A General Systematic Method for Model-Set Design

Model-set design is one of the most important topics of the multiple-model (MM) approach, which is the state of the art for many estimation, control, and modeling problems. The work presented here proposes a general systematic model-set design method in the parameter space of a system based on number theoretic (NT) methods for design of statistical experiments. The system is characterized by uncertain parameters that describe the mode space, and the models used in the model set are designed to approximate the mode by minimizing distribution mismatch. Two types of F-uniform model sets that perform well are proposed: one by the NT methods, the other according to an F-centered discrepancy. In order to improve the performance of the F-uniform model sets further, two types of expected mode augmentation (EMA) are applied. Simulation examples are given and compared with results from the Monte-Carlo method to demonstrate the designs and their performance.

[1]  Tony Warnock,et al.  Computational investigations of low-discrepancy point-sets. , 1972 .

[2]  D. Lainiotis.  Optimal adaptive estimation: Structure and parameter adaptation , 1970 .

[3]  Youmin Zhang,et al.  Multiple-model estimation with variable structure: model-group switching algorithm , 1997, Proceedings of the 36th IEEE Conference on Decision and Control.

[4]  Kumpati S. Narendra,et al.  Adaptation and learning using multiple models, switching, and tuning , 1995 .

[5]  Grigorios N. Beligiannis,et al.  Genetically determined variable structure multiple model estimation , 2001, IEEE Trans. Signal Process..

[6]  Remarks Concerning Numerical Integration , 2005 .

[7]  K. Fang,et al.  Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points , 1997 .

[8]  渡辺 桂吾,et al.  Adaptive estimation and control : partitioning approach , 1991 .

[9]  X. Rong Li,et al.  Multiple-model estimation with variable structure- part VI: expected-mode augmentation , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[10]  X. Rong Li,et al.  Multiple-Model Estimation with Variable Structure—Part II: Model-Set Adaptation , 2000 .

[11]  V. Jilkov,et al.  Survey of maneuvering target tracking. Part V. Multiple-model methods , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[12]  Kai-Tai Fang,et al.  UNIFORM DESIGNS BASED ON LATIN SQUARES , 1999 .

[13]  L Hua.  ON UNIFORM DISTRIBUTION AND NUMERICAL ANALYSIS (III) (NUMBER-THEORETIC METHOD) , 1973 .

[14]  K Ang,et al.  A NOTE ON UNIFORM DISTRIBUTION AND EXPERIMENTAL DESIGN , 1981 .

[15]  Peter S. Maybeck,et al.  An optimizing design strategy for multiple model adaptive estimation and control , 1990, 29th IEEE Conference on Decision and Control.

[16]  Fred J. Hickernell,et al.  A generalized discrepancy and quadrature error bound , 1998, Math. Comput..

[17]  Y. Baram,et al.  An information theoretic approach to dynamical systems modeling and identification , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[18]  E. Hlawka.  Zur angenäherten Berechnung mehrfacher Integrale , 1962 .

[19]  X. Rong Li,et al.  General model-set design methods for multiple-model approach , 2005, IEEE Transactions on Automatic Control.

[20]  David D. Sworder,et al.  Estimation Problems in Hybrid Systems , 1999 .

[21]  Amir Averbuch,et al.  Interacting Multiple Model Methods in Target Tracking: A Survey , 1988 .

[22]  Peter Maybeck,et al.  Investigation of moving-bank multiple model adaptive algorithms , 1985, 1985 24th IEEE Conference on Decision and Control.

[23]  D. Magill.  Optimal adaptive estimation of sampled stochastic processes , 1965 .

[24]  D. Lainiotis.  Optimal adaptive estimation: Structure and parameter adaption , 1971 .

[25]  X. Rong Li,et al.  Measuring Estimator's Credibility: Noncredibility Index , 2006, 2006 9th International Conference on Information Fusion.

[26]  Thia Kirubarajan,et al.  Estimation with Applications to Tracking and Navigation: Theory, Algorithms and Software , 2001 .

[27]  Y. Bar-Shalom,et al.  Multiple-model estimation with variable structure , 1996, IEEE Trans. Autom. Control..

[28]  X. Rong Li,et al.  Multiple-model estimation with variable structure. II. Model-set adaptation , 2000, IEEE Trans. Autom. Control..

[29]  X. Rong Li,et al.  Hybrid Estimation Techniques , 1996 .

[30]  X. R. Li,et al.  Optimal selection of estimate for multiple-model estimation with uncertain parameters , 1998 .

[31]  X. R. Li,et al.  Multiple-model estimation with variable structure. IV. Design and evaluation of model-group switching algorithm , 1999 .

[32]  Peter S. Maybeck,et al.  Stochastic Models, Estimation And Control , 2012 .

[33]  Harald Niederreiter,et al.  Random number generation and Quasi-Monte Carlo methods , 1992, CBMS-NSF regional conference series in applied mathematics.

[34]  Y Wang.  NUMBER THEORETIC METHOD IN APPLIED STATISTICS , 1990 .

[35]  Chongzhao Han,et al.  Model-set design: Uniformly distributed models , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[36]  Y. Bar-Shalom,et al.  The interacting multiple model algorithm for systems with Markovian switching coefficients , 1988 .

[37]  H. Keng,et al.  Applications of number theory to numerical analysis , 1981 .

[38]  Roderick Murray-Smith,et al.  Multiple Model Approaches to Modelling and Control , 1997 .