Least-Square Identification with Error Bounds for Real-Time Signal Processing and Control

Proceedings of the IEEE

Volumn 81, Issue 6, 1993, Pages 815-849

  Deller, John R ^a   Nayeri, Majid ^a   Odeh, Souheil F ^b  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b UNIVERSITY OF JORDAN   (Jordan)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; CONTROL SYSTEMS; ERROR ANALYSIS; LEAST SQUARES APPROXIMATIONS; MATHEMATICAL MODELS; SIGNAL PROCESSING; SYSTEMS ANALYSIS;

ERROR BOUNDS; OPTIMAL BOUNDING ELLIPSOID (OBE) ALGORITHMS; SET MEMBERSHIP IDENTIFICATION;

IDENTIFICATION (CONTROL SYSTEMS);

EID: 0027607901     PISSN: 00189219     EISSN: 15582256     Source Type: Journal    
DOI: 10.1109/5.257681     Document Type: Article

References (137)

1. B. I. Anan’ev and A. B. Kurzhanski, “The nonlinear filtering problem for a multistage system with statistical uncertainty,” in ptoc. 2nd 1FAC Symp., pp. 19–23, 1986.
2. L. V. R. Amida and G. Favier, “A review and a comparison of robust estimation methods,” in Proc. 9th IFAC / IFORS Symp. on Identification and System Parameter Estimation, vol. 2, Budapest, pp. 1027–1032, July 1991.
3. Cs. Bányász and L. Keviczky (editors), in Proc. 9th IFAC / IFORS Symp. on Identification and System Parameter Estimation, vols. 1 & 2, Budapest, July 1991.
4. B. R. Barmish and J. Sankaran, “The propagation of parametric uncertainty via polytopes,” IEEE Trans. Automatic Control, vol. AC-24, pp. 346–349, 1979.
5. G. Belforte and B. Bona, “An improved parameter identification algorithm for signals with unknown-but-bounded errors,” in Proc. 7th IFAC/IFORS Symp. on Identification and System Parameter Estimation, York, pp. 1507–1512, 1985.
6. G. Belforte and M. Milanese, “Uncertainty interval evaluation in presence of unknown-but-bounded errors: Nonlinear families of models,” in Proc. Ist IASTED Int. Symp. Modeling, Identification, and Control, Davos, pp. 75–79, 1981.
7. G. Belforte and T. T. Tay, “Recursive estimation for linear models with set-membership measurement error,” in Proc. 9th IFAC / IFORS Symp. on Identification and System Parameter Estimation, vol. 2, Budapest, pp. 872–877, July 1991.
8. G. Belforte, B. Bona, and V. Cerone, “Identification, structure selection and validation of uncertain models with set-membership error description,” Mathematics and Computers in Simulation, vol. 32, pp. 561–569, 1990.
9. G. Belforte, B. Bona, and V. Cerone, “Parameter estimation algorithms for a set-membership description of uncertainty,” Automatica, vol. 26, pp. 887–898, 1990.
10. G. Belforte, B. Bona, and V. Cerone, “Parameter estimation with set membership uncertainty: Nonlinear families of models,” in Proc. 8th IFAC/IFORS Symp. on Identification and System Parameter Estimation, Beijing, pp. 399–404, 1988.
11. G. Belforte, B. Bona, and V. Cerone, “A bounded error approach to the tuning of a digital voltmeter,” in Proc. 12th IMACS World Congress, Paris, 1988.
12. G. Belforte, B. Bona, and S. Frediani, “Optimal sampling schedule for parameter estimation of linear models with unknown-but-bounded measurements errors,” IEEE Trans. Automatic Control, vol. AC-32, pp. 179–182, 1987.
13. G. Belforte, B. Bona, E. Canute, F. Donati, F. Feraris, I. Gorini, S. Morei, M. Peisino, and S. Sartori, “Coordinate measuring machine and machine tool self calibration and error correction,” Annals CIRP, vol. 36, pp. 359–364, 1987.
14. G. Belforte, B. Bona, and M. Milanese, “Advanced modelling and identification techniques for metabolic processes,” CRC J. Biomed. Engr” vol. 10, pp. 275–316, 1983.
15. D. P. Bertsekas and I. B. Rhodes, “Recursive state estimation for a set-membership description of uncertainty,” IEEE Trans. Automatic Control, vol. AC-16, pp. 117–128, 1971.
16. V. Broman and M. J. Shensa, “A compact algorithm for the intersection and approximation of A-dimensional polytopes,” Mathematics and Computers in Simulation, vol. 32, pp. 469–480, 1990.
17. V. Broman and M. J. Shensa, “Polytopes, a novel approach to tracking,” in Proc. 25th IEEE Conf. Decision and Control, Athens, pp. 1749–1752, 1986.
18. M. F. Cheung, S. Yurkovich, and K. M. Passino, “An optimal volume ellipsoid algorithm for parameter set estimation,” in Proc. 30th IEEE Conf. Decision and Control, Brighton, pp. 969–974, 1991.
19. T. Clément and S. Gentil, “Recursive membership set estimation for output-error models,” Mathematics and Computers in Simulation, vol. 32, pp. 505–513, 1990.
20. T. Clement and S. Gentil, “Reformulation of parameter identification with unknown-but-bounded errors,” Mathematics and Computers in Simulation, vol. 30, pp. 257–270, 1988.
21. P. L. Combettes, Set Theoretic Estimation in Digital Signal Processing (Ph. D. Dissertation), North Carolina State University, ‘ Raleigh, 1989.
22. P. L. Combettes, “The foundations of set-theoretic estimation,” Proc. IEEE vol. 81, no. 2, pp. 182–208, 1993.
23. P. L. Combettes and H. J. Trussell, “The use of noise properties in set-theoretic estimation,” IEEE Trans. Signal Process., vol. 39, pp. 1630–1641, 1991.
24. P. L. Combettes and H. J. Trussell, “General order moments in set-theoretic estimation,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process. ’89, Glasgow, vol. 4, pp. 2101–2104, May 1989.
25. P. L. Combettes and H. J. Trussell, “Stability of the linear prediction filter: A set theoretic approach,” in Proc. IEEE Int. Conf Acoust., Speech, and Signal Process. ‘88, New York, vol. 4, pp. 2288–2291, 1988.
26. S. Dasgupta and Y. F. Huang, “Asymptotically convergent modified recursive least squares with data dependent updating and forgetting factor for systems with bounded noise,” IEEE Trans. Information Theory, vol. IT-33, pp. 383–392, 1987.
27. J. R. Deller, Jr., ‘Toward the use of set-membership identification in efficient training of feedforward neural nets,” in Proc. 1990 IEEE Int. Symp. Circuits and Systems, vol. 3, New Orleans, pp. 2041–2044, 1990.
28. J. R. Deller, Jr., “A ‘systolic array’ formulation of the optimal bounding ellipsoid algorithm,” IEEE Trans. Acoust., Speech, and Signal Process., vol. 37, pp. 1432–1436, Sept. 1989.
29. J. R. Deller, Jr., “Set-membership identification in digital signal processing,” IEEE AS$P Magazine, vol. 6, pp. 4–22, Oct. 1989.
30. J. R. Deller, Jr. and D. Hsu, “An alternative adaptive sequential regression algorithm and its application to the recognition of cerebral palsy speech,” IEEE Trans. Circuits and Systems, vol. CAS-34, pp. 782–787, July 1987.
31. J. R. Deller, Jr. and T. C. Luk, “Linear prediction analysis of speech based on set-membership theory,” Computer Speech and Language, vol. 3, pp. 301–327, Oct. 1989.
32. J. R. Deller, Jr. and T. C. Luk, “Set-membership theory applied to linear prediction analysis of speech,” in Proc. IEEE Int. Conf Acoust., Speech, and Signal Process. ’87, vol. 2, Dallas, pp. 653–656, 1987.
33. J. R. Deller, Jr. and S. F. Odeh, “Implementing the optimal bounding ellipsoid algorithm on a fast processor,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process. ’89, vol. 2, Glasgow, pp. 1067–1070, May 1989.
34. J. R. Deller, Jr. and S. F. Odeh, “SM-WRLS algorithms with an efficient test for innovation,” in Proc. 9th IFAC / IFORS Symp. on Identification and System Parameter Estimation, vol. 2, Budapest, pp. 1044–1049, July 1991.
35. J. R. Deller, Jr. and G. P. Picachd, “Advantages of a Givens rotation approach to temporally recursive linear prediction analysis of speech,” IEEE Trans. Acoust., Speech, and Signal Process., vol. 37, pp. 429–431, Mar. 1989.
36. J. R. Deller, Jr., M. Nayeri, and M. S. Liu, “Unifying the landmark developments in OBE processing,” Int. J. Automatic Control and Signal Process., in press.
37. J. R. Deller, Jr. and M. Nayeri (Organizers), Special session on set-membership-based signal processing and control, in Proc. IEEE Int. Conf, on Circuits and Sys. ’93, vol. 1, pp. 774–809, May 1993.
38. J. G. Ecker, “Geometric programming: Methods, computations, and applications,” SIAM Rev., vol. 22, pp. 338–362, 1980.
39. J. Falk, “Global solutions of signomial programs,” George Washington University, Washington, DC, Technical Report T-274, 1973.
40. K. Fedra, G. Van Straten, and M. B. Beck, “Uncertainty and arbitrariness in ecosystems modeling: A lake modeling example,” Ecological Modeling, vol. 13, pp. 87–110, 1981.
41. M. L. Feron, “Membership set system identification with pulse train input,” M. S. Dissertation, Illinois Institute of Technology, Chicago, 1982.
42. M. L. Feron and J. R. Deller, Jr., “‘Membership set’ identification applied to the impulse train excited AR model” (abstract), Final Program: SIAM 1983 National Mtg., Denver, p. 30, 1983.
43. G. Fiorio, S. Malan, M. Milanese, and A. Vicino, “Guaranteed specification control design of inertial platforms for a high accuracy calibration device,” in Proc. 29th IEEE Conf. on Decision and Control, Honolulu, 1990.
44. E. Fogel, “System identification via membership set constraints with energy constrained noise,” IEEE Trans. Automatic Control, vol. AC-24, pp. 752–758, 1979.
45. E. Fogel and Y. F. Huang, “On the value of information in system identification—Bounded noise case,” Automatica, vol. 18, pp. 229–238, 1982.
46. K. F. Gauss, “Theoria motus corporum coelestium,” Hamburg, 1809.
47. W. M. Gentleman, “Least squares computations by Givens transformations without square roots,” J. Inst. of Math. and its Appl., Vol. 12, pp. 329–336, 1973.
48. W. M. Gentleman and H. T. Kung, “Matrix triangularization by systolic arrays,” in Proc. Soc. Photo-Optical Instrumentation Engineers: Real-Time Signal Processing IV, vol. 298, pp. 19–26, 1981.
49. R. Gomeni, H. Piet-Lahanier, and E. Walter, “Study of the phamacokinetics of betaxolol using set-membership set estimation,” in Proc. 3rd IMEKO Congress on Measurements in Clinical Medicine, Edinburgh, 1986.
50. D. Graupe, Time Series Analysis, Identification, and Adaptive Systems, Malabar, Florida: Krieger, Ch. 5, 1989.
51. G. H. Golub and C. F. Van Loan, Matrix Computations. Baltimore, MD: Johns-Hopkins Univ. Press, Ch. 5, 1989.
52. G. C. Goodwin and K. S. Sin, Adaptive Filtering, Prediction, and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984.
53. S. Haykin, Adaptive Filter Theory. Englewood Cliffs, New Jersey: Prentice-Hall, 1986.
54. Y. F. Huang, “A recursive estimation algorithm using selective updating for spectral analysis and adaptive signal processing,” IEEE Trans. Acoust., Speech, and Signal Processing, vol. ASSP-34, pp. 1331–1334, Oct. 1986.
55. Y. F. Huang and J. R. Deller, Jr., “On the tracking capabilities of optimal bounding ellipsoid algorithms,” in Proc. 30th Annual Allerton Conf. on Comm., Control, and Comp., Oct. 1992.
56. S. C. Huang and Y. F. Huang, “Learning algorithms for perceptrons using back-propagation with selective updates,” IEEE Control Systems Magazine, pp. 56–61, Apr. 1990.
57. Y.-F. Huang and A. K. Rao, “Application of a recursive estimation algorithm with information-dependent updating to ARMAX models and ARMA models with unknown inputs,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process. ‘87, Dallas, vol. 2, pp. 1007–1010, 1987.
58. IEEE Trans. Automatic Control, vol. 37, July 1992.
59. C. R. Johnson, Lectures on Adaptive Parameter Estimation, Englewood Cliffs, New Jersey: Prentice-Hall, 1988.
60. R. M. Johnstone and B. D. O. Anderson, “Exponential convergence of recursive least squares with exponential foigetting factor adaptive control,” Sys. and Control Letters, vol. 2, pp. 69–76, 1982.
61. W. Kahan, “Circumscribing an ellipsoid about the intersection of two ellipsoids,” Canadian Math. Bull., vol. 11, p. 437, 1968.
62. I.Ya. Kats and A. B. Kurzhanski, “Minimax multistep filtering in statistically indeterminate solutions,” Automat. i Telemekh., vol. 11, p. 79, 1978.
63. K. Keesman, “Robust identification and prediction for output-error models,” in Proc. 9th IFAC / IFORS Symp. on Identification and System Parameter Estimation, vol. 2, pp. 878–882, Budapest, July 1991.
64. K. Keesman, “Membership-set estimation using random scanning and principal component analysis,” Mathematics and Computers in Simulation, vol. 32, pp. 535–543, 1990.
65. K. Keesman, “A set-membership approach to the identification and prediction of ill-defined systems: Application to a water quality system,” Ph.D. Dissertation, University of Twente, 1989.
66. K. J. Keesman and G. Van Straten, “Modified set-theoretic identification of an ill-defined water quality system from poor data,” in Proc. of IAWPRC Symp. on System Analysis in Water Quality Management, 1987.
67. H. Konig and D. Pallaschke, “On Khachian’s algorithm and minimal ellipsoids,” Numer. Math., vol. 36, pp. 211–223, 1981.
68. R. L. Kosut, “Adaptive robust control via parameter set estimation,” Int. J. Adaptive Control and Signal Process., vol. 2, pp. 371–399, 1988.
69. R. L. Kosut, M. K. Lau, and S. P. Boyd, “Set-membership identification of systems with parametric and nonparametric uncer-tainty,” IEEE Trans. Automatic Control, vol. 37, pp. 929–941, July 1992.
70. N. N. Krasnovski, “On the theory of controllability and observability of linear dynamic systems,” Prikl. Mat. Mech., vol. 28, no. 1, 1964.
71. J. M. Krause, G. Stein, and P. P. Khargonekar, “Robust performance of adaptive controllers with generally uncertain struc-ture,” in Proc. 29th IEEE Conf on Decision and Control, Honolulu, 1990.
72. A. J. Krener, “Kalman-Bucy and minimax filtering,” IEEE Trans. Automatic Control, vol. 25, pp. 291–292, 1980.
73. M. M. Krunz, “Numerical stability and convergence issues in the SM-WRLS algorithm,” M. S. Dissertation, Michigan State University, 1992.
74. S. Y. Kung, VLSI Array Processors. Englewood Cliffs, NJ: Prentice Hall, Ch. 3, 1988.
75. H. T. Kung and C. Leiserson, “Algorithms for VLSI processor arrays,” Dept. of Computer Sci., Camegie-Mellon Univ., Report No. MU-CS-79-103, 1978; also reprinted in C. Mead and L. Conway, Introduction to VLSI Systems, Reading, MA: Addison-Wesley, Section 8. 3, 1980.
76. A. B. Kurzhanski and I. Vályi, “Guaranteed state estimation for dynamic systems: Beyond the overviews,” in Proc. 9th IFAC / IFORS Symp. Identification and System Parameter Estimation, vol. 2, pp. 1033–1037, Budapest, July 1991.
77. M. K. Lau, R. L. Kosut, and S. Boyd, “Parameter set estimation of systems with uncertain nonparametric dynamics and distur-bances,” in Proc. 29 th IEEE Conf on Decision and Control, Honolulu, 1990.
78. A. M. Legendre, “Nouvelles methodes pour la determination des orbites des cométes,” Paris, 1806. Appendice sur la méthode des moindres carrés.
79. L. jung and T. Soderstrom, Theory and Practice of Recursive Identification, Cambridge, Mass.: MIT Press, pp. 14–15 & Sect. 2.2.1., 1983.
80. L. jung and B. Wahlbeig, “Influence of model order on change detection in noise-free complex systems,” in Proc. 1990 American Control Conf., San Diego, 1990.
81. T. C. Luk, “Fast optimal identification of autoregressive systems with a class of correlated inputs,” Ph. D. Dissertation, Illinois Institute of Technology, Chicago, 1985.
82. T. C. Luk and J. R. Deller, Jr., “A nonclassical WRLS algorithm,” in Proc. 23rdAnn. Allerton Conf, pp. 732–741, 1985.
83. J. G. McWhirter, “Recursive least squares minimization using a systolic array,” in Proc. Soc. Photo-Optical Instrumentation En-gineers: Real-Time Signal Processing VI, vol. 431, pp. 105–112, 1983.
84. M. Milanese and G. Belforte, “Estimation theory and uncertainty intervals evaluation in the presence of unknown but bounded errors: Linear families of models and estimators,” IEEE Trans. Automatic Control, vol. AC-27, pp. 408–414, 1982.
85. M. Milanese and A. Vicino, “Robust estimation and exact uncertainty intervals evaluation for nonlinear models,” in System Modeling and Simulation. Amsterdam: North-Holland, pp. 91–96, 1989.
86. M. Milanese and A. Vicino, “Estimation theory for dynamic systems with unknown but bounded uncertainty: An overview,” in Proc. 9th IFAC / IFORS Symp. Identification and System Parameter Estimation, vol. 2, pp. 859–867, Budapest, July 1991.
87. M. Milanese and A. Vicino, “Estimation theory for dynamic systems with unknown but bounded uncertainty: An overview,” Automatica, vol. 27, pp. 997–1009, 1991.
88. M. Milanese, R. Tempo, and A. Vicino, “Optimal error prediction for economic models,” Int. J. System Sci., vol. 19, pp. 1189–1200, 1988.
89. S. H. Mo, Computation of Bounded-parameter Models of Dynamical Systems from Bounded-Noise Records, Ph. D. Dissertation, University of Birmingham, Birmingham, England 1989.
90. S. H. Mo and J. P. Norton, “Fast and robust algorithm to compute exact polytope parameter bounds,” Mathematics and Computers in Simulation, vol. 32, pp. 481-493, 1990.
91. D. R. Morrell and W. C. Stirling, “Set-valued filtering and smoothing,” IEEE Trans. Systems, Man, and Cybernetics, vol. 21, pp. 184–193, 1991.
92. M. Nayeri, J. R. Deller, Jr., and M. M. Krunz, “Convergence and colored noise issues in bounding ellipsoid identification,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process. ’92, San Francisco, vol. 5, pp. 337–340, Mar. 1992.
93. M. Nayeri, J. R. Deller, Jr., and M. S. Liu, “A converging and interpretable OBE algorithm,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process. ’93, vol. IV, pp. 472–475, Apr. 1993.
94. M. Nayeri, J. R. Deller, Jr., and M. S. Liu, “Optimal bounding ellipsoid algorithms with adaptive tracking capabilities,” in Proc. 26th Annual Asilomar Conf. on Signals, Sys., and Comp., Pacific Grove, Calif., pp. 20–24, Oct. 1992.
95. J. P. Norton, An Introduction to Identification, London and Orlando, Florida: Academic Press, 1986.
96. J. P. Norton, “Problems in identifying the dynamics of biological systems from very short records,” in Proc. 25th IEEE Conf. on Decision and Control, Athens, 1986.
97. J. P. Norton, “Recursive computation of inner bounds for the parameters of linear models,” Int. J. Control, vol. 50, pp. 2423–2430, 1989.
98. J. P. Norton, “Identification of parameter bounds of ARMAX models from records with bounded noise,” Int. J. Control, vol. 45, pp. 375–390, 1987.
99. J. P. Norton, “Identification and application of bounded-parameter models,” Automatical vol. 23, pp. 497–507, 1987.
100. J. P. Norton and S. H. Mo, “Parameter bounding for time-varying systems,” Mathematics and Computers in Simulation, vol. 32, pp. 527–534, 1990.
101. J. P. Norton (editor), Int. J. Automatic Control and Signal Process., Special issue on bounded error methods in control and signal processing (in press).
102. S. F. Odeh, “Algorithms and architectures for adaptive set membership-based signal processing,” Ph. D. Dissertation, Michigan State University, East Lansing, 1990.
103. S. F. Odeh and J. R. Deller, Jr., “Systolic algorithms for adaptive set-membership identification,” in Proc. IEEE Int. Cortf. Acoust., Speech, and Signal Process. ’90, Albuquerque, vol. 5, pp. 2419–2422, Apr. 1990.
104. S. F. Odeh and J. R. Deller, Jr., “An SM-WRLS algorithm with an efficient test for innovation: Simulation studies and complexity issues,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Process. ’91, Toronto, vol. 5, pp. 3413–3416, May 1991.
105. H. Piet-Lahanier and E. Walter, “Characterization of non-connected parameter uncertainty regions,” Mathematics and Computers in Simulation, vol. 32, pp. 553–560, 1990.
106. H. Piet-Lahanier and E. Walter, “Further results on recursive polyhedral description of parameter uncertainty in the bounded-error context,” in Proc. 28th IEEE Conf Decision and Control, Tampa, pp. 1964–1966, 1989.
107. H. Piet-Lahanier and E. Walter, “Practical implementation of an exact and recursive algorithm for characterizing likelihood sets,” in Proc. 12th IMACS World Congress on Scientific Computation, Paris, July 1988.
108. H. Piet-Lahanier, E. Walter, and R. Gomeni, “OMNE: a new robust membership set estimator for the parameters of nonlinear models,” J. Pharmacokin. Biopharm., vol. 15, pp. 203–219, 1987.
109. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetter-ling, Numerical Recipes in C: The Art of Scientific Computing, Cambridge, Massachusetts: Cambridge University Press, 1988.
110. L. Pronzato and E. Walter, “Experiment design for bounded-error models,” Mathematics and Computers in Simulation, vol. 32, pp. 571–584, 1990.
111. L. Pronzato, E. Walter, and H. Piet-Lahanier, “Mathematical equivalence of two ellipsoidal algorithms for bounded-error estimation,” in Proc. 28th IEEE Conf. Decision and Control, Tampa, pp. 1952–1955, 1989.
112. L. Pronzato, E. Walter, A. Venot, and J. F. Lebruchec, “A general-purpose global optimizer: Implementation and applications,” Mathematics and Computers in Simulation, vol. 26, pp. 412–422, 1984.
113. B. N. Pshenichnyi and V. G. Pokotilo, “On observation problems in discrete systems,” PMM J. Appl. Math. Mechanics, vol. 45, pp. 1–6, 1981.
114. A. K. Rao, Membership-Set Parameter Estimation via Optimal Bounding Ellipsoids, Ph. D. Dissertation, University of Notre Dame, 1989.
115. A. K. Rao and Y. F. Huang, “Recent developments in optimal bounding ellipsoid parameter estimation, Mathematics and Computers in Simulation, vol. 32, pp. 515–526, Dec. 1990.
116. A. K. Rao and Y. F. Huang, “Analysis of finite precision effects on an OBE algorithm,” in Proc. IEEE Int. Conf Acoust., Speech, and Signal Process. ‘89, Glasgow, vol. 2, pp. 853–856, May 1989.
117. A. K. Rao and Y. F. Huang, ‘Tracking characteristics of an OBE parameter estimation algorithm,” IEEE Trans. Signal Process., vol. 41, Mar. 1993.
118. A. K. Rao, Y.-F. Huang, and S. Dasgupta, “ARMA parameter estimation using a novel recursive estimation algorithm with selective updating,” IEEE Trans. Acoust., Speech, and Signal Process., vol. 38, pp. 447–457, Mar. 1990.
119. F. C. Schweppe, “Recursive state estimation: Unknown but bounded errors and system inputs,” IEEE Trans. Automatic Control, vol. AC-13, pp. 22–28, 1968.
120. N. Shor and V. Gershovich, “Family of algorithms for solving convex programming problems,” Cybernetics, vol. 15, pp. 502–507, 1979.
121. M. K. Smit, “A novel approach to the solution of indirect measurement problems with minimal error propagation,” Measurement, vol. 1, pp. 181–190, 1983.
122. M. K. Smit and Ch. Van Vliet, “OMTP: Fortran program for optimally solving indirect measurement problems,” Measurement, vol. 1, pp. 209–211, 1983.
123. R. Tempo, “Robust estimation and filtering in the presence of bounded noise,” IEEE Trans. Automatic Control, vol. AC-33, pp. 864–867, 1988.
124. R. Tempo and A. Vicino, “Optimal algorithms for system identification: A review of some recent results,” Mathematics and Computers in Simulation, vol. 32, pp. 585–595, 1990.
125. H. J. Trassell and M. R. Civanlar, “The feasible solution in signal restoration,” IEEE Trans. Acoustics, Speech, and Signal Process., vol. 32, pp. 201–212, 1984.
126. G. Van Straten, “Analytical methods for parameter space delimitation and application to shallow-lake phytoplankton dynamics modelling,” Appl. Math. and Computing, vol. 17, pp. 459–482, 1985.
127. J. W. Veihoof and M. K. Smit, “Error analysis for ellipsometry,” in Proc. 12th IMACS World Congress, Paris, 1988.
128. A. Venot, L. Pronzato, E. Walter, and J. F. Lebruchec, “A distribution-free criterion for robust identification with applications in system modelling and image processing,” Automatica, vol. 22, pp. 105–109, 1986.
129. S. M. Veres and J. P. Norton, “Bound-based worst-case self-tuning controllers,” in Proc. 9th IFAC / IFORS Symp. on Identification and System Parameter Estimation, vol. 1, Budapest, pp. 773–778, July 1991.
130. S. M. Veres and J. P. Norton, “Parameter bounding algorithms for linear errors in variables models,” in Prvc. 9th IFAC/IFORS Symp. on Identification and System Parameter Estimation, vol. 2, Budapest, pp. 1038–1043, July 1991.
131. S. M. Veres and J. P. Norton, “Structure identification of parameter-bounding models by use of noise-structure bounds,” Int. J. Control, vol. 50, pp. 639–649, 1989.
132. A. Vicino and M. Milanese, “Optimal approximation of feasible parameter set in estimation with unknown but bounded noise,” in Proc. 9th IFAC / IFORS Symp. on Identification and System Parameter Estimation, vol. 2, Budapest, pp. 1365–1369, July 1991.
133. A. Vicino and M. Milanese, “Optimal inner bounds of feasible parameter sets in linear estimation with bounded noise,” in Proc. 28th IEEE Conf. Decision and Control, Tampa, pp. 2576–2580, 1989.
134. A. Vicino, A. Tesi, and M. Milanese, “Computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties,” IEEE Trans. Automatic Control, vol. 35, pp. 835–841, 1990.
135. A. Vicino, R. Tempo, R. Genesio, and M. Milanese, “Optimal error and GMDH predictors: A comparison with some statistical techniques,” Int. J. Forecasting, vol. 2, pp. 313–328, 1987.
136. B. Wahlberg and L. Ljung, “Hard frequency-domain model error bounds from least-squares-like identification techniques,” IEEE Trans. Automatic Control, vol. 37, pp. 900–912, July 1992.
137. E. Walter (editor), Mathematics and Computers in Simulation, Special issue on parameter identification with error bound, vol. 32, Dec. 1990.