Measurement Data Modeling and Parameter Estimation integrates mathematical theory with engineering practice in the field of measurement data processing. Presenting the first-hand insights and experiences of the authors and their research group, it summarizes cutting-edge research to facilitate the application of mathematical theory in measurement and control engineering, particularly for those interested in aeronautics, astronautics, instrumentation, and economics.
Requiring a basic knowledge of linear algebra, computing, and probability and statistics, the book illustrates key lessons with tables, examples, and exercises. It emphasizes the mathematical processing methods of measurement data and avoids the derivation procedures of specific formulas to help readers grasp key points quickly and easily. Employing the theories and methods of parameter estimation as the fundamental analysis tool, this reference:
- Introduces the basic concepts of measurements and errors
- Applies ideas from mathematical branches, such as numerical analysis and statistics, to the modeling and processing of measurement data
- Examines methods of regression analysis that are closely related to the mathematical processing of dynamic measurement data
- Covers Kalman filtering with colored noises and its applications
Converting time series models into problems of parameter estimation, the authors discuss modeling methods for the true signals to be estimated as well as systematic errors. They provide comprehensive coverage that includes model establishment, parameter estimation, abnormal data detection, hypothesis tests, systematic errors, trajectory parameters, and modeling of radar measurement data. Although the book is based on the authors’ research and teaching experience in aeronautics and astronautics data processing, the theories and methods introduced are applicable to processing dynamic measurement data across a wide range of fields.
Table of Contents
Error Theory. Parameterized Representation of Estimated Function. Modern Regression Analysis Methods. Time Series Analysis Method. Discrete Kalman Filter. Radar Measurement Data Processing. On-board GPS Measurement Data Processing.
Dr. Zhengming Wang received his BS and MS degrees in applied mathematics and a PhD degree in system engineering in 1982, 1986, and 1998, respectively. Currently, he is a professor in applied mathematics. He is also Standing Director of the Chinese Association for Quality Assurance Agencies in Higher Education, Director of Chinese Mathematical Society, Chairman of the Hunan Institute of Computational Mathematics and Application Software, and Associate Provost of National University of Defense Technology. He has completed four projects funded by the National Science Foundation of China. He has won five State Awards of Science and Technology Progress. He has co-published four monographs (all ranked first) and well over 80 papers, including 50 SCI or EI-indexed ones. His research interests cover areas such as mathematical modeling in tracking data, image processing, experiment evaluation, and data fusion.
Dr. Dongyun Yi received his BS and MS degrees in applied mathematics and a PhD degree in system engineering in 1985, 1992, and 2003, respectively. Currently, he is a professor in Systems Analysis and Integration. He is now the Director of the Department of Mathematics and Systems Science, College of Science, National University of Defense Technology. He has been engaged in data intelligent processing research for over twenty years. He is in charge of the National Foundation Research Project "The Structural Properties of Resource Aggregation—Analysis and Applications" and also participates in the National Science Foundation of China "Pattern Recognition Research Based on High-Dimensional Data Structure" as a deputy chair. He has co-published two monographs and published more than 60 papers. His research interests include data fusion, parameter estimation of satellite positioning, mathematical modeling, and analysis of financial data.
Dr. Xiaojun Duan received her BS and MS degrees in applied mathematics and a PhD degree in system engineering in 1997, 2000, and 2003, respectively. She also had one year of visiting scholar experience at Ohio State University during 2007–2008. Currently, she is an associate professor in Systems Analysis and Integration. She teaches data analysis, systems science, linear algebra, probability and statistics, and mathematical modeling and trains undergraduates as a faculty advisor for participation in the Mathematical Contest in Modeling, which is held by the Society for Industry and Applied Mathematics in the United States. By teaching courses in data analysis, she gained valuable experience and also received suggestions from students on how to better organize materials so as to impart knowledge of data analysis. Her research is funded by the Natural Science Foundation of China, Spaceflight Science Foundation in China. She has published about 30 SCI or EI-indexed research papers. Her research interests cover areas such as data analysis, mathematical positioning and geodesy, complex system test, and evaluation.
Dr. Jing Yao received her BS and MS degrees in applied mathematics and a PhD degree in systems analysis and integration in 2001, 2003, and 2008, respectively. Currently, she is a lecturer at the Department of Mathematics and Systems Science, College of Science, National University of Defense Technology. She teaches probability and statistics for the undergraduate level and time series analysis with applications for the graduate level. Some of her research is funded by the National Science Foundation of China and Spaceflight Science Foundation in China. She has published more than 20 research papers. Her research interests include mathematical geodesy, data analysis, and processing in navigation systems.
Dr. Defeng Gu received his BS degree in applied mathematics and a PhD degree in systems analysis and integration in 2003 and 2009, respectively. Currently, he is a lecturer at the Department of Mathematics and Systems Science, College of Science, National University of Defense Technology. He has published more than 20 research papers. His research interests are in mathematical modeling, data analysis, and spaceborne Global Positioning System data processing. The GPS processing software that is being maintained by Dr. Gu has achieved success in real satellite orbit determination.