn.
(Wiley-Interscience, Hoboken, 2006)
56. G.L. Smith, S.F. Schmidt, L.A. McGee, Application of statistical filter theory to the optimal
estimation of position and velocity on board a circumlunar vehicle. NASA Technical Report
(1962)
57. C. Snyder, T. Bengtsson, P. Bickel, J. Anderson, Obstacles to high-dimensional particle
filtering. Monthly Weather Rev. 136(12), 4629–4640 (2008)
58. B.D. Tapley, B.E. Schutz, G.H. Born, Statistical Orbit Determination, 1st edn. (Elsevier
Academic, San Diego, 2004)
59. R. Van der Merwe, Sigma-point kalman filters for probabilistic inference in dynamic statespace models. Doctoral Thesis at Oregon Health & Science University (2004)
60. R. Van der Merwe, E.A. Wan, Kalman Filtering and Neural Networks (Wiley, Hoboken, 2002)
61. R. Van Der Merwe, A. Doucet, N. De Freitas, E.A. Wan, The unscented particle filter, in
Advances in Neural Information Processing Systems (2001)
62. P.J. van Leeuwen, Aspects of particle filtering in high-dimensional spaces, in Dynamic DataDriven Environmental Systems Science (Springer, Cham, 2015)
63. E.A. Wan, R. Van der Merwe, The unscented Kalman filter for nonlinear estimation, in
Proceedings of IEEE Adaptive Systems for Signal Processing, Communications, and Control
Symposium (2000). https://doi.org/10.1109/ASSPCC.2000.882463
64. Y. Wu, D. Hu, M. Wu, X. Hu, Unscented Kalman filtering for additive noise case: augmented
versus nonaugmented. IEEE Signal Proc. Lett. 12(5), 357–360 (2005)
65. Y. Wu, D. Hu, M. Wu, X. Hu, A numerical-integration perspective on Gaussian filters. IEEE
Trans. Signal Proc. 54(8), 2910–2921 (2006)
66. P. Zarchan, H. Musoff, F.K. Lu, Fundamentals of Kalman Filtering: A Practical Approach, 3rd
edn. (American Institute of Aeronautics & Astronautics, Reston, 2009)
C. Greco and M. Vasile
45. K. Murphy, S. Russell, Rao-Blackwellised particle filtering for dynamic Bayesian networks, in
Sequential Monte Carlo Methods in Practice (Springer, Berlin, 2001)
46. M.K. Pitt, N. Shephard, Filtering via simulation: auxiliary particle filters. J. Amer. Stat. Asso.
94(446), 590–599 (1999)
47. H. Risken, The Fokker-Planck Equation: Methods of Solution and Applications, 2nd edn.
(Springer, Berlin, 1989)
48. B. Ristic, Particle Filters for Random Set Models (Springer, New York, 2013) https://doi.org/
10.1007/978-1-4614-6316-0
49. B. Ristic, S. Arulampalam, N. Gordon, Beyond the Kalman Filter: Particle Filters for Tracking
Applications (Artech House, Norwood, 2004)
50. T.P. Sapsis, G. Athanassoulis, New partial differential equations governing the responseexcitation joint probability distributions of nonlinear systems under general stochastic excitation. Probab. Eng. Mech. 23(2–3), 289–306 (2008). https://doi.org/10.1016/j.probengmech.
2007.12.028
51. S. Sarkka, Bayesian Filtering and Smoothing, 1st edn. (Cambridge University Press, New York,
2013)
52. F.H. Schlee, C.J. Standish, N.F. Toda, Divergence in the Kalman filter. AIAA J. 5(6), 1114–
1120 (1967)
53. S.N. Sharma, A Kolmogorov-Fokker-Planck approach for a stochastic Duffing-van der Pol
system. Differ. Equ. Dyn. Syst. 16(4), 351–377 (2008). https://doi.org/10.1007/s12591-0080019-x
54. A.N. Shiryaev, Probability, 2nd edn. (Springer, Berlin, 1996)
55. D. Simon, Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches, 1st edn.
(Wiley-Interscience, Hoboken, 2006)
56. G.L. Smith, S.F. Schmidt, L.A. McGee, Application of statistical filter theory to the optimal
estimation of position and velocity on board a circumlunar vehicle. NASA Technical Report
(1962)
57. C. Snyder, T. Bengtsson, P. Bickel, J. Anderson, Obstacles to high-dimensional particle
filtering. Monthly Weather Rev. 136(12), 4629–4640 (2008)
58. B.D. Tapley, B.E. Schutz, G.H. Born, Statistical Orbit Determination, 1st edn. (Elsevier
Academic, San Diego, 2004)
59. R. Van der Merwe, Sigma-point kalman filters for probabilistic inference in dynamic statespace models. Doctoral Thesis at Oregon Health & Science University (2004)
60. R. Van der Merwe, E.A. Wan, Kalman Filtering and Neural Networks (Wiley, Hoboken, 2002)
61. R. Van Der Merwe, A. Doucet, N. De Freitas, E.A. Wan, The unscented particle filter, in
Advances in Neural Information Processing Systems (2001)
62. P.J. van Leeuwen, Aspects of particle filtering in high-dimensional spaces, in Dynamic DataDriven Environmental Systems Science (Springer, Cham, 2015)
63. E.A. Wan, R. Van der Merwe, The unscented Kalman filter for nonlinear estimation, in
Proceedings of IEEE Adaptive Systems for Signal Processing, Communications, and Control
Symposium (2000). https://doi.org/10.1109/ASSPCC.2000.882463
64. Y. Wu, D. Hu, M. Wu, X. Hu, Unscented Kalman filtering for additive noise case: augmented
versus nonaugmented. IEEE Signal Proc. Lett. 12(5), 357–360 (2005)
65. Y. Wu, D. Hu, M. Wu, X. Hu, A numerical-integration perspective on Gaussian filters. IEEE
Trans. Signal Proc. 54(8), 2910–2921 (2006)
66. P. Zarchan, H. Musoff, F.K. Lu, Fundamentals of Kalman Filtering: A Practical Approach, 3rd
edn. (American Institute of Aeronautics & Astronautics, Reston, 2009)