Bayesian filtering and smoothing

Bayesian Filtering and Smoothing

Volumn , Issue , 2010, Pages 1-232

  Särkkä, Simo ^a,b  

^a AALTO UNIVERSITY   (Finland)

^b TAMPERE UNIVERSITY OF TECHNOLOGY   (Finland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84926148250     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1017/CBO9781139344203     Document Type: Book

References (182)

1. Agamennoni, G., Nieto, J., and Nebot, E. 2011. An outlier-robust Kalman filter. Pages 1551–1558 of: IEEE International Conference on Robotics and Automation (ICRA).
2. Akashi, H. and Kumamoto, H. 1977. Random sampling approach to state estimation in switching environments. Automatica, 13(4), 429–434.
3. Alspach, D. L. and Sorenson, H. W. 1972. Nonlinear Bayesian estimation using Gaussian sum approximations. IEEE Transactions on Automatic Control, 17(4).
4. Andrieu, C., De Freitas, N., and Doucet, A. 2002. Rao-Blackwellised particle filtering via data augmentation. In: Dietterich, T. G., Becker, S., and Ghahramani, Z. (eds.), Advances in Neural Information Processing Systems 14. MIT Press.
5. Andrieu, C., Doucet, A., Singh, S., and Tadic, V. 2004. Particle methods for change detection, system identification, and control. Proceedings of the IEEE, 92(3), 423–438.
6. Andrieu, C. and Thoms, J. 2008. A tutorial on adaptive MCMC. Statistics and Computing, 18(4), 343–373.
7. Andrieu, C., Doucet, A., and Holenstein, R. 2010. Particle Markov chain Monte Carlo methods. The Royal Statistical Society: Series B (Statistical Methodology), 72(3), 269–342.
8. Arasaratnam, I. and Haykin, S. 2009. Cubature Kalman filters. IEEE Transactions on Automatic Control, 54(6), 1254–1269.
9. Arasaratnam, I. and Haykin, S. 2011. Cubature Kalman smoothers. Automatica, 47(10), 2245–2250.
10. Arasaratnam, I., Haykin, S., and Elliott, R. J. 2007. Discrete-time nonlinear filtering algorithms using Gauss–Hermite quadrature. Proceedings of the IEEE, 95(5), 953–977.
11. Arasaratnam, I., Haykin, S., and Hurd, T. R. 2010. Cubature Kalman filtering for continuous-discrete systems: theory and simulations. IEEE Transactions on Signal Processing, 58(10), 4977–4993.
12. Bar-Shalom, Y. and Li, X.-R. 1995. Multitarget-Multisensor Tracking: Principles and Techniques. YBS Publishing.
13. Bar-Shalom, Y., Li, X.-R., and Kirubarajan, T. 2001. Estimation with Applications to Tracking and Navigation. Wiley.
14. Barber, D. 2006. Expectation correction for smoothed inference in switching linear dynamical systems. The Journal of Machine Learning Research, 7, 2515–2540.
15. Barber, D. 2011. Approximate inference in switching linear dynamical systems using Gaussian mixtures. Chapter 8, pages 166–181 of: Barber, D., Cemgil, A. T., and Chiappa, S. (eds.), Bayesian Time Series Models. Cambridge University Press.
16. Berger, J. O. 1985. Statistical Decision Theory and Bayesian Analysis. Springer.
17. Bernardo, J. M. and Smith, A. F. M. 1994. Bayesian Theory. John Wiley & Sons.
18. Bierman, G. J. 1977. Factorization Methods for Discrete Sequential Estimation. Academic Press.
19. Bishop, C. M. 2006. Pattern Recognition and Machine Learning. Springer.
20. Blackman, S. and Popoli, R. 1999. Design and Analysis of Modern Tracking Systems. Artech House Radar Library.
21. Briers, M., Doucet, A., and Maskell, S. 2010. Smoothing algorithms for state-space models. Annals of the Institute of Statistical Mathematics, 62(1), 61–89.
22. Brooks, S., Gelman, A., Jones, G. L., and Meng, X.-L. 2011. Handbook of Markov Chain Monte Carlo. Chapman & Hall/CRC.
23. Cappé, O., Moulines, E., and Rydén, T. 2005. Inference in Hidden Markov Models. Springer.
24. Challa, S., Morelande, M. R., Mušicki, D., and Evans, R. J. 2011. Fundamentals of Object Tracking. Cambridge University Press.
25. Chen, R. and Liu, J. S. 2000. Mixture Kalman filters. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 62(3), 493–508.
26. Cox, H. 1964. On the estimation of state variables and parameters for noisy dynamic systems. IEEE Transactions on Automatic Control, 9(1), 5–12.
27. Crassidis, J. L. and Junkins, J. L. 2004. Optimal Estimation of Dynamic Systems. Chapman & Hall/CRC.
28. Creal, D. 2012. A survey of sequentialMonte Carlo methods for economics and finance. Econometric Reviews, 31(3), 245–296.
29. Crisan, D. and Doucet, A. 2002. A survey of convergence results on particle filtering for practitioners. IEEE Transactions on Signal Processing, 50(3), 736–746.
30. Crisan, D. and Rozovskii, B. (eds.) 2011. The Oxford Handbook of Nonlinear Filtering. Oxford University Press.
31. Daum, F. and Huang, J. 2003. Curse of dimensionality and particle filters. Pages 1979–1993 of: Proceedings of the IEEE Aerospace Conference, vol. 4.
32. Deisenroth, M. P., Huber, M. F., and Hanebeck, U. D. 2009. Analytic moment-based Gaussian process filtering. In: Proceedings of the 26th International Conference on Machine Learning.
33. Deisenroth, M., Turner, R., Huber, M., Hanebeck, U., and Rasmussen, C. 2012. Robust filtering and smoothing with Gaussian processes. IEEE Transactions on Automatic Control, 57(7), 1865–1871.
34. Dempster, A., Laird, N., and Rubin, D. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 39(1), 1–38.
35. Djuric, P. and Miguez, J. 2002. Sequential particle filtering in the presence of additive Gaussian noise with unknown parameters. Pages 1621–1624 of: IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), vol. 2.
36. Douc, R., Garivier, A., Moulines, E., and Olsson, J. 2011. Sequential Monte Carlo smoothing for general state space hidden Markov models. Annals of Applied Probability, 21(6), 2109–2145.
37. Doucet, A., Godsill, S. J., and Andrieu, C. 2000. On sequential Monte Carlo sampling methods for Bayesian filtering. Statistics and Computing, 10(3), 197–208.
38. Doucet, A., De Freitas, N., and Gordon, N. 2001. Sequential Monte Carlo Methods in Practice. Springer.
39. Duane, S., Kennedy, A. D., Pendleton, B. J., and Roweth, D. 1987. Hybrid Monte Carlo. Physics Letters B, 195(2), 216–222.
40. Fearnhead, P. 2002. Markov chain Monte Carlo, sufficient statistics, and particle filters. Journal of Computational and Graphical Statistics, 11(4), 848–862.
41. Fearnhead, P. and Clifford, P. 2003. On-line inference for Hidden Markov models via particle filters. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 65(4), 887–899.
42. Fong, W., Godsill, S. J., Doucet, A., and West, M. 2002. Monte Carlo smoothing with application to audio signal enhancement. IEEE Transactions on Signal Processing, 50(2), 438–449.
43. Fraser, D. and Potter, J. 1969. The optimum linear smoother as a combination of two optimum linear filters. IEEE Transactions on Automatic Control, 14(4), 387–390.
44. Gelb, A. 1974. Applied Optimal Estimation. MIT Press.
45. Gelb, A. and Vander Velde, W. 1968. Multiple-Input Describing Functions and Nonlinear System Design. McGraw-Hill.
46. Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. R. 2004. Bayesian Data Analysis. Second edn. Chapman & Hall.
47. Gilks, W., Richardson, S., and Spiegelhalter, D. (eds.) 1996. Markov Chain Monte Carlo in Practice. Chapman & Hall.
48. Godsill, S. J. and Rayner, P. J. 1998. Digital Audio Restoration: a Statistical Model Based Approach. Springer-Verlag.
49. Godsill, S. J., Doucet, A., and West, M. 2004. Monte Carlo smoothing for nonlinear time series. Journal of the American Statistical Association, 99(465), 156–168.
50. Golub, G. H. and van Loan, C. F. 1996. Matrix Computations. Third edn. The Johns Hopkins University Press.
51. Golub, G. H. and Welsch, J. H. 1969. Calculation of Gauss quadrature rules. Mathematics of Computation, 23(106), 221–230.
52. Gonzalez, R. C. and Woods, R. E. 2008. Digital Image Processing. Third edn. Prentice Hall.
53. Gordon, N. J., Salmond, D. J., and Smith, A. F. M. 1993. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. Pages 107–113 of: IEEE Proceedings on Radar and Signal Processing, vol. 140.
54. Grewal, M. S. and Andrews, A. P. 2001. Kalman Filtering, Theory and Practice Using MATLAB. Wiley.
55. Grewal, M. S., Miyasako, R. S., and Smith, J. M. 1988. Application of fixed point smoothing to the calibration, alignment and navigation data of inertial navigation systems. Pages 476–479 of: Position Location and Navigation Symposium.
56. Grewal, M. S., Weill, L. R., and Andrews, A. P. 2001. Global Positioning Systems, Inertial Navigation and Integration. Wiley.
57. Gupta, N. and Mehra, R. 1974. Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations. IEEE Transactions on Automatic Control, 19(6), 774–783.
58. Gustafsson, F. and Hendeby, G. 2012. Some relations between extended and unscented Kalman filters. IEEE Transactions on Signal Processing, 60(2), 545–555.
59. Haario, H., Saksman, E., and Tamminen, J. 1999. Adaptive proposal distribution for random walk Metropolis algorithm. Computational Statistics, 14(3), 375–395.
60. Haario, H., Saksman, E., and Tamminen, J. 2001. An adaptive Metropolis algorithm. Bernoulli, 7(2), 223–242.
61. Hartikainen, J. and Särkkä, S. 2010. Kalman filtering and smoothing solutions to temporal Gaussian process regression models. Pages 379–384 of: Proceedings of IEEE International Workshop on Machine Learning for Signal Processing (MLSP).
62. Hauk, O. 2004. Keep it simple: a case for using classical minimum norm estimation in the analysis of EEG and MEG data. NeuroImage, 21(4), 1612–1621.
63. Hayes, M. H. 1996. Statistical Digital Signal Processing and Modeling. John Wiley & Sons, Inc.
64. Haykin, S. 2001. Kalman Filtering and Neural Networks. Wiley.
65. Hiltunen, P., Särkkä, S., Nissilä, I., Lajunen, A., and Lampinen, J. 2011. State space regularization in the nonstationary inverse problem for diffuse optical tomography. Inverse Problems, 27, 025009.
66. Ho, Y. C. and Lee, R. C. K. 1964. A Bayesian approach to problems in stochastic estimation and control. IEEE Transactions on Automatic Control, 9(4), 333–339.
67. Hu, X., Schön, T., and Ljung, L. 2008. A basic convergence result for particle filtering. IEEE Transactions on Signal Processing, 56(4), 1337–1348.
68. Hu, X., Schön, T., and Ljung, L. 2011. A general convergence result for particle filtering. IEEE Transactions on Signal Processing, 59(7), 3424–3429.
69. Hürzeler, M. and Kunsch, H. R. 1998. Monte Carlo approximations for general statespace models. Journal of Computational and Graphical Statistics, 7(2), 175–193.
70. Ito, K. and Xiong, K. 2000. Gaussian filters for nonlinear filtering problems. IEEE Transactions on Automatic Control, 45(5), 910–927.
71. Jazwinski, A. H. 1966. Filtering for nonlinear dynamical systems. IEEE Transactions on Automatic Control, 11(4), 765–766.
72. Jazwinski, A. H. 1970. Stochastic Processes and Filtering Theory. Academic Press.
73. Julier, S. J. and Uhlmann, J. K. 1995. A General Method of Approximating Nonlinear Transformations of Probability Distributions. Tech. rept. Robotics Research Group, Department of Engineering Science, University of Oxford.
74. Julier, S. J. and Uhlmann, J. K. 2004. Unscented filtering and nonlinear estimation. Proceedings of the IEEE, 92(3), 401–422.
75. Julier, S. J., Uhlmann, J. K., and Durrant-Whyte, H. F. 1995. A new approach for filtering nonlinear systems. Pages 1628–1632 of: Proceedings of the 1995 American Control, Conference, Seattle, Washington.
76. Julier, S. J., Uhlmann, J. K., and Durrant-Whyte, H. F. 2000. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Transactions on Automatic Control, 45(3), 477–482.
77. Kailath, T., Sayed, A. H., and Hassibi, B. 2000. Linear Estimation. Prentice Hall.
78. Kaipio, J. and Somersalo, E. 2005. Statistical and Computational Inverse Problems. Applied Mathematical Sciences, no. 160. Springer.
79. Kalman, R. E. 1960a. Contributions to the theory of optimal control. Boletin de la Sociedad Matematica Mexicana, 5(1), 102–119.
80. Kalman, R. E. 1960b. A new approach to linear filtering and prediction problems. Transactions of the ASME, Journal of Basic Engineering, 82(1), 35–45.
81. Kalman, R. E. and Bucy, R. S. 1961. New results in linear filtering and prediction theory. Transactions of the ASME, Journal of Basic Engineering, 83(3), 95–108.
82. Kantas, N., Doucet, A., Singh, S., and Maciejowski, J. 2009. An overview of sequential Monte Carlo methods for parameter estimation in general state-space models. In: Proceedings IFAC Symposium on System Identification (SYSID).
83. Kaplan, E. D. 1996. Understanding GPS, Principles and Applications. Artech House.
84. Keeling, M. and Rohani, P. 2007. Modeling Infectious Diseases in Humans and Animals. Princeton University Press.
85. Kelly, C. N. and Anderson, B. D. O. 1971. On the stability of fixed-lag smoothing algorithms. Journal of Franklin Institute, 291(4), 271–281.
86. Kim, C.-J. 1994. Dynamic linear models with Markov-switching. Journal of Econometrics, 60, 1–22.
87. Kitagawa, G. 1987. Non-Gaussian state-space modeling of nonstationary time series. Journal of the American Statistical Association, 82(400), 1032–1041.
88. Kitagawa, G. 1994. The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother. Annals of the Institute of Statistical Mathematics, 46(4), 605–623.
89. Kitagawa, G. 1996. Monte Carlo filter and smoother for Non-Gaussian nonlinear state space models. Journal of Computational and Graphical Statistics, 5(1), 1–25.
90. Lee, R. C. K. 1964. Optimal Estimation, Identification and Control. MIT Press.
91. Lefebvre, T., Bruyninckx, H., and Schutter, J. D. 2002. Comment on “A new method for the nonlinear transformation of means and covariances in filters and estimators” [and authors’ reply]. IEEE Transactions on Automatic Control, 47(8), 1406–1409.
92. Leondes, C. T., Peller, J. B., and Stear, E. B. 1970. Nonlinear smoothing theory. IEEE Transactions on Systems Science and Cybernetics, 6(1), 63–71.
93. Lin, F.-H., Wald, L. L., Ahlfors, S. P., Hämäläinen, M. S., Kwong, K. K., and Belliveau, J. W. 2006. Dynamic magnetic resonance inverse imaging of human brain function. Magnetic Resonance in Medicine, 56(4), 787–802.
94. Lindsten, F. 2011. Rao–Blackwellised Particle Methods for Inference and Identification. Licentiate’s thesis, Linköping University.
95. Liu, J. S. 2001. Monte Carlo Strategies in Scientific Computing. Springer.
96. Liu, J. S. and Chen, R. 1995. Blind deconvolution via sequential imputations. Journal of the American Statistical Association, 90(430), 567–576.
97. Luenberger, D. G. and Ye, Y. 2008. Linear and Nonlinear Programming. Third edn. Springer.
98. Maybeck, P. 1982a. Stochastic Models, Estimation and Control. Vol. 3. Academic Press.
99. Maybeck, P. 1982b. Stochastic Models, Estimation and Control. Vol. 2. Academic Press.
100. Mbalawata, I. S., Särkkä, S., and Haario, H. 2013. Parameter estimation in stochastic differential equations with Markov chain Monte Carlo and non-linear Kalman filtering. Computational Statistics, 28(3), 1195–1223.
101. Meditch, J. S. 1969. Stochastic Optimal Linear Estimation and Control. McGraw-Hill.
102. Milton, J. S. and Arnold, J. C. 1995. Introduction to Probability and Statistics, Principles and Applications for Engineering and the Computing Sciences. McGraw-Hill.
103. Moore, J. B. 1973. Discrete-time fixed-lag smoothing algorithms. Automatica, 9(2), 163–174.
104. Moore, J. B. and Tam, P. 1973. Fixed-lag smoothing of nonlinear systems with discrete measurement. Information Sciences, 6, 151–160.
105. Morf, M., Lévy, B., and Kailath, T. 1978. Square-root algorithms for the continuoustime linear least-square estimation problem. IEEE Transactions on Automatic Control, 23(5), 907–911.
106. Murray, J. D. 1993. Mathematical Biology. Springer.
107. Murray, L. and Storkey, A. 2011. Particle smoothing in continuous time: a fast approach via density estimation. IEEE Transactions on Signal Processing, 59(3), 1017–1026.
108. Neal, R. M. 2011. MCMC using Hamiltonian dynamics. Chapter 5 of: Brooks, S., Gelman, A., Jones, G. L., and Meng, X.-L. (eds.), Handbook of Markov ChainMonte Carlo. Chapman & Hall/CRC.
109. Neal, R. and Hinton, G. 1999. A view of the EM algorithm that justifies incremental, sparse, and other variants. Pages 355–370 of: Jordan, M. I. (ed.), Learning in Graphical Models. MIT Press.
110. Ninness, B. and Henriksen, S. 2010. Bayesian system identification via Markov chain Monte Carlo techniques. Automatica, 46(1), 40–51.
111. Ninness, B., Wills, A., and Schön, T. B. 2010. Estimation of general nonlinear statespace systems. Pages 6371–6376 of: Proceedings of the 49th IEEE Conference on Decision and Control (CDC), Atlanta, USA.
112. Nørgaard, M., Poulsen, N. K., and Ravn, O. 2000. New developments in state estimation for nonlinear systems. Automatica, 36(11), 1627–1638.
113. O’Hagan, A. 1991. Bayes-Hermite quadrature. Journal of Statistical Planning and Inference, 29(3), 245–260.
114. Øksendal, B. 2003. Stochastic Differential Equations: an Introduction with Applications. Sixth edn. Springer-Verlag.
115. Olsson, R., Petersen, K., and Lehn-Schiøler, T. 2007. State-space models: from the EM algorithm to a gradient approach. Neural Computation, 19(4), 1097–1111.
116. Piché, R., Särkkä, S., and Hartikainen, J. 2012. Recursive outlier-robust filtering and smoothing for nonlinear systems using the multivariate Student-t distribution. In: Proceedings of IEEE International Workshop on Machine Learning for Signal Processing (MLSP).
117. Pitt, M. K. and Shephard, N. 1999. Filtering via simulation: auxiliary particle filters. Journal of the American Statistical Association, 94(446), 590–599.
118. Poyiadjis, G., Doucet, A., and Singh, S. 2011. Particle approximations of the score and observed information matrix in state space models with application to parameter estimation. Biometrika, 98(1), 65–80.
119. Proakis, J. G. 2001. Digital Communications. Fourth edn. McGraw-Hill.
120. Punskaya, E., Doucet, A., and Fitzgerald, W. J. 2002. On the use and misuse of particle filtering in digital communications. In: Proceedings of EUSIPCO.
121. Raiffa, H. and Schlaifer, R. 2000. Applied Statistical Decision Theory. John Wiley & Sons, Wiley Classics Library.
122. Rasmussen, C. E. and Williams, C. K. I. 2006. Gaussian Processes for Machine Learning. MIT Press.
123. Rauch, H. E. 1963. Solutions to the linear smoothing problem. IEEE Transactions on Automatic Control, 8(4), 371–372.
124. Rauch, H. E., Tung, F., and Striebel, C. T. 1965. Maximum likelihood estimates of linear dynamic systems. AIAA Journal, 3(8), 1445–1450.
125. Ristic, B., Arulampalam, S., and Gordon, N. 2004. Beyond the Kalman Filter. Artech House.
126. Roberts, G. O. and Rosenthal, J. S. 2001. Optimal scaling for various Metropolis– Hastings algorithms. Statistical Science, 16(4), 351–367.
127. Roweis, S. and Ghahramani, Z. 2001. Learning nonlinear dynamical systems using the expectation–maximization algorithm. Chapter 6, pages 175–220 of: Haykin, S. (ed.), Kalman Filtering and Neural Networks. Wiley-Interscience.
128. Sage, A. P. and Melsa, J. L. 1971. Estimation Theory with Applications to Communications and Control. McGraw-Hill.
129. Saha, S., Ozkan, E., Gustafsson, F., and Smidl, V. 2010. Marginalized particle filters for Bayesian estimation of Gaussian noise parameters. Pages 1–8 of: 13th Conference on Information Fusion (FUSION).
130. Sandblom, F. and Svensson, L. 2012. Moment estimation using a marginalized transform. IEEE Transactions on Signal Processing, 60(12), 6138–6150.
131. Särkkä, S. 2006. Recursive Bayesian Inference on Stochastic Differential Equations. Doctoral dissertation, Helsinki University of Technology.
132. Särkkä, S. 2007. On unscented Kalman filtering for state estimation of continuous-time nonlinear systems. IEEE Transactions on Automatic Control, 52(9), 1631–1641.
133. Särkkä, S. 2008. Unscented Rauch-Tung-Striebel smoother. IEEE Transactions on Automatic Control, 53(3), 845–849.
134. Särkkä, S. 2010. Continuous-time and continuous-discrete-time unscented Rauch- Tung-Striebel smoothers. Signal Processing, 90(1), 225–235.
135. Särkkä, S. 2011. Linear operators and stochastic partial differential equations in Gaussian process regression. In: Proceedings of ICANN.
136. Särkkä, S. and Hartikainen, J. 2010a. On Gaussian optimal smoothing of non-linear state space models. IEEE Transactions on Automatic Control, 55(8), 1938–1941.
137. Särkkä, S. and Hartikainen, J. 2010b. Sigma point methods in optimal smoothing of non-linear stochastic state space models. Pages 184–189 of: Proceedings of IEEE International Workshop on Machine Learning for Signal Processing (MLSP).
138. Särkkä, S. and Hartikainen, J. 2012. Infinite-dimensional Kalman filtering approach to spatio-temporal Gaussian process regression. In: Proceedings of AISTATS 2012.
139. Särkkä, S. and Nummenmaa, A. 2009. Recursive noise adaptive Kalman filtering by variational Bayesian approximations. IEEE Transactions on Automatic Control, 54(3), 596–600.
140. Särkkä, S. and Sarmavuori, J. 2013. Gaussian filtering and smoothing for continuousdiscrete dynamic systems. Signal Processing, 93(2), 500–510.
141. Särkkä, S. and Solin, A. 2012. On continuous-discrete cubature Kalman filtering. Pages 1210–1215 of: Proceedings of SYSID2012.
142. Särkkä, S. and Sottinen, T. 2008. Application of Girsanov theorem to particle filtering of discretely observed continuous-time non-linear systems. Bayesian Analysis, 3(3), 555–584.
143. Särkkä, S., Vehtari, A., and Lampinen, J. 2007a. CATS benchmark time series prediction by Kalman smoother with cross-validated noise density. Neurocomputing, 70(13–15), 2331–2341.
144. Särkkä, S., Vehtari, A., and Lampinen, J. 2007b. Rao-Blackwellized particle filter for multiple target tracking. Information Fusion Journal, 8(1), 2–15.
145. Särkkä, S., Bunch, P., and Godsill, S. J. 2012a. A backward-simulation based Rao- Blackwellized particle smoother for conditionally linear Gaussian models. Pages 506–511 of: Proceedings of SYSID 2012.
146. Särkkä, S., Solin, A., Nummenmaa, A., Vehtari, A., Auranen, T., Vanni, S., and Lin, F.-H. 2012b. Dynamic retrospective filtering of physiological noise in BOLD fMRI: DRIFTER. NeuroImage, 60(2), 1517–1527.
147. Sarmavuori, J. and Särkkä, S. 2012a. Fourier-Hermite Kalman filter. IEEE Transactions on Automatic Control, 57(6), 1511–1515.
148. Sarmavuori, J. and Särkkä, S. 2012b. Fourier-Hermite Rauch-Tung-Striebel Smoother. In: Proceedings of EUSIPCO.
149. Schön, T. and Gustafsson, F. 2003. Particle filters for system identification of statespace models linear in either parameters or states. Pages 1287–1292 of: Proceedings of the 13th IFAC Symposium on System Identification, Rotterdam, The Netherlands.
150. Schön, T., Gustafsson, F., and Nordlund, P.-J. 2005. Marginalized particle filters for mixed linear/nonlinear state-space models. IEEE Transactions on Signal Processing, 53(7), 2279–2289.
151. Schön, T., Wills, A., and Ninness, B. 2011. System identification of nonlinear statespace models. Automatica, 47(1), 39–49.
152. Segal, M. and Weinstein, E. 1989. A new method for evaluating the log-likelihood gradient, the Hessian, and the Fisher information matrix for linear dynamic systems. IEEE Transactions on Information Theory, 35(3), 682–687.
153. Shiryaev, A. N. 1996. Probability. Springer.
154. Shumway, R. and Stoffer, D. 1982. An approach to time series smoothing and forecasting using the EM algorithm. Journal of Time Series Analysis, 3(4), 253–264.
155. Šimandl, M. and Duník, J. 2006. Design of derivative-free smoothers and predictors. Pages 991–996 of: Preprints of the 14th IFAC Symposium on System Identification.
156. Singer, H. 2008. Nonlinear continuous time modeling approaches in panel research. Statistica Neerlandica, 62(1), 29–57.
157. Singer, H. 2011. Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms. AStA Advances in Statistical Analysis, 95(4), 375–413.
158. Snyder, C., Bengtsson, T., Bickel, P., and Anderson, J. 2008. Obstacles to highdimensional particle filtering. Monthly Weather Review, 136(12), 4629–4640.
159. Stengel, R. F. 1994. Optimal Control and Estimation. Dover.
160. Stone, L. D., Barlow, C. A., and Corwin, T. L. 1999. BayesianMultiple Target Tracking. Artech House.
161. Storvik, G. 2002. Particle filters in state space models with the presence of unknown static parameters. IEEE Transactions on Signal Processing, 50(2), 281–289.
162. Stratonovich, R. L. 1968. Conditional Markov Processes and Their Application to the Theory of Optimal Control. Elsevier.
163. Striebel, C. T. 1965. Partial differential equations for the conditional distribution of a Markov process given noisy observations. Journal of Mathematical Analysis and Applications, 11, 151–159.
164. Tam, P., Tam, D., and Moore, J. 1973. Fixed-lag demodulation of discrete noisy measurements of FM signals. Automatica, 9(6), 725–729.
165. Tarantola, A. 2004. Inverse Problem Theory and Methods for Model Parameter Estimation. SIAM.
166. Titterton, D. H. and Weston, J. L. 1997. Strapdown Inertial Navigation Technology. Peter Peregrinus Ltd.
167. Väänänen, V. 2012. Gaussian Filtering and Smoothing Based Parameter Estimation in Nonlinear Models for Sequential Data. Master’s Thesis, Aalto University.
168. Van der Merwe, R. and Wan, E. 2003. Sigma-point Kalman filters for probabilistic inference in dynamic state-space models. In: Proceedings of the Workshop on Advances in Machine Learning.
169. Van der Merwe, R. and Wan, E. A. 2001. The square-root unscented Kalman filter for state and parameter estimation. Pages 3461–3464 of: International Conference on Acoustics, Speech, and Signal Processing.
170. Van der Merwe, R., De Freitas, N., Doucet, A., and Wan, E. 2001. The unscented particle filter. Pages 584–590 of: Advances in Neural Information Processing Systems13.
171. Van Trees, H. L. 1968. Detection, Estimation, and Modulation Theory Part I. John Wiley & Sons.
172. Van Trees, H. L. 1971. Detection, Estimation, and Modulation Theory Part II. John Wiley & Sons.
173. Vihola, M. 2012. Robust adaptive Metropolis algorithm with coerced acceptance rate. Statistics and Computing, 22(5), 997–1008.
174. Viterbi, A. J. 1967. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory, 13(2).
175. Wan, E. A. and Van der Merwe, R. 2001. The unscented Kalman filter. Chapter 7 of: Haykin, S. (ed.), Kalman Filtering and Neural Networks. Wiley.
176. West, M. and Harrison, J. 1997. Bayesian Forecasting and Dynamic Models. Springer- Verlag.
177. Wiener, N. 1950. Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications. John Wiley & Sons.
178. Wills, A., Schön, T. B., Ljung, L., and Ninness, B. 2013. Identification of Hammerstein–Wiener models. Automatica, 49(1), 70–81.
179. Wu, Y., Hu, D., Wu, M., and Hu, X. 2005. Unscented Kalman filtering for additive noise case: augmented versus nonaugmented. IEEE Signal Processing Letters, 12(5), 357–360.
180. Wu, Y., Hu, D., Wu, M., and Hu, X. 2006. A numerical-integration perspective on Gaussian filters. IEEE Transactions on Signal Processing, 54(8), 2910–2921.
181. Ypma, A. and Heskes, T. 2005. Novel approximations for inference in nonlinear dynamical systems using expectation propagation. Neurocomputing, 69(1), 85–99.
182. Zoeter, O. and Heskes, T. 2011. Expectation propagation and generalized EP methods for inference in switching linear dynamical systems. Chapter 7, pages 141–165 of: Bayesian Time Series Models. Cambridge University Press.