×

zbMATH — the first resource for mathematics

Gaussian sum approximations in nonlinear filtering and control. (English) Zbl 0291.93053

MSC:
93E10 Estimation and detection in stochastic control theory
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Kalman, R.E., A new approach to linear filtering and prediction problems, J. basic eng., 82D, 35-45, (1960)
[2] Sorenson, H.W., Kalman filtering techniques, (), Chap. 5 · Zbl 0178.44402
[3] Wishner, R.P.; Tabaczynski, J.A.; Athans, M., A comparison of three nonlinear filters, Automatica, 5, 487-496, (1969) · Zbl 0214.47303
[4] Cox, H., Recursive nonlinear filtering, ()
[5] (), No. 629, 7, 058:519. 61:629. 78
[6] Ho, Y.C.; Lee, R.C.K., A Bayesian approach to problems in stochastic estimation and control, (), 382-387
[7] Bucy, R.S., Linear and nonlinear filtering, (), 854-864
[8] Wiener, N., The Fourier integral and certain of its applications, (1933), Cambridge University Press Cambridge · JFM 59.0416.01
[9] Alspach, D.L., A Bayesian approximation technique for estimation and control of time-discrete stochastic systems, Ph.D. dissertation UCSD, (1970) · Zbl 0313.93044
[10] Sorenson, H.W.; Alspach, D.L., Recursive Bayesian estimation using Gaussian sums, Automatica, 7, No. 4, (1971) · Zbl 0219.93020
[11] Spragins, J.D., Reproducing distributions for machine learning, Stanford elect. labs, tech. report no. 6103-7, (1963)
[12] Aoki, M., Optimal Bayesian and MIN-MAX control of a class of stochastic and adaptive dynamic systems, (), 77-84
[13] Cameron, A.V., Control and estimation of linear systems with Nongaussian a priori distributions, ()
[14] Lainiotis, D.G.; Lainiotis, D.G., Optimal adaptive estimation: structure and parameter adaptation, (), AC16, 160-170, (1971) · Zbl 0229.68034
[15] Lainiotis, D.G., Optimal state-vector estimation for non-Gaussian initial state vector, IEEE trans. autom. control, AC16, 197-198, (1971)
[16] Lainiotis, D.G., Optimal non-linear estimation, Int. J. control, 14, 1137-1148, (1971) · Zbl 0225.93034
[17] Lo, J.T.H., Finite-dimensional sensor orbits and optimal nonlinear filtering, IEEE trans. inform. theory, IT18, No. 5, (1972)
[18] Park, S.K.; Lainiotis, D.G., Monte-Carlo study of the optimal nonlinear estimator: linear systems with non-Gaussian initial states, Int. J. control, 16, 1029-1040, (1972) · Zbl 0246.93035
[19] Alspach, D.L.; Sorenson, H.W., Nonlinear Bayesian estimation using Gaussian sum approximations, IEEE trans. auto. control, AC17, No. 4, 439-448, (1972) · Zbl 0264.93023
[20] Dreyfus, S.E., Some types of optimal control of stochastic systems, J. SIAM control, ser, A2, 120-134, (1962) · Zbl 0144.12501
[21] Simon, H.A., Dynamic programming under uncertainty with quadratic criterion function, Econometrica, 24, 74-81, (1956) · Zbl 0073.15508
[22] Alspach, D.L.; Sorenson, H.W., Stochastic optimal control for linear but non-Gaussian systems, Int. J. control, 13, 1167-1181, (1971) · Zbl 0219.93027
[23] Alspach, D.L., Dual-control based on approximate a posteriori density functions, () · Zbl 0261.93046
[24] Dajani, M.Z.; Campion, G., Closed loop control design for nonlinear, nonqua-dratic systems, ()
[25] Edison, Tse, Parallel computation of the conditional Mean state estimate for nonlinear systems, () · Zbl 0314.93019
[26] Bucy, R.S.; Senne, K.D., Digital synthesis of nonlinear filters, Automatica, 7, No. 3, 287-298, (1971) · Zbl 0269.93070
[27] de Figueredo, R.J.D.; Jan, Y.O., Spline filters, ()
[28] Center, J.L., Practical nonlinear filtering of discrete observations by generalized least squares approximation of the conditional probability distribution, () · Zbl 0314.93031
[29] Lainiotis, D.G., Adaptive decomposition of mixtures: a unifying approach, (), 104-106 · Zbl 0229.68034
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.