Revealing Latent Structural Patterns in Processes and Signals: From Space Research up to Analysis of Market Trends

Description

Acronyms and Abbreviations
Foreword of Scientific Editor
Author’s preface
Introduction
Chapter

Analysis of the structure and prediction of processes containing latent periodicities
1.1.General characteristics of the problem
1.2.Review of the known methods of revealing latent periodicities
1.3.On the possibility and correctness of application of the Fourier harmonic analysis for revealing latent periodicities
1.4.Family of D-methods for revealing latent periodicities
1.5.Finite-difference pattern of D-methods for n = 1 (D1-method)
1.6.Minimization of function DX(τ) and practical calculation of the periodicities’ parameters
1.7.Determination of the order of the polynomial non‑periodic component
1.8.Some peculiarities of application of the discrete algorithm of D-method
1.9.The results of testing of D-method and its comparison with some known ones
1.10.General qualitative features of D-methods
Chapter

Some non-traditional approaches to approximation of processes using their measurements
2.1.Generalization of the weighted root-mean-square criterion and a notion of the weighted orthogonality
2.2.The method of consecutive correction of the generalized polynomial coefficients
2.3.The block approximation method
2.4.The subcase of approximating function Φ1
2.5.The peculiarities of algorithms of the block approximation method
2.6.Comparison of the classical weighted root-mean-square method with its generalization and the method of consecutive correction of coefficients
2.7.Investigation of the block approximation method using test cases
Chapter
Application of the developed methods of revealing latent periodicities and the generalized approximation methods to the analysis of structure and propagation of some real processes
3.1.Analysis of the structure and prediction of change of the space object orbit elements
3.2.The forecast of the solar activity
3.3.Analysis of photometric signatures of space objects
3.4.Analysis of radar signatures of space objects
3.5.Analysis of radio signatures for the sake of recognition of space objects
3.6.Analysis and prediction of processes like the transient response
3.7.Analysis of some geo- and astrophysical processes
3.8.Analysis of vibrograms
Conclusion
El autor
Stanislav S. Veniaminov
Doctor of sciences, professor, laureate of the international award of the American Association for the Advancement of Science (AAAS), academician of the International Academy for Integration of Science and Business, academician of the International Public Development Academy, member of the Interagency Space Debris Coordination Committee (since 1993), member of the Committee on Space Debris of the National Research Council of USA (1993–1995), member of the Expert Working Group on Space Threats of RAS (since 2012), co-chairman of the US–Russian Space Surveillance Workshop (since 1994). An expert in the fields of control of complex systems, operations research, mathematical methods of discrete optimization, planning the search for space objects, problems of technogenic contamination of space. Leading scientist of the Scientific Research Center “Kosmos” in the field of space surveillance. Author of more than 430 scientific publications.