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Annotated BibUography
Reuven Ackner and Thomas Kailath. Complementary models and smoothing. IEEE Transactions on Automatic Control. 34:963-969. 1989.
Presents alternative complementary models for the continuous-time case and investigates the Markovian property of the smoothing error.
Reuven Ackner and Thomas Kailath. Discrete-time complementary models and smoothing. IntemattonalJoumalojControl. 49:1665-1682.1989.
The discrete-time version of the previous reference.
Milton B. Adams. Alan S. Willsky. and Bernard C. Levy. Linear estimation of boundary value stochastic processes-Part I: The role and construction of complementary models. IEEE Transactions on Automatic Control. 29:803-811, 1984.
The first study of smoothing for boundary value models.
Milton B. Adams. Alan S. Willsky. and Bernard C. Levy. Linear estimation of boundary value stochastic processes-Part II: I-D smoothing problems. IEEE Transactions on Automatic Control. 29:811-821. 1984.
A continuation of the previous reference.
100 ANNOTATED BIBLIOGRAPHY
Uri M. Ascher, Robert M. M. MattheiJ, and Robert D. Russell. Numerical Solution oj Boundary Value Problems jor Ordinary Differential Equations. Prentice Hall, Englewood Cliffs, 1988.
A good background source on continuous and discrete boundary value problems.
Faris A. Badawi and Anders Lindquist. A stochastic realization approach to the discrete-time Mayne-Fraser smoothing formula. In Frequency Domain and State Space Methods jor Linear Systems, Christopher I. Byrnes and Anders Lindquist, editors, NorthHolland, Amsterdam, 1986, pages 251-262.
A study of the two-filter smoother.
Faris A. Badawi, Anders Lindquist, and Michele Pavon. A stochastic realization approach to the smoothing problem. IEEE Transactions on Automatic Contro~ 24:878-888, 1979.
The continuous-time version of the previous reference.
Arunabha Bagchi and Hans Westdijk. Smoothing and likelihood ratio for Gaussian boundary value processes. IEEE Transactions on Automatic Contro~ 34:954-962, 1989.
Derives the Hamiltonian equations for two-point boundary value models.
Martin G. Bello, Alan S. Willsky, and Bernard C. Levy. Construction and applications of discrete-time smoothing error models. IntemationalJoumal ojContro~ 50:203-223, 1989.
Derives forward and backward Markov models for the smoothing error and applies these results to map updating problems.
Martin G. Bello, Alan S. Willsky' Bernard C. Levy, and David A. Castanon. Smoothing error dynamics and their use in the solution of smoothing and mapping problems. IEEE Transactions on Injormation Theory, 32:483-495, 1986.
The continuous-time version of the previous reference.
ANNOTATED BIBUOGRAPHY 101
Andrew F. Bennett and W. Paul Budgell. The Kalman smoother for a linear quasi-geostrophic model of ocean circulation. Dynamics of Atmospheres and Oceans, 13:219-267, 1989.
An oceanographic application of smoothing.
Gerald J. Bierman. Fixed interval smoothing with discrete measurements. In.tematiDnalJownal of Control, 18:65-75, 1973.
Uses a version of the second forward-backward algorithm for interpolated smoothing with a continuous state equation and discrete measurements.
Gerald J. Bierman. Sequential square root filtering and smoothing of discrete linear systems. Automatica, 10: 147-158, 1974.
Gives an early version of the first forward-backward algorithm and its square root implementation.
Gerald J. Bierman. Factorization Methods for Discrete Sequential Estimation. Academic Press, New York, 1977.
A standard reference on square root algorithms.
G. J. Bierman. A new computationally efficient fixed-interval, discrete-time smoother. Automatica, 19:503-511, 1983.
Gives a version of the first forward-backward square root algorithm.
Robert F. Brammer, Ralph P. Pass, and James V. White. Bathymetric and oceanographic applications of Kalman filtering techniques. IEEE Transactions on Automatic Control, 28:363-371, 1983.
Smoothing applied to oceanography.
Arthur E. Bryson and Malcolm Frazier. Smoothing for linear and nonlinear dynamic systems. In Proceedings of the Optimwn System Synthesis Conference, 1963, pages 354-364. Reprinted in Linear Least-Squares Estimation, Thomas Kailath, editor, Dowden, Hutchinson and Ross, Stroudsburg, 1977, pages 290-300.
The first presentation of the Hamiltonian equations for the continuous-time smoothed estimate.
102 ANNarAlED BIBLIOGRAPHY
Arthur E. Bryson and W. Earl Hall. Modal methods in optimal control synthesis. In volume 16 of Control and Dynamic Systems, C. T. Leondes, editor, Academic Press, New York, 1980, pages 53-80.
Contains a derivation of all four basic continuous-time smoothing algorithms, without the error covariance equations.
Arthur E. Bryson and Yu-Chi Ho. Applied Optimal Control. Ginn, Waltham, 1969.
An early reference on the second forward-backward smoother.
C. B. Chang, R. H. Whiting, L. Youens, and M. Athans. Application of the fixed-interval smoother to maneuvering trajectory estimation. IEEE Transactions on Automatic Control, 22:876-879, 1977.
An aerospace application of smoothing.
Kenneth C. Chou, Alan S. Willsky, and Albert Benveniste. Multiscale recursive estimation, data fusion, and regularization. IEEE Transactions on Automatic Contro~ 39:464-478, 1994.
A study of the smoothing problem for multiscale stochastic models.
Kenneth C. Chou, Alan S. Willsky, and Ramine Nikoukhah. Multiscale systems, Kalman filters, and Riccati equations. IEEE Transactions on Automatic Contro~ 39:479-492, 1994.
A continuation of the work in the previous reference.
A. B. Cox and A. E. Bryson. Identification by a combined smoothing nonlinear programming algorithm. Automatica, 16:689-694,1980.
Uses smoothing for aircraft parameter estimation.
ANNOTATED BIBLIOGRAPHY 103
Henry Cox. On the estimation of state variables and parameters for noisy dynamic systems. IEEE Transactions on Automatic Control. 9:5-12. 1964.
For the discrete case. one of the original sources of the Hamiltonian equations. and the original source for the second forward-backward smoother (without the error covariance equation).
Uday B. Desai. Howard L. Weinert. and Gene J. Yusypchuk. Discrete-time complementary models and smoothing algorithms: The correlated noise case. IEEE Transactions on Automatic Control. 28:536-539. 1983.
The original source for discrete-time complementary models and for the error covariance equation of the discrete backward-forward smoother.
Robert W. Dijkerman. Ravi R. Mazumdar. and Arunabha Bagchi. Reciprocal processes on a tree-modeling and estimation issues. IEEE Transactions on Automatic ControL 40:330-335. 1995.
Derives a recursive smoothing algorithm for reciprocal processes defined on truncated binary trees.
Christoforos E. Economakos and Howard L. Weinert. Smoothing for random fields modeled by partial differential equations. IEEE Transactions on Automatic ControL 41:575-578. 1996.
Develops a fast FFT-based smoother for multidimensional systems modeled by partial differential equations.
Eric Fabre. New fast smoothers for multiscale systems. IEEE Transactions on Signal Processing. 44: 1893-1911. 1996.
Studies the smoothing problem for multiscale stochastic systems based on the wavelet transform.
Donald C. Fraser and James E. Potter. The optimum linear smoother as a combination of two optimum linear filters. IEEE Transactions on Automatic ControL 14:387-390. 1969.
One of the original references on the two-filter smoother. Uses the Kalman filter as the forward filter.
104 ANNOfATED BIBUOGRAPHY
Gene H. Golub and Charles F. Van Loan. Matrix Computations. Third edition. Johns Hopkins University Press. Baltimore, 1996.
An excellent reference on numerical linear algebra.
Christian Gourieroux and Alain Monfort. Time Series and Dynamic Models. Cambridge University Press. Cambridge. 1997.
Presents econometric applications of fixed-interval smoothing for time series represented by state space models.
P. J. Green and B. W. Silverman. Nonparametric Regression and Generalized Linear Models: A Roughness Penalty Approach. Chapman & Hall. London. 1994.
An excellent treatment of smoothing splines.
Calvin D. Greene and Bernard C. Levy. Some new smoother implementations for discrete-time Gaussian reciprocal processes. IntemationalJoumal ojContro~ 54: 1233-1247, 1991.
Presents a two-filter smoother for reciprocal processes.
Mohinder S. Grewal and Angus P. Andrews. Kalman Filtering. Prentice Hall. Englewood Cliffs, 1993.
A standard reference on Kalman filtering including square root implementations.
Babak Hassibi. Ali H. Sayed. and Thomas Kailath. IndejiniteQuadratic Estimation and Control: A Unified Approach to fI2 and HOO Theories. Society for Industrial and Applied Mathematics. Philadelphia. 1999.
A unified approach to robust estimation and control in the framework of Krein spaces.
Nicholas J. Higham. Accuracy and Stability oj Numerical Algorithms. Society for Industrial and Applied Mathematics, Philadelphia.1996.
An excellent reference on numerical linear algebra.
ANNOTATED BIBLIOGRAPHY 105
Anil K. Jain and Joachim Jasiulek. Fast Fourier transform algorithms for linear estimation. smoothing. and Riccati equations. IEEE Transactions on Acoustics. Speech. and Signal Processing. 31: 1435-1446. 1983.
Gives a nonrecursive. FIT-based smoothing algorithm for time-invariant. discrete autoregressive-moving average models. The smoothing error covariance is not computed.
T. Kailath. Supplement to M A survey of data smoothing". Automatica. 11: 109-111. 1975.
An addendum to Meditch's 1973 survey article.
Thomas Kailath and Paul Frost. An innovations approach to least-squares estimation-Part II: Linear smoothing in additive white noise. IEEE Transactions on Automatic Control. 13:655-660. 1968.
An early reference on the second forward-backward smoother in continuous time.
Thomas Kailath and Lennart Ljung. Two filter smoothing formulae by diagonalization of the Hamiltonian equations. International Journal oj Control, 36: 663-673. 1982.
A study of the two-filter smoother.
Thomas Kailath. Ali H. Sayed. and Babak Hassibi. Linear Estimation. Prentice Hall. Upper Saddle River. 2000.
An excellent and encyclopedic reference on linear least-squares estimation.
Thomas Kailath and Mati Wax. A note on the complementary model of Weinert and Desai. IEEE Transactions on Automatic Control, 29:551-552. 1984.
An alternative derivation of the discrete complementary model.
106 ANNOfATED BIBLIOGRAPHY
Paul G. Kaminski. Square Root FYltering and Smoothing for Discrete Processes. Ph.D. dissertation. Stanford University. Stanford. CA. August 1971.
Presents an early version of the first forward-backward smoother and its square root implementation.
Siem Jan Koopman. Disturbance smoother for state space models. Biometrika, 80: 117-126. 1993.
Rediscovers formulas for estimating the input of a state space model using the discrete second forwardbackward smoother. Discusses applications to time series parameter estimation.
Siem Jan Koopman. Exact initial Kalman filtering and smoothing for non stationary time series models. Journal of the American StatisticalAssociation, 92:1630-1638. 1997.
An attempt to modifY the second forward-backward and two-filter smoothers to handle a diffuse initial condition.
Siem Jan Koopman and Neil Shephard. Exact score for time series models in state space form. Biometrika, 79:823-826. 1992.
An application of smoothing to maximum likelihood parameter estimation.
Alan J. Laub and Arno Linnemann. Hessenberg and Hessenberg/ triangular forms in linear system theory. International Journal of Control, 44: 1523-1547. 1986.
An study of certain condensed forms for state space models.
Robert C. K. Lee. Optimal Estimation, Identification, and ControL MIT Press. Cambridge. 1964.
One of the original sources of the discrete Hamiltonian equations.
ANNOTATED BIBLIOGRAPHY 107
Robert P. Leland. Shape estimation of a circular antenna from observations on the boundary. Multidimensional Systems and Signal Processing, 7:53-63, 1996.
Uses smoothing to estimate defonnation in an antenna.
Bernard C. Levy, Milton B. Adams, and Alan S. Willsky. Solution and linear estimation of 2-D nearest-neighbor models. Proceedings of the IEEE, 7~:627-641, 1990.
Gives a two-filter smoother for nearest-neighbor models.
Bernard C. Levy, Ruggero Frezza, and Arthur J. Krener. Modeling and estimation of discrete-time Gaussian reciprocal processes. IEEE Transactions on Automatic Contro~ 35: 1013-1023, 1990.
Derives a backward-forward smoother for reciprocal processes.
Lennart Ljung and Thomas Kailath. A unified approach to smoothing formulas. Automatica, 12: 147-157, 1976.
Derives smoothing algorithms using results from scattering theory.
David G. Luenberger. Optimization by Vector Space Methods. Wiley, New York, 1969.
A classic reference on Hilbert spaces and orthogonal proj ections.
Mark R. Luettgen and Alan S. Willsky. Multiscale smoothing error models. IEEE Transactions on Automatic Contro~ 40: 173-175, 1995.
Characterizes the error associated with smoothed estimates of multiscale stochastic processes.
D. Q. Mayne. A solution of the smoothing problem for linear dynamic systems. Automatica, 4:73-92, 1966.
One of the original sources of the two-filter smoother, with the Kalman filter as the forward filter. Also the original source of the backward-forward smoother without the error covariance equation.
108 ANNOI'ATED BIBLIOGRAPHY
Stephen R. McReynolds. Fixed interval smoothing: Revisited. Journal of Guidance, Control and Dynwnics, 13:913-921. 1990.
A sUIVey of some aspects of the smoothing problem.
J. S. Meditch. On optimal linear smoothing theory. Information and Control 10:598-615. 1967.
Coins the terms "fixed-interval." "fixed-point." "fixedlag" for the various types of smoothing problems.
J. S. Meditch. A survey of data smoothing for linear and nonlinear dynamic systems. Automatica, 9:151-162, 1973.
An early brief survey of developments in smoothing.
Jerry M. Mendel. White-noise estimators for seismic data processing in oil exploration. IEEE Transactions on Automatic Control 22:694-706, 1977.
Uses the second forward-backward smoother to compute estimates of the input to the state space model.
H. R. Merkus. D. S. G. Pollock. and A. F. de Vos. A synopsis of the smoothing formulae associated with the Kalman filter. Computational Economics. 6: 177-200. 1993.
A survey of discrete smoothing algorithms which overlooks some important results in the engineering literature.
Gunter H. Meyer. Initial Value Methods for Boundary Value Problems. Academic Press. New York. 1973.
A good reference on the use of variable changes to solve boundary value problems.
Srinivas N. Mohan. Gerald J. Bierman. Nancy E. Hamata. and Robert L. Stavert. Seasat orbit refinement for altimetry application. The Journal of the Astronautical Sciences. 28:405-417. 1980.
An aerospace application of smoothing.
ANNOTA"mD BIBUOGRAPHY 109
V. A MOiseenko and O. A Saenko. Using the Kalman smoother to analyse and process oceanographic data. Russian Journal of Numeri.cal Analysis and Mathematical Modelling, 7:241-254, 1992.
Estimates ocean state in a partial differential equation model using spatio-temporal data.
V. A Moiseenko, o. A Saenko, and A. S. Sarkisyan. Ocean state diagnosis based on the Kalman smoother. Russian Journal of NwnericalAnalysis and Mathematical ModeUing, 9:475-487,1994.
A continuation of the work in the previous reference.
Krishan M. Nagpal and Pramod P. Khargonekar. Filtering and smoothing in an Roo setting. IEEE Transactions on Automatic Control, 36: 152-166, 1991.
Shows that linear least-squares and H"" smoothers have the same mathematical structure.
Raymond A Nash and Stanley K. Jordan. Statistical geodesy-An engineering perspective. Proceedings of the IEEE, 66:532-550, 1978.
Uses smoothing to estimate Earth's gravity field.
Raymond A Nash, Joseph F. Kasper, Bard S. Crawford, and Stephen A. Levine. Application of optimal smoothing to the testing and evaluation of inertial navigation systems and components. IEEE Transactions on Automatic Control, 16:806-816, 1971.
An aerospace application of smoothing.
Ramine Nikoukhah, Milton B. Adams, Alan S. Willsky, and Bernard C. Levy. Estimation for boundary-value descriptor systems. Circuits, Systems, and Signal Processing, 8:25-48, 1989.
Derives a two-filter smoother for boundary value deSCriptor models.
110 ANNOTATED BIBLIOGRAPHY
PooGyeon Park and Thomas Kailath. Square-root Bryson-Frazier smoothing algOrithms. IEEE Transactions on Automatic Control, 40:761-766, 1995.
The original source of the second forward-backward square root algorithm.
PooGyeon Park and Thomas Kailath. New square-root algorithms for Kalman filtering. IEEE Transactions on Automatic Control, 40:895-899, 1995.
Presents several new square root implementations for the Kalman filter.
PooGyeon Park and Thomas Kailath. New square-root smoothing algorithms. IEEE Transactions on Automatic Control, 41:727-732, 1996.
The original source of the square root two-filter smoother. Also gives versions of the backward-forward and first forward-backward square root algorithms.
Michele Pavon. Optimal interpolation for linear stochastic systems. SIAM Journal on Control and Optimization, 22:618-629, 1984.
Considers the continuous-time interpolated smoothing problem.
J. O. Ramsay and B. W. Silverman. Functional Data Analysis. Springer, New York, 1997.
An excellent reference on smoothing splines.
H. E. Rauch, F. Tung, and C. T. Striebel. Maximum likelihood estimates of linear dynamic systems. AIAAJournal, 3: 1445-1450, 1965.
Gives the earliest version of the first forward-backward smoother. It is ineffiCient since it reqUires the solution of two Riccati equations.
ANNarATED BIBLIOGRAPHY III
Laurence R. Riddle and Howard L. Weinert. Recursive linear smoothing for dissipative hyperbolic systems. Mechanical Systems and Signal Processing. 2:77-96. 1988.
Develops a smoothing algorithm for vibrating systems. with an acoustics application.
Fred C. Schweppe. Uncertain Dynamic Systems. Prentice Hall. Englewood Cliffs. 1973.
An excellent reference on the properties and applications of stochastic state space models.
R. H. Shumway and D. S. Stoffer. An approach to time series smoothing and forecasting using the EM algorithm. Journal oj TIme Series Analysis. 3:253-264. 1982.
Smoothing applied to parameter estimation.
Victor Solo. Smoothing estimation of stochastic processes: Twofilter formulas. IEEE Transactions on Automatic Control. 27:473-476. 1982.
Derivation and interpretation of the two-filter smoother.
Ahmed H. Tewfik. Bernard C. Levy. and Alan S. Willsky. Internal models and recursive estimation for 2-D isotropic random fields. IEEE Transactions on InJonnanon Theory. 37: 1055-lO66. 1991.
Solves the smoothing problem for a class of isotropic random fields.
George Verghese. Benjamin Friedlander. and Thomas Kailath. Scattering theory and linear least-squares estimation-Part III: The estimates. IEEE Transactions on Automatic Control. 25:794-802. 1980.
Derives smoothing algorithms using results from scattering theory.
112 ANNurATED BIBLIOGRAPHY
Michel Verhaegen and Paul Van Oooren. Numerical aspects of different Kalman filter implementations. IEEE Transactions on Automatic Control 31:907-917. 1986.
One of the few thorough investigations of the comparative numerical properties of several popular (including square root) implementations of the Kalman filter.
Grace Wahba. Spline Models jor Observational Data. Society for Industrial and Applied Mathematics. Philadelphia. 1990.
An excellent study of spline functions and their links with fixed-interval smoothing.
Joseph E. Wall. Alan S. Willsky. and Nils R. Sandell. On the fixedinterval smoothing problem. Stochastics. 5: 1-41. 1981.
A study of the two-filter smoother using backward Markov models.
Keigo Watanabe. A new forward-pass fixed-interval smoother using the U-O information matrix factorization. Automatica. 22:465-475. 1986.
Gives a version of the square root backward-forward algorithm.
K. Watanabe and S. G. Tzafestas. New computationally efficient formula for backward-pass fixed-interval smoother and its UO factOrisation algorithm. IEE Proceedings-D. 136:73-78. 1989.
The origin of the current version of the first forwardbackward smoother and of a Similar version of its square root implementation.
Howard L. Weinert. editor. Reproducing Kernel Hilbert Spaces: Applications in Statistical Signal Processing. Hutchinson Ross. Stroudsburg. 1982.
Reprints of claSSic papers that examine the link between smoothing and spline fitting.
ANNarATED BIBLIOGRAPHY 113
Howard L. Weinert. Sample function properties of a class of smoothed estimates. IEEE Transactions on Automatic Control. 28:803-805. 1983.
Studies the functional form and degree of continuity of sample functions of smoothed estimates in the case of interpolated smoothing with a continuous state equation.
Howard L. Weinert. The complementary model in continuousdiscrete smoothing. In Time Series Analysis oj Irregularly Observed Data. Emanuel Parzen. editor. Springer. Berlin. 1984. pages 353-363.
Derives a complementary model and algorithms for interpolated smoothing with a continuous state equation.
Howard L. Weinert. On the inversion of linear systems. IEEE Transactions on Automatic Control 29:956-958. 1984.
Uses a complementary model to parametrize the set of all possible initial states and inputs that could produce a given output in a continuous state space model.
Howard L. Weinert. A note on effiCient smoothing for boundary value models. International Journal oj Control 53:503-507. 1991.
Derives a backward-forward smoother for continuous two-point boundary value models.
Howard L. Weinert. Smoothing for multipoint boundary value models. Systems and Control Letters. 17:445-452. 1991.
Derives a backward-forward smoother for continuous multipoint boundary value models.
Howard L. Weinert and Edward S. Chomoboy. Smoothing with blackouts. In Modelling and Application oj Stochastic Processes. Uday B. Desai. editor. Kluwer. Boston. 1986. pages 273-278.
Studies the interpolated smoothing problem for a continuous state equation and interrupted continuoustime measurements.
114 ANNarATED BIBLIOGRAPHY
Howard L. Weinert and Uday B. Desai. On complementary models and fixed-interval smoothing. IEEE Transactions on Automatic Control, 26:863-867, 1981.
The original source of the continuous-time complementary model and of the error covariance equation in the continuous backward-forward smoother.
Ehud Weinstein, Alan V. Oppenheim, Meir Feder, and John R. Buck. Iterative and sequential algorithms for multi sensor signal enhancement. IEEE Transactions on Signal Processing, 42:846-859, 1994.
An application of smoothing to parameter estimation.
P. Young, C. Ng, and P. Armitage. A systems approach to recursive economic forecasting and seasonal adjustment. Computers and Mathematics with Applications, 18:481-501, 1989.
Uses an inefficient version of the first forwardbackward algorithm to smooth economic time series.
Author Index
Ackner. R. 27. 63. 79
Adams. M. B .. 96
Andrews. A. P .. 65
Armitage. P .. 11
Ascher. U. M .• 67
Athans. M .• 10
Badawi. F. A.. 63. 79
Bagchi. A.. 9. 97
Bello. M. G .. 63. 79
Bennett. A. F .. 11
Benveniste. A.. 9
Biennan. G. J .. 10.61, 64-65
Brammer. R F .. 11
Bryson. A. E .. 10.26.61.65. 78.80
Buck. J. R. 10
Budgell. W. P .. 11
Castanon. D. A.. 11
Chang. C. B .. 10
Chomoboy. E. S .. 27. 66
Chou. K. C .. 9
Cox. A. B .. 10
Cox. H .. 27. 61
Crawford. B. S .. 10
Desai. U. B .• 26. 61. 77
De Vos. A. F .. 12
Dijkennan. R W .. 9
Economakos. C. E .. 97
Fabre. E .. 9
116
Feder. M .• 10
Fraser. D. C .. 62. 79
Frazier. M .. 26
Frezza. R. 9
FIiedlander. B .. 80
Frost. P .. 78
Golub. G. H .. 65
GouIieroux. C.. II
Green. P. J .. 66
Greene. C. D .• 9
Grewal. M. S .. 65
Hall. W. E .. 80
Hamata. N. E .. 10
Hassibi. B .. 8. 10. 65
Higham. N. J .. 65
Ho. Y.-C .• 61. 65. 78
Jain. A. K.. 63
Jasiulek. J .• 63
Jordan. S. K.. 12
Kailath. T .. 8. 10. 12. 26-27. 63-65. 78-80
Kaminski. P. G .• 61, 64
Kasper. J. F .. 10
AUTIiOR INDEX
Khargonekar. P. P .. 9
Koopman.S.J .. 10.62.67
Krener. A. J .. 9
Laub. A. J .. 8
Lee. R C. K.. 27
Leland. R P .. 12
Levine. S. A.. 10
Levy. B. C .. 9. 63. 79. 96-97
Lindquist. A.. 63. 79
Linnemann. A.. 8
Ljung. L.. 79-80
Luenberger. D. G .. 28
Luettgen. M. R. 9
Mattheij. R M. M .. 67
Mayne. D. Q .. 60. 62. 77-78
Mazumdar. R R. 9
McReynolds. S. R. 12
Meditch. J. S.. 12
Mendel. J. M .. 11.62
Merkus. H. R. 12
Meyer. G. H .. 67
Mohan. S. N .. 10
AUTIiOR INDEX
Moiseenko, V. A, 11
Monfort, A, 11
NagpaI, K M., 9
Nash, R A, 10, 12
Nikoukhah, R, 9, 96
Ng, C., 11
Oppenheim, A V., 10
Park, P., 63-65
Pass, R P., 11
Pavon, M., 66, 79
Pollock, D. S. G., 12
Potter, J. E., 62, 79
Ramsay, J. 0., 66
Rauch, H. E., 61, 77
Riddle, L. R, 11,97
Russell, RD., 67
Saenko, O. A, 11
Sandell, N. R, 62, 79
Sarkisyan, AS., 11
Sayed, A H., 8, 10,65
Schweppe, F. C., 8
Shephard, N., 10
Shumway, R H., 10
Sllvennan, B. W., 66
Solo, V., 79
Stavert, R L., 10
Stoffer, D. S., 10
Striebel, C. T., 61, 77
Tewfik, A H., 97
Tung, F., 61, 77
Tzafestas, S. G., 61, 63
Van Dooren, P., 8, 65
Van Loan, C. F., 65
Verghese, G., 80
Verhaegen, M., 8, 65
Wahba, G., 66
Wall, J. E., 62, 79
Watanabe, K, 61, 63
Wax, M., 26
117
Weinert, H. L., 11,26-28,61, 66, 77, 96-97
Weinstein, E., 10
Westdijk, H., 97
White, J. V., 11
Whiting, R H., 10
118
Willsky. AS .. 9. 62-63. 79. 96-97
Youens. L .. 10
Young. P .. 11
Yusypchuk. G. J .. 26. 61
AUTI-IOR INDEX
Subject Index
backward-forward smoother, 30-36, 46-52, 57-61, 63, 66-67, 70-73, 77, 80-81, 87-96
complementary model, 18,22-23,25-28,81,84,96
complementary state, 18, 22, 25,42,76,83
complementary variables, 16, 19,22,24,82,85
computational complexity, 7-8, 50-52
diffuse initial condition, 66-67
forward-backward smoothers first, 36-40, 52-53, 55, 57,
61, 63-64, 73-74, 77-78, second, 40-42, 53-55, 57,
61-62,64,67,74-76, 78,80
generating variables, 2-4, 13-
16,18,34 input estimate, 62
Kalman fIlter, 41, 44-45, 55, 59-60, 62, 75, 79
information form, 44, 57, 61,78
Markov property, 9, 18, 35, 62-63,72,79
Riccati equation, 30-31, 36, 40-41, 46, 50, 70, 73, 75,78
spline, 66-67
square root implementations, 46-60, 63, 65, 95
fast, 50-52, 55, 57-59, 65, 95
stationarity, 8
two-filter smoother, 42-45, 55-60,62-64,67,76-80, 96-97
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