Optimal state estimation: Kalman, H∞, and nonlinear approaches

Optimal State Estimation: Kalman, H∞, and Nonlinear Approaches

Volumn , Issue , 2006, Pages 1-526

  Simon, Dan ^a  

^a CLEVELAND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

FILTRATION; KALMAN FILTERS; MATLAB; STATE ESTIMATION;

CONSTRAINED STATE ESTIMATION; ESTIMATION TECHNIQUES; GRADUATE LEVEL COURSE; INTUITIVE UNDERSTANDING; OPTIMAL STATE ESTIMATION; REDUCED-ORDER FILTERING; ROBUST KALMAN FILTERING; SCIENCE AND ENGINEERING;

ESTIMATION;

EID: 84889830739     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/0470045345     Document Type: Book

References (381)

1. H. Abou-Kandil, G. Freiling, V. Ionescu, and G. Jank, Matrix Riccati Equations in Control and Systems Theory, Birkhauser, Boston, Massachusetts, 2003.
2. V. Aidala and S. Hammel, "Utilization of modified polar coordinates for bearings-only tracking," IEEE Transactions on Automatic Control, AC-28(3), pp. 283-294 (March 1983).
3. B. Akin, U. Orguner, and A. Ersak, "State estimation of induction motor using unscented Kalman filter," Conference on Control Applications, pp. 915-919 (June 2003).
4. H. Alexander, "State estimation for distributed systems with sensing delay," Proceedings of the SPIE, Data Structures and Target Classification, 1470, pp. 103-111 (1991).
5. D. Alspach and H. Sorenson, "Nonlinear Bayesian estimation using Gaussian sum approximations," IEEE Transactions on Automatic Control, AC-17(4), pp. 439-448 (August 1972).
6. D. Alspach, "Gaussian sum approximations in nonlinear filtering and control," Information Sciences, 7, pp. 271-290 (1974).
7. D. Alspach, "A parallel filtering algorithm for linear systems with unknown time varying noise statistics," IEEE Transactions on Automatic Control, AC-19(5), pp. 552-556 (October 1974).
8. B. Anderson and J. Moore, Optimal Filtering, Prentice-Hall, Englewood Cliffs, New Jersey, 1979.
9. A. Andrews, "A square root formulation of the Kalman covariance equations," AIAA Journal, 6(6), pp. 1165-1166 (June 1968).
10. C. Andrieu, A. Doucet, S. Singh, and V. Tadic, "Particle methods for change detection, system identification, and control," Proceedings of the IEEE, 92(3), pp. 42-438 (March 2004).
11. A. Antoulas, Mathematical System Theory, Springer-Verlag, New York, 1991.
12. M. Aoki, "Optimal Bayesian and min-max control of a class of stochastic and adaptive dynamic systems," Symposium on Systems Engineering for Control System Design, pp. 77-84 (1965).
13. M. Aoki, Optimization of Stochastic Systems, Academic Press, New York, 1967.
14. J. Aranda, J. De La Cruz, S. Dormido, P. Ruiperez, and R. Hernandez, "Reduced-order Kalman filter for alignment," Cybernetics and Systems, 25, pp. 1-16 (1994).
15. M. Aralampalam, S. Maskell, N. Gordon, and T. Clapp, "A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking," IEEE Transactions on Signal Processing, 50(2), pp. 174-188 (February 2002).
16. M. Athans, R. Wishner, and A. Bertolini, "Suboptimal state estimation for continuous-time nonlinear systems from discrete measurements," IEEE Transactions on Automatic Control, AC-13(5), pp. 504-514 (October 1968).
17. M. Athans, R. Whiting, and M. Gruber, "A suboptimal estimation algorithm with probabilistic editing for false measurements with applications to target tracking with wake phenomena," IEEE Transactions on Automatic Control, AC-22(3), pp. 372-384 (June 1977).
18. K. Atkinson, An Introduction to Numerical Analysis, John Wiley & Sons, New York, 1989.
19. E. Bai, K. Nagpal, and R. Tempo, "Bounded error parameter estimation: Noise models, recursive algorithms and Hoc optimality," American Control Conference, pp. 3065-3069, June 1995.
20. A. Balakrishnan, Kalman Filtering Theory, Optimization Software, New York, 1987.
21. J. Ballabrera-Poy, A. Busalacchi, and R. Murtugudde, "Application of a reduced-order Kalman filter to initialize a coupled atmosphere-ocean model: Impact on the prediction of El Nino," Journal of Climate, 14, pp. 1720-1737 (April 2001).
22. R. Banavar and J. Speyer, "A linear-quadratic game approach to estimation and smoothing," American Control Conference, pp. 2818-2822 (1991).
23. R. Banavar, "A game theoretic approach to linear dynamic estimation," Doctoral Dissertation, University of Texas at Austin, May 1992.
24. I. Bar-Itzhack and Y. Medan, "Efficient square root algorithm for measurement update in Kalman filtering," Journal of Guidance, Control, and Dynamics, 6(3), pp. 129-134 (May 1983).
25. Y. Bar-Shalom, "Tracking methods in a multitarget environment," IEEE Transactions on Automatic Control, AC-23(4), pp. 618-626 (August 1978).
26. Y. Bar-Shalom and X. Li, Multitarget-Multisensor Tracking: Principles and Techniques, YBS Publishing, Storrs, Connecticut, 1995.
27. Y. Bar-Shalom and X. Li, Estimation and Tracking: Principles, Techniques, and Software, YBS Publishing, Storrs, Connecticut, 1998.
28. Y. Bar-Shalom, X. Li, and T. Kirubarajan, Estimation with Applications to Tracking and Navigation, John Wiley & Sons, New York, 2001.
29. Y. Bar-Shalom, "Update with out-of-sequence measurements in tracking: Exact solution," IEEE Transactions on Aerospace and Electronic Systems, 38(3), pp. 769-778 (July 2002).
30. 2 filtering for uncertain linear systems: LMI based methods with parametric Lyapunov functions," Systems and Control Letters, 54(3), pp. 251-262 (March 2005).
31. O. Bas, B. Shafai, and S. Linder, "Design of optimal gains for the proportional integral Kalman filter with application to single particle tracking," IEEE Conference on Decision and Control, pp. 4567-4571 (December 1999).
32. R. Bass, V. Norum, and L. Swartz, "Optimal multichannel nonlinear filtering," Journal of Mathematical Analysis and Applications, 16(1), pp. 152-164 (1966).
33. R. Battin, "A statistical optimizing navigation procedure for space flight," American Rocket Society Journal, 32, pp. 1681-1696 (November 1962).
34. R. Battin, Astronautical Guidance, McGraw-Hill, New York, 1964.
35. R. Battin, "Space guidance evolution - A personal narrative," Journal of Guidance, 5(2), pp. 97-110 (March-April 1982).
36. J. Bay, Fundamentals of Linear State Space Systems, McGraw-Hill, New York, 1999.
37. J. Bellantoni and K. Dodge, "A square root formulation of the Kalman-Schmidt filter," AIAA Journal, 5, pp. 1309-1314, 1967.
38. R. Bellman, Introduction to Matrix Analysis, McGraw-Hill, New York, 1960.
39. R. Bellman, Adaptive Control Processes: A Guided Tour, Princeton University Press, Princeton, New Jersey, 1961.
40. R. Bellman, "Some consequences of the nonnegativity of the elements of the matrix exponential," Nonlinear Analysis, Theory, Methods and Applications, 4(4), pp. 735-736 (1980).
41. T. Benedict and G. Bordner, "Synthesis of an optimal set of radar track-while-scan smoothing equations," IRE Transactions on Automatic Control, AC-7(4), pp. 27-32 (July 1962).
42. D. Bernstein and D. Hyland, "The optimal projection equations for reduced-order state estimation," IEEE Transactions on Automatic Control, AC-30(6), pp. 583-585 (June 1985).
43. D. Bernstein and W. Haddad, "Steady-state Kalman filtering with an H∞ error bound," Systems and Control Letters, 12, pp. 9-16 (1989).
44. D. Bernstein, Matrix Mathematics, Princeton University Press, Princeton, New Jersey, 2005.
45. M. Bettayeb and D. Kavranoglu, "Reduced order H∞ filtering," American Control Conference, pp. 1884-1888 (June 1994).
46. G. Bierman, "A comparison of discrete linear filtering algorithms," IEEE Transactions on Aerospace and Electronic Systems, AES-9(1), pp. 28-37 (January 1973).
47. G. Bierman, "Measurement updating using the U-D factorization," Automatica, 12(4), pp. 375-382 (July 1976).
48. G. Bierman and C. Thornton, "Numerical comparison of Kalman filter algorithms: Orbit determination case study," Automatica, 13(1), pp. 23-35 (January 1977).
49. G. Bierman, Factorization Methods for Discrete Sequential Estimation, Academic Press, San Diego, California, 1977.
50. P. Billingsley, Probability and Measure, Wiley-Interscience, New York, 1995.
51. R. Bitmead, M. Gevers, I. Petersen, and R. Kaye, "Monotonicity and stabiliz-ability properties of solutions of the Riccati difference equation: Propositions, lemmas, theorems, fallacious conjectures and counterexamples," Systems and Control Letters, 5(5), pp. 309-315 (April 1985).
52. S. Bittanti, A. Laub, and J. Willems (eds.), The Riccati Equation, Springer-Verlag, New York, 1991.
53. A. Bjorck, "Solving linear least squares problems by Gram-Schmidt orthogo-nalization," BIT, 7, pp. 1-21 (1967).
54. S. Blackman and R. Popoli, Design and Analysis of Modern Tracking Systems, Artech House, Dedham, Massachusetts, 1999.
55. R. Booton, "An optimization theory for time-varying linear systems with non-stationary statistical inputs," Proceedings of the IRE, 40, pp. 977-981 (August 1952).
56. P. Borjesson and C. Sundberg, "Simple approximations of the error function Q(x) for communications applications," IEEE Transactions on Communications, COM-27(3), pp. 639-643 (March 1979).
57. S. Bozic, Digital and Kalman Filtering, Halsted Press, New York, 1994.
58. K. Brammer and G. Siffling, Kalman-Bucy Filters, Artech House, Dedham, Massachusetts, 1989.
59. P. Brockwell and R. Davis, Time Series: Theory and Methods, Springer-Verlag, New York, 1991.
60. E. Brookner, Tracking and Kalman Filtering Made Easy, John Wiley & Sons, New York, 1998.
61. R. Brown and P. Hwang, Introduction to Random Signals and Applied Kalman Filtering, John Wiley & Sons, New York, 1996.
62. A. Bryson and D. Johanson, "Linear filtering for time-varying systems using measurements containing colored noise," IEEE Transactions on Automatic Control, AC-10(1), pp. 4-10 (January 1965).
63. A. Bryson and L. Henrikson, "Estimation using sampled data containing sequentially correlated noise," Journal of Spacecraft and Rockets, 5(6), pp. 662-665 (June 1968).
64. R. Bucy, "Nonlinear filtering," IEEE Transactions on Automatic Control, 10(1), p. 198 (January 1965).
65. R. Bucy, "Global theory of the Riccati equation," Journal of Computer and System Sciences, 1, pp. 349-361 (December 1967).
66. R. Bucy and P. Joseph, Filtering for Stochastic Processes with Applications to Guidance, John Wiley & Sons, New York, 1968.
67. R. Bucy, "Bayes theorem and digital realizations for non-linear filters," The Journal of the A stronautical Sciences, 17(2), pp. 80-94 (September-October 1969).
68. R. Bucy and K. Senne, "Digital synthesis of non-linear filters," Automatica, 7(3), pp. 287-298 (May 1971).
69. J. Burl, "A reduced order extended Kalman filter for sequential images containing a moving object," IEEE Transactions on Image Processing, 2(3), pp. 285-295 (July 1993).
70. J. Burl, Linear Optimal Control, Addison-Wesley, Reading, Massachusetts, 1999.
71. P. Caines, Linear Stochastic Systems, John Wiley & Sons, New York, 1988.
72. A. Cameron, "Control and estimation of linear systems with nongaussian a priori distributions," Sixth Annual Allerton Conference on Circuit and System Theory (1968).
73. M. Campbell and S. Brunke, "Nonlinear estimation of aircraft models for online control customization," IEEE Aerospace Conference, pp. 621-628 (2001).
74. N. Carlson, "Fast triangular formulation of the square root filter," AIAA Journal, 11(9), pp. 1259-1265 (September 1973).
75. J. Carpenter, P. Clifford, and P. Fearnhead, "Improved particle filter for nonlinear problems," IEE Proceedings Part F: Radar and Sonar Navigation, 146, pp. 2-7 (February 1999).
76. D. Catlin, Estimation, Control, and the Discrete Kalman Filter, SpringerVerlag, New York, 1989.
77. S. Chandrasekhar, "On the radiative equilibrium of a stellar atmosphere, Part XXI," The Astrophysical Journal, 106, pp. 152-216 (1947).
78. S. Chandrasekhar, "On the radiative equilibrium of a stellar atmosphere, Part XXII," The Astrophysical Journal, 107, pp. 48-72 (1948).
79. S. Charleston and M. Azimi-Sadjadi, "Reduced order Kalman filtering for the enhancement of respiratory sounds," IEEE Transactions on Biomedical Engineering, 43(4), pp. 421-424 (April 1996).
80. C. Chen, Linear System Theory and Design, Oxford University Press, 1999.
81. G. Chen, Approximate Kalman Filtering, World Scientific, Singapore, 1993.
82. H. Chen, Recursive Estimation and Control for Stochastic Systems, John Wiley & Sons, New York, 1985.
83. T. Chia, Parameter Identification and State Estimation of Constrained Systems, Doctoral Dissertation, Case Western Reserve University, Cleveland, Ohio, 1985.
84. C. Chui and G. Chen, Kalman Filtering with Real-Time Applications, Springer-Verlag, New York, 1987.
85. S. Cohn and R. Todling, "Approximate data assimilation scheme for stable and unstable dynamics," Journal of the Meteorological Society of Japan, 74(1), pp. 63-75 (1996).
86. H. Cox, "On the estimation of state variables and parameters for noisy dynamic systems," IEEE Transactions on Automatic Control, AC-9(1), pp. 5-12 (January 1964).
87. H. Coxeter, Regular Polytopes, Dover, New York, 1973.
88. J. Crassidis and J. Junkins, Optimal Estimation of Dynamic Systems, CRC Press, New York, 2004.
89. D. Crisan and A. Doucet, "A survey of convergence results on particle filtering methods for practitioners," IEEE Transactions on Signal Processing, 50(3), pp. 736-746 (March 2002).
90. J. Darragh and D. Looze, "Noncausal minimax linear state estimation for systems with uncertain second-order statistics," IEEE Transactions on Automatic Control, AC-29(6), pp. 555-557 (June 1984).
91. M. Davis, Linear Estimation and Stochastic Control, Chapman & Hall, London, 1977.
92. R. de Figueiredo and Y. Jan, "Spline filters," Symposium on Nonlinear Estimation Theory and Its Applications, pp. 127-138 (1971).
93. B. de Finetti, Theory of Probability: A Critical Introductory Treatment, John Wiley & Sons, New York, 1974.
94. N. de Freitas, "Rao-Blackwellised particle filtering for fault diagnosis," IEEE Aerospace Conference, pp. 1767-1772 (2002).
95. R. Deutsch, Estimation Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1965.
96. L. Devroye and G. Lugosi, Combinatorial Methods in Density Estimation, Springer-Verlag, New York, 2001.
97. P. Dewallef and O. Leonard, "On-line performance monitoring and engine diagnostic using robust Kalman filtering techniques," ASME Turbo Expo, Paper GT2003-38379 (2003).
98. P. Dewallef, O. Leonard, and K. Mathioudakis, "On-line aircraft engine diagnostic using a soft-constrained Kalman filter," ASME Turbo Expo, Paper GT2004-53539 (2004).
99. F. Deza, E. Busvelle, J. Gauthier, and D. Rakotopara, "High gain estimation for nonlinear systems," Systems and Control Letters, 18, pp. 295-299 (1992).
100. G. Diderrich, "The Kalman filter from the perspective of the Goldberger-Thiel estimators," The American Statistician, 39(3), pp. 193-198 (August 1985).
101. G. Didinsky, Z. Pan, and T. Basar, "Parameter identification for uncertain plants using H∞ methods," Automatica, 31(9), pp. 1227-1250 (September 1995).
102. A. Doucet, N. de Freitas, and N. Gordon (eds.), Sequential Monte Carlo Methods in Practice, Springer-Verlag, New York, 2001.
103. W. Duncan, "Some devices for the solution of large sets of simultaneous linear equations (with an appendix on the reciprocation of partitioned matrices)," The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Seventh Series, 35, pp. 660-670 (1944).
104. P. Dyer and S. McReynolds, "Extension of square-root filtering to include process noise," Journal of Optimization Theory and Applications, 3(6), pp. 444-459 (1969).
105. V. Fadeeva, Computational Methods of Linear Algebra, Dover, New York, 1959.
106. R. Feynman, R. Leighton, and M. Sands, The Feynman Lectures on Physics: Volume 1, Addison-Wesley, Reading, Massachusetts, 1963.
107. R. Fitzgerald, "Divergence of the Kalman filter," IEEE Transactions on Automatic Control, AC-16, pp. 736-747 (December 1971).
108. R. Fletcher, Practical Methods of Optimization - Volume 2: Constrained Optimization, John Wiley k. Sons, New York, 1981.
109. S. Fomin and I. Gelfand, Calculus of Variations, Dover, New York, 2000.
110. D. Fräser and J. Potter, "The optimum linear smoother as a combination of two optimum linear filters," IEEE Transactions on Automatic Control, 14(4), pp. 387-390 (August 1969).
111. B. Friedland and I. Bernstein, "Estimation of the state of a nonlinear process in the presence of nongaussian noise and disturbances," Journal of the Franklin Institute, 281(6), pp. 455-480 (June 1966).
112. B. Friedland, "On the properties of reduced-order Kalman filters," IEEE Transactions on Automatic Control, 34(3), pp. 321-324 (March 1989).
113. C. Gauss, Theory of Motion of the Heavenly Bodies Moving About the Sun in Conic Sections: A Translation of Theoria Motus, Dover, New York, 2004.
114. J. De Geeter, H. Van Brüssel, and J. De Schutter, "A smoothly constrained Kalman filter," IEEE Transactions on Pattern Analysis and Machine Intelligence, 19(10), pp. 1171-1177 (October 1997).
115. A. Gelb (ed.), Applied Optimal Estimation, MIT Press, Cambridge, Massachusetts, 1974.
116. W. Gilks and C. Berzuini, "Following a moving target - Monte Carlo inference for dynamic Bayesian models," Journal of the Royal Statistical Society, B, 63, pp. 127-146 (2001).
117. P. Gill, W. Murray, and M. Wright, Practical Optimization, Academic Press, New York, 1981.
118. L. Glielmo, P. Marino, R. Setola, and F. Vasca, "Reduced Kalman filtering for indirect adaptive control of the induction motor," International Journal of Adaptive Control and Signal Processing, 8, pp. 527-541 (1994).
119. G. Golub, "Numerical methods for solving linear least squares problems," Numerische Mathematik, 7, pp. 206-216 (1965).
120. G. Golub and C. Van Loan, Matrix Computations, The Johns Hopkins University Press, Baltimore, Maryland, 1989.
121. G. Goodwin and K. Sin, Adaptive Filtering, Prediction and Control, Prentice-Hall, Englewood Cliffs, New Jersey, 1984.
122. G. Goodwin, M. Seron, and J. De Dona, Constrained control and estimation, Springer-Verlag, London, 2005.
123. G. Goodwin, J. De Dona, M. Seron, and X. Zhuo, "Lagrangian duality between constrained estimation and control," Automatica, 41(6), pp. 935-944 (June 2005).
124. N. Gordon, D. Salmond, and A. Smith, "Novel approach to nonlinear/non-Gaussian Bayesian state estimation," IEEE Proceedings-F, 140(2), pp. 107-113 (April 1993).
125. J. Gray and W. Murray, "A derivation of an analytic expression for the tracking index for the alpha-beta-gamma filter," IEEE Transactions on Aerospace and Electronic Systems, 29(3), pp. 1064-1065 (July 1993).
126. M. Grewal and A. Andrews, Kalman Filtering, John Wiley & Sons, New York, 2001.
127. 2 - L∞ filtering via linear matrix inequalities," IEEE Transactions on Aerospace and Electronic Systems, 33(4), pp. 1326-1338 (October 1997).
128. M. Grimble, "H∞ design of optimal linear filters," in Linear Circuits, Systems and Signal Processing: Theory and Applications, C. Byrnes, C. Martin, and R. Saeks (Eds.) North-Holland, Amsterdam, The Netherlands, 1988, pp. 533-540.
129. M. Grimble and A. El Sayed, "Solution of the H∞ optimal linear filtering problem for discrete-time systems," IEEE Transactions on Acoustics, Speech, and Signal Processing, 38(7), pp. 1092-1104 (July 1990).
130. M. Grimble, "H∞ fixed lag smoothing filter for scalar systems," IEEE Transactions on Signal Processing, 39(9), pp. 1955-1963 (September 1991).
131. M. Grimble and M. Johnson, ".Hoo robust control design - A tutorial review," Computing and Control Engineering Journal, 2(6), pp. 275-282 (November 1991).
132. S. Habibi and R. Burton, "The variable structure filter," ASME Journal of Dynamic Systems, Measurement, and Control, 125(3), pp. 287-293 (September 2003).
133. 2/H∞ regulation and estimation: The discrete-time case," Systems and Control Letters, 16, pp. 235-247 (1991).
134. D. Haessig and B. Friedland, "Separate-bias estimation with reduced-order Kalman filters," IEEE Transactions on Automatic Control, 43(7), pp. 983-987. (July 1998).
135. A. Hald, "T. N. Thiele's contributions to statistics," International Statistics Review, 49, pp. 1-20 (1981).
136. A. Harvey, Forecasting, Structural Time Series Models and the Kalman Filter, Cambridge University Press, New York, 1989.
137. B. Hassibi and T. Kailath, "H∞ adaptive filtering," IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 949-952 (1995).
138. B. Hassibi, A. Sayed, and T. Kailath, "Linear estimation in Krein spaces -Part I: Theory," IEEE Transactions on Automatic Control, 41(1), pp. 18-33 (January 1996).
139. B. Hassibi, A. Sayed, and T. Kailath, "Linear estimation in Krein spaces - Part II: Applications," IEEE Transactions on Automatic Control, 41(1), pp. 34-49 (January 1996).
140. B. Hassibi, A. Sayed, T. Kailath, Indefinite-Quadratic Estimation and Control, SIAM, Philadelphia, Pennsylvania, 1999.
141. S. Hayward, "Constrained Kalman filter for least-squares estimation of time-varying beamforming weights," in Mathematics in Signal Processing IV, J. McWhirter and I. Proudler (Eds.), Oxford University Press, pp. 113-125, 1998.
142. C. Hecht, "Digital realization of non-linear filters," Symposium on Nonlinear Estimation Theory and Its Applications, pp. 152-158 (1971).
143. C. Hecht, "Systems identification using Bayesian estimation," Symposium on Nonlinear Estimation Theory and Its Applications, pp. 107-113 (1973).
144. H. Heffes, "The effect of erroneous models on the Kalman filter response," IEEE Transactions on Automatic Control, AC-11, pp. 541-543 (July 1966).
145. Y. Hel-Or and M. Werman, "Recognition and localization of articulated objects," IEEE Workshop on Motion of Non-Rigid and Articulated Objects, pp. 116-123 (November 1994).
146. H. Henderson and S. Searle, "On deriving the inverse of a sum of matrices," SIAM Review, 23(1), pp. 53-60 (January 1981).
147. R. Henriksen, "The truncated second-order nonlinear filter revisited," IEEE Transactions on Automatic Control, AC-27(1), pp. 247-251 (February 1982).
148. C. Hide, T. Moore, and M. Smith, "Adaptive Kalman filtering for low-cost INS/GPS," The Journal of Navigation, 56, pp. 143-152 (2003).
149. Y. Ho and R. Lee, "A Bayesian approach to problems in stochastic estimation and control," IEEE Transactions on Automatic Control, AC-9, pp. 333-339 (1964).
150. Y. Ho and D. Pepyne, "Simple explanation of the no-free-lunch theorem and its implications," Journal of Optimization Theory and Applications, 155(3). 549-570. (December 2002).
151. R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, New York, 1985.
152. A. Householder, Principles of Numerical Analysis, McGraw-Hill, New York, 1953.
153. A. Householder, The Theory of Matrices in Numerical Analysis, Blaisdell, New York, 1964.
154. F. Hsiao and S. Pan, "Robust Kalman filter synthesis for uncertain multiple time-delay stochastic systems," Journal of Dynamic Systems, Measurement, and Control, 118, pp. 803-808 (December 1996).
155. R. Hughes, Analog Automatic Control Loops in Radar and EW, Artech House, Dedham, Massachusetts, 1988.
156. Y. Hung and F. Yang, "Robust H∞ filtering with error variance constraints for discrete time-varying systems with uncertainty," Automatica, 39(7), pp. 1185-1194 (July 2003).
157. C. Hutchinson, "The Kalman filter applied to aerospace and electronic systems," IEEE Transactions on Aerospace and Electronic Systems, AES-20(4), pp. 500-504 (July 1984).
158. Y. Iba, "Population Monte Carlo algorithms," Transactions of the Japanese Society for Artificial Intelligence, 16(2), pp. 279-286. (2001).
159. V. Ionescu, C. Oara, and M. Weiss, Generalized Riccati Theory and Robust Control, John Wiley & Sons, New York, 1999.
160. M. Isaard and A. Blake, "Contour tracking by stochastic propagation of conditional density," European Conference on Computer Vision, Cambridge, pp. 343-356, 1996.
161. M. Isard and A. Blake, "Condensation - Conditional density propagation for visual tracking," International Journal of Computer Vision, 29(1), pp. 5-28. (1998).
162. M. Isard and A. Blake, "ICondensation: Unifying low-level and high-level tracking in a stochastic framework," Lecture Notes in Computer Science, 1406, pp. 893-908. (1998).
163. A. Jazwinski, "Filtering for nonlinear dynamical systems," IEEE Transactions on Automatic Control, AC-11(5), pp. 765-766 (October 1966).
164. A. Jazwinski, "Adaptive filtering," Automatica, 5(4), pp. 475-485 (July 1969).
165. A. Jazwinski, Stochastic Processes and Filtering Theory, Academic Press, New York, 1970.
166. G. Johnson, "A deterministic theory of estimation and control," IEEE Transactions on Automatic Control, 14(4), pp. 380-384 (August 1969).
167. T. Jordan, "Experiments on error growth associated with some linear least-squares procedures," Mathematics of Computation, 22, pp. 579-588 (1968).
168. J. Juang, Applied System Identification, Prentice-Hall, Upper Saddle River, New Jersey, 1993.
169. S. Julier, J. Uhlmann, and H. Durrant-Whyte, "A new approach for filtering nonlinear systems," American Control Conference, pp. 1628-1632 (1995).
170. S. Julier, J. Uhlmann, and H. Durrant-Whyte, "A new method for the nonlinear transformation of means and covariances in filters and estimators," IEEE Transactions on Automatic Control, 45(3), pp. 477-482 (March 2000).
171. S. Julier and J. Uhlmann, "Reduced sigma point filters for the propagation of means and covariances through nonlinear transformations," American Control Conference, pp. 887-892, 2002.
172. S. Julier, "The spherical simplex unscented transformation," American Control Conference, pp. 2430-2434, 2003.
173. S. Julier and J. Uhlmann, "Unscented filtering and nonlinear estimation," Proceedings of the IEEE, 92(3), pp. 401-422 (March 2004).
174. T. Kailath, "An innovations approach to least-squares estimation - Part I: Linear filtering in additive white noise," IEEE Transactions on Automatic Control, AC-13(6), pp. 646-655 (December 1968).
175. T. Kailath, "Some new algorithms for recursive estimation in constant linear systems," IEEE Transactions on Information Theory, IT-19(6), pp. 750-760 (November 1973).
176. T. Kailath, "A view of three decades of linear filtering theory," IEEE Transactions on Information Theory, IT-20(2), pp. 146-181 (March 1974).
177. T. Kailath (ed.), Linear Least Squares Estimation, Dowden, Hutchinson & Ross, Stroudsburg, Pennsylvania, 1977.
178. T. Kailath, Linear Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1980.
179. T. Kailath, Lectures on Wiener and Kalman Filtering, Springer-Verlag, New York, 1981.
180. T. Kailath, A. Sayed, and B. Hassibi, Linear Estimation, Prentice-Hall, Upper Saddle River, New Jersey, 2000.
181. P. Kalata, "The tracking index: A generalized parameter for α-β and α-β γ target trackers," IEEE Transactions on Aerospace and Electronic Systems, AES-20(2), pp. 174-182.
182. R. Kalman, "A new approach to linear filtering and prediction problems," ASME Journal of Basic Engineering, 82, pp. 35-45 (March 1960).
183. R. Kalman, "Contributions to the theory of optimal control," Boletin de la Sociedad Matematica Mexicana, 5, pp. 102-119 (1960).
184. R. Kalman, "On the general theory of control systems," Proceedings of the 1st IFAC Congress, pp. 481-492, Butterworth's, London, 1960.
185. R. Kalman and R. Bucy, "New results in linear filtering and prediction theory," ASME Journal of Basic Engineering, 83, pp. 95-108 (March 1961).
186. R. Kalman, Y. Ho, and K. Narendra, "Controllability of linear dynamical systems," Contributions to Differential Equations, 1(2), pp. 189-213 (1963).
187. P. Kaminski, A. Bryson, and S. Schmidt, "Discrete square root filtering: A survey of current techniques," IEEE Transactions on Automatic Control, AC-16, pp. 727-736 (December 1971).
188. K. Kanazawa, D. Roller, and S. Russell, "Stochastic simulation algorithms for dynamics probabilistic networks," Eleventh Annual Conference on Uncertainty in AI, pp. 346-351, 1995.
189. E. Kaskurewicz and A. Bhaya, "Discrete-time state estimation with two counters and measurement delay," IEEE Conference on Decision and Control, pp. 1472-1476, 1996.
190. J. Keller and M. Darouach, "Reduced-order Kalman filter with unknown inputs," Automatica, 34(11), pp. 1463-1468 (November 1998).
191. J. Keller, "A new strategy for designing a reduced-order Kalman filter," International Journal of Systems Science, 30(11), pp. 1161-1166 (1999).
192. M. Kendall, "Daniel Bernoulli on maximum likelihood," Biometrika, 48, pp. 1-18 (1961).
193. G. Kitagawa, "Non-Gaussian state-space modelling of non-stationary time series (with discussion)," Journal of the American Statistical Association, 82(400), pp. 1032-1063 (December 1987).
194. G. Kitagawa, "Non-Gaussian seasonal adjustment," Computers and Mathematics with Applications, 18(6,7), pp. 503-514 (1989).
195. G. Kitagawa, "The two-filter formula for smoothing and an implementation of the Gaussian-sum smoother," Annals of the Institute of Statistical Mathematics, 46(4), pp. 605-623 (1994).
196. G. Kitagawa, Smoothness Priors Analysis of Time Series, Springer-Verlag, New York, 1996.
197. G. Kitagawa, "Monte Carlo filter and smoother for non-Gaussian nonlinear state space models," Journal of Computational and Graphical Statistics, 5(1), pp. 1-25 (1996).
198. S. Ko and R. Bitmead, "State estimation for linear systems with state equality constraints," Automatica, 2006.
199. T. Kobayashi and D.L. Simon, "Application of a bank of Kalman filters for aircraft engine fault diagnosis," ASME Turbo Expo, Atlanta, paper GT2003-38550, June 2003.
200. A. Kolmogorov, "Interpolation and extrapolation of stationary random sequences," in Selected Works of A. N. Kolmogorov, Volume II, V. Tikhomirov (Ed.), Kluwer Academic Publishers, Dordrecht, The Netherlands, pp. 272-280 (1992).
201. R. Kopp and R. Orford, "Linear regression applied to system identification for adaptive control systems," AIAA Journal, 1, pp. 2300-2306 (October 1963).
202. S. Kosanam and D. Simon, "Kalman filtering with uncertain noise covariances," Intelligent Systems and Control, Honolulu, Hawaii, pp. 375-379, August 2004.
203. S. Kramer and H. Sorenson, "Recursive Bayesian estimation using piece-wise constant approximations," Automatica, 24(6), pp. 789-801 (November 1988).
204. V. Krishnan, Nonlinear Filtering and Smoothing: An Introduction to Martingales, Stochastic Integrals and Estimation, John Wiley & Sons, New York, 1984.
205. H. Kushner, "Dynamical equations for optimal nonlinear filtering," Journal of Differential Equations, 3, pp. 179-190 (1967).
206. H. Kushner, "Approximations to optimal nonlinear filters," IEEE Transactions on Automatic Control, AC-12(5), pp. 546-556 (October 1967).
207. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems, John Wiley &; Sons, New York, 1972.
208. C. Kwok, D. Fox, and M. Meila, "Real-time particle filters," Proceedings of the IEEE, 92(3), pp. 469-484 (March 2004).
209. S. Kwon and W. Chung, "Combined synthesis of state estimator and perturbation observer," ASME Journal of Dynamic Systems, Measurement, and Control, 125(1), pp. 19-26 (March 2003).
210. D. Lainiotis, "Estimation: A brief survey," Information Sciences, 7, pp. 191-202 (1974).
211. P. Lancaster and L. Rodman, Algebraic Riccati Equations, Oxford University Press, New York, 1995.
212. T. Larsen, N. Andersen, O. Ravn, and N. Poulsen, "Incorporation of time delayed measurements in a discrete-time Kalman filter," IEEE Conference on Decision and Control, pp. 3972-3977, 1998.
213. S. Lauritzen, "Time series analysis in 1880: A discussion of contributions made by T. N. Thiele," International Statistics Review, 49, pp. 319-331 (1981).
214. R. Lee, Optimal Estimation, Identification, and Control, The MIT Press, Cambridge, Massachusetts, 1964.
215. K. Lewin, Field Theory in Social Science; Selected Theoretical Papers, Harper & Row, New York, 1951.
216. F. Lewis, Optimal Control, John Wiley & Sons, New York, 1986.
217. F. Lewis, Optimal Estimation, John Wiley & Sons, New York, 1986.
218. H. Lewis, Foundations of Fuzzy Control, Plenum, New York, 1997.
219. P. Liebelt, An Introduction to Optimal Estimation, Addison-Wesley, Reading, Massachusetts, 1967.
220. C. Liu and S. Marcus, "Estimator performance for a class of nonlinear estimation problems," IEEE Transactions on Automatic Control, AC-25(2), pp. 299-302 (April 1980).
221. J. Liu and R. Chen, "Sequential Monte Carlo methods for dynamical systems," Journal of the American Statistical Association, 93, pp. 1032-1044 (1998).
222. L. Ljung, System Identification: Theory for the User, Prentice-Hall, Upper Saddle River, New Jersey, 1998.
223. D. Luenberger, Linear and Nonlinear Programming, Addison-Wesley, Reading, Massachusetts, 1984.
224. J. MacCormick and A. Blake, "A probabilistic exclusion principle for tracking multiple objects," International Conference on Computer Vision, pp. 572-578, 1999.
225. K. Mahata and T. Soderstrom, "Improved estimation performance using known linear constraints," Automatica, 40(8), pp. 1307-1318 (August 2004).
226. M. Mahmoud, "Resilient linear filtering of uncertain systems," Automatica, 40(10), pp. 1797-1802 (October 2004).
227. J. Maindonald, Statistical Computation, John Wiley & Sons, New York, 1984.
228. M. Mallick, S. Coraluppi, and C. Carthel, "Advances in asynchronous and decentralized estimation," IEEE Aerospace Conference, pp. 1873-1888, 2001.
229. H. Marquez and M. Riaz, "Robust state observer design with application to an industrial boiler system," Control Engineering Practice, 13(6), pp. 713-728 (June 2005).
230. C. Masreliez, "Approximate non-Gaussian filtering with linear state and observation relations," IEEE Transactions on Automatic Control, AC-20, pp. 107-110 (February 1975).
231. C. Masrielez and R. Martin, "Robust Bayesian estimation for the linear model and robustifying the Kalman filter," IEEE Transactions on Automatic Control, AC-22(3), pp. 361-371 (June 1977).
232. P. Maybeck, Stochastic Models, Estimation, and Control - Volume 1, Academic Press, New York, 1979.
233. P. Maybeck, Stochastic Models, Estimation, and Control - Volume 2, Academic Press, New York, 1982.
234. P. Maybeck, Stochastic Models, Estimation, and Control - Volume 3, Academic Press, New York, 1984.
235. T. McGarty, Stochastic Systems and State Estimation, John Wiley & Sons, New York, 1974.
236. L. McGee and S. Schmidt, "Discovery of the Kalman filter as a practical tool for aerospace and industry," NASA Technical Memo 86847, November 1985.
237. S. McReynolds, "Multidimensional Hermite-Gaussian quadrature formulae and their application to nonlinear estimation," Symposium on Nonlinear Estimation Theory and Its Applications, pp. 188-191 (1975).
238. E. Mechler, J. Russell, and M. Preston, "The basis for the optimum aided-tracking time constant," Journal of the Franklin Institute, 248, pp. 327-334 (October 1949).
239. J. Meditch, Stochastic Optimal Linear Estimation and Control, McGraw-Hill, New York, 1969.
240. J. Meditch, "A survey of data smoothing for linear and nonlinear dynamic systems," Automatica, 9(2), pp. 151-162 (March 1973).
241. R. Mehra, "On the identification of variances and adaptive Kalman filtering," IEEE Transactions on Automatic Control, AC-15(2), pp. 175-184 (April 1970).
242. R. Mehra, "Approaches to adaptive filtering," IEEE Transactions on Automatic Control, AC-17(5), pp. 693-698 (October 1972).
243. J. Mendel, Lessons in Digital Estimation Theory, Prentice-Hall, Englewood Cliffs, New Jersey, 1987.
244. N. Metropolis and S. Ulam, "The Monte Carlo method," Journal of the American Statistical Association, 44(247), pp. 335-341 (September 1949).
245. G. Minkler and J. Minkler, Theory and Application of Kalman Filtering, Magellan Book Company, Palm Bay, Florida, 1993.
246. L. Mirsky, An Introduction to Linear Algebra, Dover, New York, 1990.
247. C. Moler and C. Van Loan, "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later," SIAM Review, 45(1), pp. 3-49 (January 2003).
248. T. Moon and W. Stirling, Mathematical Methods and Algorithms for Signal Processing, Prentice-Hall, Upper Saddle River, New Jersey, 2000.
249. P. Moral, "Measure valued processes and interacting particle systems: Application to non-linear filtering problems," Annals of Applied Probability, 8(2), pp. 438-495, 1998.
250. R. Morales-Menendez, N. de Freitas, and D. Poole, "Estimation and control of industrial processes with particle filters," American Control Conference, pp. 579-584, 2003.
251. M. Morf, R. Levy, and T. Kailath, "Square-root algorithms for the continuous-time linear least-square estimation problem," IEEE Transactions on Automatic Control, AC-23(5), pp. 907-911 (October 1978).
252. P. Muller, "Monte Carlo integration in general dynamic models," Contemporary Mathematics, 115, pp. 145-163 (1991).
253. K. Myers and B. Tapley, "Adaptive sequential estimation with unknown noise statistics," IEEE Transactions on Automatic Control, AC-21(4), pp. 520-523 (August 1976).
254. K. Nagpal, R. Helmick, and C. Sims, "Reduced-order estimation: Part I. Filtering," International Journal of Control, 45, pp. 1867-1888 (1987).
255. K. Nagpal and P. Khargonekar, "Filtering and smoothing in an H∞ setting," IEEE Transactions on Automatic Control, 36(2), pp. 152-166 (February 1991).
256. N. Nahi, "Optimal recursive estimation with uncertain observation," IEEE Transactions on Information Theory, IT-15(4), pp. 457-462 (July 1969).
257. E. Nelson, Radically Elementary Probability Theory, Princeton University Press, Princeton, New Jersey, 1987.
258. M. Netto, L. Gimeno, and M. Mendes, "On the optimal and suboptimal nonlinear filtering problem for discrete-time systems," IEEE Transactions on Automatic Control, AC-23(6), pp. 1062-1067 (December 1978).
259. T. Nishimura, "On the a priori information in sequential estimation problems," IEEE Transactions on Automatic Control, AC-11, pp. 197-204 (April 1966).
260. M. Norgaard, N. Poulsen, and O. Ravn, "New developments in state estimation for nonlinear systems," Automatica, 36(11), pp. 1627-1638 (November 2000).
261. J. O'Connor and E. Robertson, Matrices and Determinants, http://www-history.mcs.st-andrews.ac.uk/HistTopics/Matrices.and-determinants.html (1996).
262. P. Otter, Dynamic Feature Space Modelling, Filtering and Self-Tuning Control of Stochastic Systems, Springer-Verlag, New York, 1985.
263. Z. Pan and T. Basar, "Parameter identification for uncertain linear systems with partial state measurements under an H∞ criterion," IEEE Transactions on Automatic Control, 41(9), pp. 1295-1311 (September 1996).
264. A. Papoulis and S. Pillai, Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, 2002.
265. A. Patti, A. Tekalp, and M. Sezan, "A new motion-compensated reduced-order model Kalman filter for space-varying restoration of progressive and interlaced video," IEEE Transactions on Image Processing, 7(4), pp. 543-554 (April 1998).
266. P. Peebles, Probability, Random Variables, and Random Signal Principles, McGraw-Hill, New York, 2001.
267. D. Pham, J. Verron, and M. Roubaud, "A singular evolutive extended Kalman filter for data assimilation in oceanography," Journal of Marine Systems, 16, pp. 323-240 (1998).
268. M. Pitt and N. Shephard, "Filtering via simulation: Auxiliary particle filters," Journal of the American Statistical Association, 94(446), pp. 590-599 (1999).
269. R. Plackett, "Some theorems in least squares," Biometrika, 37, pp. 149-157 (1950).
270. V. Poor and D. Looze, "Minimax state estimation for linear stochastic systems with noise uncertainty," IEEE Transactions on Automatic Control, AC-26(4), pp. 902-906 (August 1981).
271. J. Porrill, "Optimal combination and constraints for geometrical sensor data," International Journal of Robotics Research, 7(6), pp. 66-77 (December 1988).
272. M. Poubelle, I. Petersen, M. Gevers, and R. Bitmead, "A miscellany of results on an equation of Count J. F. Riccati," IEEE Transactions on Automatic Control, AC-31(7), pp. 651-654 (July 1986).
273. W. Press, B. Flannery, S. Teukolsky, and W. Vetterling, Numerical Recipes in C : The Art of Scientific Computing, Cambridge University Press, New York, 1992.
274. C. Rao, J. Rawlings, and D. Mayne, "Constrained state estimation for nonlinear discrete-time systems: Stability and moving horizon approximations," IEEE Transactions on Automatic Control, 48(2), pp. 246-258 (February 2003).
275. H. Rauch, F. Tung, and C. Striebel, "Maximum likelihood estimates of linear dynamic systems," AIAA Journal, 3(8), pp. 1445-1450 (August 1965).
276. W. Reid, Riccati Differential Equations, Academic Press, New York, 1972.
277. K. Reif, F. Sonnemann, and R. Unbehauen, "An EKF-based nonlinear observer with a prescribed degree of stability," Automatica, 34(9), pp. 1119-1123 (September 1998).
278. K. Reif, F. Sonnemann, and R. Unbehauen, "Nonlinear state observation using H∞-filtering Riccati design," IEEE Transactions on Automatic Control, 44(1), pp. 203-208 (January 1999).
279. I. Rhee and J. Speyer, "A game theoretic controller and its relationship to H∞ and linear-exponential-Gaussian synthesis," IEEE Conference on Decision and Control, pp. 909-915 (1989).
280. I. Rhodes, "A tutorial introduction to estimation and filtering," IEEE Transactions on Automatic Control, AC-16(6), pp. 688-706 (December 1971).
281. B. Ripley, Stochastic Simulation, John Wiley & Sons, New York, 1987.
282. B. Ristic, S. Arularnpalam, and N. Gordon, Beyond the Kalman Filter: Particle Filters for Tracking Applications, Artech House, Norwell, Massachusetts, 2004.
283. C. Robert and G. Casella, Monte Carlo Statistical Methods, Springer-Verlag, New York, 1999.
284. P. Ruymgaart and T. Soong, Mathematics of Kalman-Bucy Filtering, Springer-Verlag, New York, 1985.
285. M. Safonov and M. Athans, "Robustness and computational aspects of nonlinear stochastic estimators and regulators," IEEE Transactions on Automatic Control, AC-23(4), pp. 717-725 (August 1978).
286. A. Sage and J. Melsa, Estimation Theory with Applications to Communications and Control, McGraw-Hill, New York, 1971.
287. F. Schlee, C. Standish, and N. Toda, "Divergence in the Kalman filter," AIAA Journal, 5, pp. 1114-1120 (June 1967).
288. S. Schmidt, "Applications of state space methods to navigation problems," in C. Leondes (Ed.), Advances in Control Systems, Vol. 3, pp. 293-340, Academic Press, New York, 1966.
289. S. Schmidt, "The Kalman filter: Its recognition and development for aerospace applications," Journal of Guidance and Control, 4(1), pp. 4-7 (January-February 1981).
290. L. Schwartz and E. Stear, "A computational comparison of several nonlinear filters," IEEE Transactions on Automatic Control, 13(1), pp. 83-86 (February 1968).
291. F. Schweppe, Uncertain Dynamic Systems, Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
292. H. Seal, "The historical development of the Gauss linear model," Biometrika, 54(1-2), pp. 1-24 (1967).
293. I. Schur, "Uber potenzreihen, die in innern des einheitskrises beschrankt sind," Journal fuer die Reine und Angewandte Mathematik, 147, pp. 205-232 (1917).
294. I. Schur, "On power series which are bounded in the interior of the unit circle, Part I," in I. Gohberg (Ed.), I. Schur Methods in Operator Theory and Signal Processing, pp. 31-88, Birkhauser, Boston, Massachusetts, 1986.
295. L. Servi and Y. Ho, "Recursive estimation in the presence of uniformly distributed measurement noise," IEEE Transactions on Automatic Control, 26(2), pp. 563-564 (April 1981).
296. W. Shanahan, "Circuit models for prediction, Wiener filtering, Levinson and Kalman filters for ARMA time series," IEEE International Conference on Acoustics, Speech and Signal Processing, pp. 266-269 (May 1982).
297. U. Shaked and Y. Theodor, "Hoo-optimal estimation: a tutorial," IEEE Conference on Decision and Control, pp. 2278-2286 (December 1992).
298. X. Shen and L. Deng, "Discrete filter design with application to speech enhancement," IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 1504-1507 (1995).
299. X. Shen and L. Deng, "Game theory approach to discrete Hoo filter design," IEEE Transactions on Signal Processing, pp. 1092-1095 (April 1997).
300. K. Shen, J. Crossley, A. Lun, S. Kangshen, and H. Liu, The Nine Chapters on the Mathematical Art: Companion and Commentary, Oxford University Press, Oxford (1999).
301. N. Shimada, Y. Shirai, Y. Kuno, and J. Miura, "Hand gesture estimation and model refinement using monocular camera - Ambiguity limitation by inequality constraints," Third IEEE International Conference on Automatic Face and Gesture Recognition, pp. 268-273 (April 1998).
302. B. Silverman, Density Estimation for Statistics and Data Analysis, Chapman & Hall, London, 1986.
303. D. Simon and H. El-Sherief, "Hybrid Kalman/minimax filtering in phase-locked loops," Control Engineering Practice, 4, pp. 615-623 (October 1996).
304. D. Simon and T. Chia, "Kalman filtering with state equality constraints," IEEE Transactions on Aerospace and Electronic Systems, 38(1), pp. 128-136 (January 2002).
305. D. Simon and D.L. Simon, "Aircraft turbofan engine health estimation using constrained Kalman filtering," ASME Journal of Engineering for Gas Turbines and Power, 127(2), pp. 323-328 (April 2005).
306. D.Simon, "Reduced order Kalman filtering without model reduction," Control and Intelligent Systems, 2006.
307. D. Simon and D.L. Simon, "Constrained Kalman filtering via density function truncation for turbofan engine health estimation," submitted for publication.
308. D. Simon, "A game theory approach to constrained minimax state estimation," IEEE Transactions on Signal Processing, 54(2), pp. 405-412 (February 2006).
309. K. Simon and A. Stubberud, "Reduced order Kalman filter," International Journal of Control, 10(5), pp. 501-509 (1969).
310. J. Simonoff, Smoothing Methods in Statistics, Springer-Verlag, New York, 1998.
311. C. Sims, "Reduced-order modelling and filtering," in C. Leondes (Ed.), Control and Dynamic Systems, Vol. 18, pp. 55-103, 1982.
312. R. Singer and R. Sea, "New results in optimizing surveillance system tracking and data correlation performance in dense multitarget environment," IEEE Transactions on Automatic Control, pp. 571-582 (December 1973).
313. G. Siouris, An Engineering Approach to Optimal Control and Estimation Theory, John Wiley & Sons, New York, 1996.
314. R. Skelton, T. Iwasaki, and K. Grigoriadis, A Unified Algebraic Approach to Linear Control Design, Taylor & Francis, London, 1998.
315. J. Sklansky, "Optimizing the dynamic parameters of a track-while-scan system," RCA Review, 18, pp. 163-185 (June 1957).
316. A. Smith and A. Gelfand, "Bayesian statistics without tears: A sampling-resampling perspective," The American Statistician, 46(2), pp. 84-88, (May 1992).
317. M. Smith and A. Roberts, "An exact equivalence between the discrete- and continuous-time formulations of the Kalman filter," Mathematics and Computers in Simulation, 20(2), pp. 102-109 (June 1978).
318. J. Snell, "A conversation with Joe Doob," Statistical Science, 12(4), pp. 301-311 (November 1997).
319. V. Sobolev, A Treatise on Radiative Transfer, Van Nostrand, Princeton, New Jersey, 1963.
320. Y. Song and J. Grizzle, "The extended Kalman filter as a local asymptotic observer for discrete-time nonlinear systems," Journal of Mathematical Systems, Estimation, and Control, 5(1), pp. 59-78.
321. T. Soong, "On a priori statistics in minimum-variance estimation problems," ASME Journal of Basic Engineering, 87D, pp. 109-112 (March 1965).
322. H. Sorenson and A. Stubberud, "Nonlinear filtering by approximation of the a posteriori density," International Journal of Control, 8(1), pp. 33-51 (1968).
323. H. Sorenson, "Least squares estimation: from Gauss to Kalman," IEEE Spectrum, 7, pp. 63-68 (July 1970).
324. H. Sorenson and J. Sacks, "Recursive fading memory filtering," Information Science, 3, pp. 101-119 (January 1971).
325. H. Sorenson and D. Alspach, "Recursive Bayesian estimation using Gaussian sums," Automatica, 7(4), pp. 465-479 (July 1971).
326. H. Sorenson, Parameter Estimation, Marcel Dekker, New York, 1980.
327. H. Sorenson (ed.), Kalman Filtering: Theory and Application, IEEE Press, New York, 1985.
328. G. Soto, E. Mendes, and A. Razek, "Reduced-order observers for rotor flux, rotor resistance and speed estimation for vector controlled induction motor drives using the extended Kalman filter technique," IEE Proceedings - Electric Power Applications, 146(3), pp. 282-288 (May 1999).
329. J. Spall (editor), Bayesian Analysis of Time Series and Dynamic Models, Marcel Dekker, New York, 1988.
330. K. Srinivasan, "State estimation by orthogonal expansion of probability distributions," IEEE Transactions on Automatic Control, AC-15(1), pp. 3-10 (February 1970).
331. E. Stear and A. Stubberud, "Optimal filtering for Gauss-Markov noise," International Journal of Control, 8(2), pp. 123-130 (July 1968).
332. P. Stein, "Some general theorems on iterants," Journal of Research of the National Bureau of Standards, 48, pp. 82-82 (1952).
333. R. Stengel, Optimal Control and Estimation, Dover, New York, 1994.
334. S. Stigler, The History of Statistics: The Measurement of Uncertainty Before 1900, Cambridge, Massachusetts, Harvard University Press, 1986.
335. A. Stoorvogel and J. Van Schuppen, "An Hoo-parameter estimator and its interpretation," IFAC Symposium on System Identification, pp. 1223-1226 (July 1994).
336. P. Strobach, Linear Prediction Theory, Springer-Verlag, New York, 1990.
337. P. Swerling, "First order error propagation in a stagewise smoothing procedure for satellite observations," The Journal of the Astronautical Sciences, 6, pp. 46-52 (1959).
338. P. Swerling, "Comment on 'A statistical optimizing navigation procedure for space flight'," AIAA Journal, 1, p. 1968 (1963).
339. P. Swerling, "Modern state estimation methods from the viewpoint of the method of least squares," IEEE Transactions on Automatic Control, AC-16, pp. 707-719 (1971).
340. B. Tapley and J. Peters, "Sequential estimation algorithm using a continuous UDUT covariance factorization," Journal of Guidance and Control, 3(4), pp. 326-331 (July 1980).
341. Y. Theodor, U. Shaked, and C. de Souza, "A game theory approach to robust discrete-time H∞ estimation," IEEE Transactions on Signal Processing, 42(6), pp. 1486-1495 (June 1994).
342. Y. Theodor and U. Shaked, "Game theory approach to Hoc-optimal discrete-time fixed-point and fixed-lag smoothing," IEEE Transactions on Automatic Control, 39(9), pp. 1944-1948 (September 1994).
343. Y. Theodor and U. Shaked, "Robust discrete-time minimum-variance filtering," IEEE Transactions on Signal Processing, 44(2), pp. 181-189 (February 1996).
344. H. Thiel and A. Goldberger, "On pure and mixed statistical estimation in economics," International Economic Review, 2(1), pp. 65-78 (January 1961).
345. S. Thomopoulos and L. Zhang, "Decentralized filtering with random sampling and delay," Information Sciences, 81, pp. 117-131 (1994).
346. S. Thomopoulos, "Decentralized filtering and control in the presence of delays: Discrete-time and continuous-time case," Information Sciences, 81, pp. 133-153 (1994).
347. C. Thornton and G. Bierman, "Gram-Schmidt algorithms for covariance propagation," International Journal of Control, 25(2), pp. 243-260 (February 1977).
348. C. Tsai and L. Kurz, "An adaptive robustizing approach to Kalman filtering," Automatica, 19(3), pp. 278-288 (May 1983).
349. J. Tse, J. Bentsman, and N. Miller, "Minimax long range parameter estimation," IEEE Conference on Decision and Control, pp. 277-282, December 1994.
350. B. Ursin, "Asymptotic convergence properties of the extended Kalman filter using filtered state estimates," IEEE Transactions on Automatic Control, AC-25(6), pp. 1207-1211 (December 1980).
351. R. Van der Merwe and E. Wan, "The square-root unscented Kalman filter for state and parameter estimation," IEEE International Conference on Acoustics, Speech, and Signal Processing, pp. 3461-3464 (May 2001).
352. D. Vaughan, "A nonrecursive algebraic solution for the discrete Riccati equation," IEEE Transactions on Automatic Control, AC-15(5), pp. 597-599 (October 1970).
353. S. Verdu and H. Poor, "Minimax linear observers and regulators for stochastic systems with uncertain second-order statistics," IEEE Transactions on Automatic Control, AC-29(6), pp. 499-511 (June 1984).
354. M. Verhaegen and P. Van Dooren, "Numerical aspects of different Kalman filter implementations," IEEE Transactions on Automatic Control, AC-31(10), pp. 907-917 (October 1986).
355. M. Verlaan and A. Hemmink, "Reduced rank square root filters for large scale data assimilation problem," Second International Symposium on Assimilation of Observations in Meteorology and Oceanography, pp. 247-252 (1995).
356. J. Vermaak, C. Andrieu, A. Doucet, and S. Godsill, "Particle methods for Bayesian modeling and enhancement of speech signals," IEEE Transactions on Speech and Audio Processing, 10, pp. 173-185 (March 2002).
357. E. Wan and R. van der Merwe, "The unscented Kalman filter," in Kalman Filtering and Neural Networks, S. Haykin (ed.), John Wiley & Sons, New York, 2001.
358. G. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, United Kingdom, 1922.
359. R. Weinstock, Calculus of Variations, Dover, New York, 1974.
360. M. Welch, "A Kalman filter perspective," The American Statistician, 41, pp. 90-91 (1987).
361. W. Wen and H. Durrant-Whyte, "Model-based multi-sensor data fusion," IEEE International Conference on Robotics and Automation, pp. 1720-1726, May 1992.
362. M. West, P. Harrison, and H. Mignon, "Dynamic generalized linear models and Bayesian forecasting," Journal of the American Statistical Association, 80(389), pp. 73-97 (March 1985).
363. N. Wiener, I Am a Mathematician, MIT Press, Cambridge, Massachusetts, 1956.
364. N. Wiener, Extrapolation, Interpolation, and Smoothing of Stationary Time Series, MIT Press, Cambridge, Massachusetts, 1964.
365. W. Willman, "Edgeworth expansions in state perturbation estimation," IEEE Transactions on Automatic Control, AC-26(2), pp. 493-498 (April 1981).
366. R. Wishner, J. Tabaczynski, and M. Athans, "A comparison of three non-linear filters," Automatica, 5(4), pp. 487-496 (July 1969).
367. R. Wishner, R. Larson, and M. Athans, "Status of radar tracking algorithms," Symposium on Nonlinear Estimation Theory and its Applications, San Diego, pp. 32-54, 1970.
368. S. Wright, Primal-Dual Interior-Point Methods, SIAM Press, Philadelphia, Pennsylvania, 1997.
369. L. Xie, C. Soh, and C. de Souza, "Robust Kalman filtering for uncertain discrete-time systems," IEEE Transactions on Automatic Control, 39(6), pp. 1310-1314 (June 1994).
370. 2 and H∞ filtering for uncertain discrete-time systems," Automatica, 40(5), pp. 873-880 (May 2004).
371. S. Xu and T. Chen, "Reduced-order H∞ filtering for stochastic systems," IEEE Transactions on Signal Processing, 50(12), pp. 2998-3007 (December 2002).
372. I. Yaesh and U. Shaked, "A transfer function approach to the problems of discrete-time systems: Hoo-optimal linear control and filtering," IEEE Transactions on Automatic Control, 36(11), pp. 1264-1271 (November 1991).
373. I. Yaesh and U. Shaked, "Game theory approach to state estimation of linear discrete-time processes and its relation to .Hoo-optimal estimation," International Journal of Control, 55(6), pp. 1443-1452 (1992).
374. I. Yaesh and U. Shaked, "Min-max Kalman filtering," Systems and Control Letters, 53(3-4), pp. 217-228 (November 2004).
375. K. Yonezawa, "Reduced-order Kalman filtering with incomplete observability," Journal of Guidance and Control, 3(3), pp. 280-282 (June 1980).
376. M. Yoon, V. Ugrinovskii, and I. Petersen, "Robust finite horizon minimax filtering for discrete-time stochastic uncertain systems," Systems and Control Letters, 52(2), pp. 99-112 (June 2004).
377. L. Zadeh and J. Ragazzini, "An extension of Wiener's theory of prediction," Journal of Applied Physics, 21, pp. 645-655 (July 1950).
378. P. Zarchan and H. Musoff, Fundamentals of Kalman Filtering: A Practical Approach, American Institute of Aeronautics and Astronautics, Reston, Virginia, 2000.
379. H. Zhang, L. Xie, Y. Chai Soh, and D. Zhang, "H∞ fixed-lag smoothing for discrete linear time-varying systems," Automatica, 41(5), pp. 839-846 (May 2005).
380. X. Zhang, A. Heemink, and J. Van Eijkeren, "Performance robustness analysis of Kalman filter for linear discrete-time systems under plant and noise uncertainty," International Journal of Systems Science, 26(2), pp. 257-275 (February 1995).
381. Y. Zhang, Y. Soh, and W. Chen, "Robust information filter for decentralized estimation," Automática, 41(12), pp. 2141-2146 (December 2005).