ESTIMATION AND PREDICTION IN THE PRESENCE OF UNKNOWN BUT BOUNDED UNCERTAINTY: A SURVEY

Many different problems such as linear and nonlinear regressions, parameter and state estimation of dynamic systems, state space and time series prediction, interpolation, smoothing, function approximation have a common general structure that here is referred to as generalized estimation problem. In all these problems one has to evaluate some unknown variable using available data (often obtained by measurements on a real process). Available data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables.

[1]  M. Smit.  A novel approach to the solution of indirect measurement problems with minimal error propagation , 1983 .

[2]  Antonio Vicino,et al.  Strongly optimal algorithms and optimal information in estimation problems , 1986, J. Complex..

[3]  Yakov Z. Tsypkin,et al.  Robust identification , 1980, Autom..

[4]  M. Milanese,et al.  Advanced modeling and identification techniques for metabolic processes. , 1984, Critical reviews in biomedical engineering.

[5]  T. J. Rivlin,et al.  Optimal Estimation in Approximation Theory , 1977 .

[6]  R. Tempo,et al.  Robust Estimation and Prediction Using Arma Models: A Nonstatistical Approach , 1988 .

[7]  E. Walter,et al.  Robust nonlinear parameter estimation in the bounded noise case , 1986, 1986 25th IEEE Conference on Decision and Control.

[8]  V. Broman,et al.  Polytopes, a novel approach to tracking , 1986, 1986 25th IEEE Conference on Decision and Control.

[9]  G. V. Straten.  Analytical methods for parameter-space delimination and application to shallow-lake phytoplankton-dynamics modeling , 1985 .

[10]  Antonio Vicino,et al.  Optimal error and GMDH predictors: A comparison with some statistical techniques , 1987 .

[11]  R. Tempo,et al.  Optimal algorithms theory for robust estimation and prediction , 1985 .

[12]  Y. F. Huang,et al.  On the value of information in system identification - Bounded noise case , 1982, Autom..

[13]  E. Walter,et al.  Identifiability and distinguishability of fundamental parameters in catalytic methanation , 1986 .

[14]  F. Schweppe.  Recursive state estimation: Unknown but bounded errors and system inputs , 1967 .

[15]  H. Witsenhausen.  Sets of possible states of linear systems given perturbed observations , 1968 .

[16]  Charles A. Micchelli,et al.  A Survey of Optimal Recovery , 1977 .

[17]  M. Milanese,et al.  Estimation theory and uncertainty intervals evaluation in presence of unknown but bounded errors: Linear families of models and estimators , 1982 .

[18]  Enrico Canuto,et al.  Coordinate Measuring Machines and Machine Tools Selfcalibration and Error Correction , 1987 .

[19]  Eric Walter,et al.  A distribution-free criterion for robust identification, with applications in system modelling and image processing , 1985, Autom..

[20]  R. Tempo,et al.  Maximum likelihood estimators and worst case optimal algorithms for system identification , 1988 .

[21]  G. Belforte,et al.  Optimal sampling schedule for parameter estimation of linear models with unknown but bounded measurement errors , 1987 .

[22]  R. Tempo.  Robust estimation and filtering in the presence of bounded noise , 1987, 26th IEEE Conference on Decision and Control.

[23]  G. Belforte,et al.  An Improved Parameter Identification Algorithm for Signals with Unknown-But-Bounded Errors , 1985 .

[24]  J. Norton,et al.  Problems in identifying the dynamics of biological systems from very short records , 1986, 1986 25th IEEE Conference on Decision and Control.

[25]  J. Norton.  Bounding Techniques for Model-Structure Selection , 1989 .

[26]  Gustavo Belforte,et al.  A bounded error approach to the tuning of a digital voltmeter , 1988 .

[27]  R. Tempo,et al.  Optimality of central and projection algorithms for bounded uncertainty , 1986 .

[28]  M. Milanese,et al.  A note on the derivation and use of reduced-order models , 1976 .

[29]  R. Tempo,et al.  Optimal error predictors for economic models , 1988 .

[30]  Antonio Vicino,et al.  Conditionally optimal algorithms and estimation of reduced order models , 1988, J. Complex..

[31]  J. Ecker.  Geometric Programming: Methods, Computations and Applications , 1980 .

[32]  J. P. Norton,et al.  Identification and application of bounded-parameter models , 1985, Autom..

[33]  V. Broman,et al.  A compact algorithm for the intersection and approximation of N -dimensional polytopes , 1990 .

[34]  Fred C. Schweppe,et al.  Uncertain dynamic systems , 1973 .

[35]  Henryk Wozniakowski,et al.  A general theory of optimal algorithms , 1980, ACM monograph series.

[36]  Antonio Vicino,et al.  Robust Parameter Estimation for Linear Models with Set-membership Uncertainty , 1988 .