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This monograph provides a sample of relevant new results on dynamical nonlinear statistical modeling and estimation which forms a basis for more effective signal processing, decision and control. While the research literature is rich in linear Gaussian methodologies, new contributions to the most relevant area of nonlinear and non-Gaussian processes have been scarce. Among the significant areas of application for which such methodologies are needed are: economics, biology, immunology, underwater acoustics, electric power generation, chemical process control, and variable structure systems in general. The latter include adaptive, intelligent, and decomposing mathematical structures or processes. The volume includes ten research papers on theory, computational methods, and applications. Topics include filtering with application to inertial navigation, structural-change detection, bilinear time-series models, bispectral estimation, threshold models, catastrophic models and a generalized eigenstructure method.
List of contents
Contents: On the Application of Kalman Filtering to Correct Errors due to Vertical Deflection in Inertial Navigation.- Filtering and Detection Problems for Nonlinear Time Series.- Spectral and Bispectral Methods for the Analysis of Nonlinear (Non-Gaussian) Time-Series Signals.- Bilinear Time Series: Theory and Application.- Bivariate Bilinear Models and Their Identification.- Nonlinear Time Series Modelling in Population Biology.- The Akaike Information Criterion in Threshold Modelling.- Nonlinear Time Series Analysis for Dynamical Systems of Catastrophe Type.- Nonlinear Processing with M-th Order Signals.- Stochastic Circulatory Lymphocyte Models.
