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Measurement Data Modeling and Parameter Estimation [Kõva köide]

(National University of Defense Technology, Changsha, PR of China), (National University of Defense Techno), (National University of Defense Technology, Changsha, PR of China), , (National University of Defense Technology, Changsha, China)
  • Formaat: Hardback, 554 pages, kõrgus x laius: 234x156 mm, kaal: 861 g, 39 Tables, black and white; 46 Illustrations, black and white
  • Sari: Systems Evaluation, Prediction, and Decision-Making
  • Ilmumisaeg: 06-Dec-2011
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1439853789
  • ISBN-13: 9781439853788
Teised raamatud teemal:
Measurement Data Modeling and Parameter EstimationSuurem pilt
  • Formaat: Hardback, 554 pages, kõrgus x laius: 234x156 mm, kaal: 861 g, 39 Tables, black and white; 46 Illustrations, black and white
  • Sari: Systems Evaluation, Prediction, and Decision-Making
  • Ilmumisaeg: 06-Dec-2011
  • Kirjastus: CRC Press Inc
  • ISBN-10: 1439853789
  • ISBN-13: 9781439853788
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781439853788.html
Märksõnad:
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.
Preface xv
Authors xix
Chapter 1 Error Theory 1(38)
1.1 Measurement
1(5)
1.1.1 Measurement Data
1(1)
1.1.2 Classification of Measurement
2(4)
1.1.2.1 Concept of Measurement
2(1)
1.1.2.2 Methods of Measurement
3(1)
1.1.2.3 Equal Precision and Unequal Precision Measurements
4(1)
1.1.2.4 Measurements of Static and Dynamic Objects
5(1)
1.2 Measurement Error
6(2)
1.2.1 Concept of Error
6(1)
1.2.2 Source of Errors
6(1)
1.2.3 Error Classification
7(1)
1.2.4 Quality of Measurement Data
8(1)
1.2.5 Summary
8(1)
1.3 Random Error in Independent Measurements with Equal Precision
8(9)
1.3.1 Postulate of Random Error and Gaussian Law of Error
9(1)
1.3.2 Numerical Characteristics of a Random Error
10(3)
1.3.2.1 Mean
10(1)
1.3.2.2 Standard Deviation
11(1)
1.3.2.3 Estimation of Standard Deviation
11(1)
1.3.2.4 Estimation of Mean and Standard Deviation
12(1)
1.3.3 Distributions and Precision Indices of Random Errors
13(4)
1.3.3.1 Distributions of Random Errors
13(2)
1.3.3.2 Precision Index of Measurement
15(2)
1.4 Systematic Errors
17(5)
1.4.1 Causes of Systematic Errors
17(1)
1.4.2 Variation Rules of Systematic Errors
18(1)
1.4.3 Identification of Systematic Errors
19(2)
1.4.4 Reduction and Elimination of Systematic Errors
21(1)
1.5 Negligent Errors
22(6)
1.5.1 Causes and Avoidance of Negligent Errors
23(1)
1.5.1.1 Causes of Negligent Errors
23(1)
1.5.1.2 Avoidance of Negligent Errors
23(1)
1.5.2 Negligent Errors in Measurement Data of Static Objects
23(5)
1.5.2.1 Romannovschi Criterion
23(4)
1.5.2.2 Grubbs Criterion
27(1)
1.5.2.3 Summary of Identification Criteria
28(1)
1.6 Synthesis of Errors
28(5)
1.6.1 Uncertainty of Measurement
28(3)
1.6.1.1 Estimation of Measurement Uncertainty
29(1)
1.6.1.2 Propagation of Uncertainties
29(2)
1.6.2 Functional Errors
31(9)
1.6.2.1 Functional Systematic Errors
31(1)
1.6.2.2 Functional Random Errors
31(2)
1.7 Steps of Data Processing: Static Measurement Data
33(3)
References
36(3)
Chapter 2 Parametric Representations Of Functions To Be Estimated 39(54)
2.1 Introduction
39(1)
2.2 Polynomial Representations of Functions to Be Estimated
40(21)
2.2.1 Weierstrass Theorem
41(2)
2.2.2 Best Approximation Polynomials
43(1)
2.2.3 Best Approximation of Induced Functions
44(2)
2.2.4 Degrees of Best Approximation Polynomials
46(2)
2.2.5 Bases of Polynomial Representations of Functions to Be Estimated
48(13)
2.2.5.1 Significance of Basis Selection
48(1)
2.2.5.2 Chebyshev Polynomials
49(1)
2.2.5.3 Bases of Interpolation Polynomials of Order n
50(4)
2.2.5.4 Chebyshev Polynomial Bases
54(5)
2.2.5.5 Bases and Coefficients
59(2)
2.3 Spline Representations of Functions to Be Estimated
61(19)
2.3.1 Basic Concept of Spline Functions
61(4)
2.3.2 Properties of Cubic Spline Functions
65(8)
2.3.3 Standard B Splines
73(5)
2.3.4 Bases of Spline Representations of Functions to Be Estimated
78(2)
2.4 Using General Solutions of Ordinary Differential Equations to Represent Functions to Be Estimated
80(5)
2.4.1 Introduction
80(1)
2.4.2 General Solutions of Linear Ordinary Differential Equations
81(2)
2.4.3 General Solutions of Nonlinear Equation or Equations
83(2)
2.5 Empirical Formulas
85(7)
2.5.1 Empirical Formulas from Scientific Laws
86(1)
2.5.2 Empirical Formulas from Experience
87(1)
2.5.3 Empirical Formulas of Mechanical Type
88(1)
2.5.4 Empirical Formulas of Progressive Type
89(3)
References
92(1)
Chapter 3 Methods Of Modern Regression Analysis 93(136)
3.1 Introduction
93(5)
3.2 Basic Methods of Linear Regression Analysis
98(20)
3.2.1 Point Estimates of Parameters
98(6)
3.2.2 Hypothesis Tests on Regression Coefficients
104(5)
3.2.3 Interval Estimates of Parameters
109(5)
3.2.4 Least Squares Estimates and Multicollinearity
114(4)
3.3 Optimization of Regression Models
118(13)
3.3.1 Dynamic Measurement Data and Regression Models
119(5)
3.3.2 Compound Models for Signals and Systematic Errors
124(7)
3.4 Variable Selection
131(26)
3.4.1 Consequences of Variable Selection
134(4)
3.4.2 Criteria of Variable Selection
138(8)
3.4.3 Fast Algorithms to Select Optimal Reduced Regression Model
146(10)
3.4.4 Summary
156(1)
3.5 Biased Estimation in Linear Regression Models
157(18)
3.5.1 Introduction
157(1)
3.5.2 Biased Estimates of Compression Type
158(3)
3.5.3 A New Method to Determine Ridge Parameters
161(5)
3.5.4 Scale Factors
166(4)
3.5.5 Numerical Examples
170(5)
3.6 The Method of Point-by-Point Elimination for Outliers
175(15)
3.6.1 Introduction
175(1)
3.6.2 Derivation of Criteria
176(11)
3.6.3 Numerical Examples
187(3)
3.7 Efficiency of Parameter Estimation in Linear Regression Models
190(10)
3.7.1 Introduction
190(4)
3.7.2 Efficiency of Parameter Estimation in Linear Regression Models with One Variable
194(3)
3.7.3 Efficiency of Parameter Estimation in Multiple Linear Regression Models
197(3)
3.8 Methods of Nonlinear Regression Analysis
200(13)
3.8.1 Models of Nonlinear Regression Analysis
200(3)
3.8.2 Methods of Parameter Estimation
203(10)
3.9 Additional Information
213(13)
3.9.1 Sources of Additional Information
213(4)
3.9.2 Applications of Additional Information
217(9)
References
226(3)
Chapter 4 Methods Of Time Series Analysis 229(70)
4.1 Introduction to Time Series
229(1)
4.1.1 Time Series and Random Process
229(1)
4.1.2 Time Series Analysis
229(1)
4.2 Stationary Time Series Models
230(21)
4.2.1 Stationary Random Processes
230(2)
4.2.2 Autoregressive Models
232(5)
4.2.3 Moving Average Model
237(3)
4.2.4 ARMA(p, 7) Model
240(5)
4.2.5 Partial Correlation Function of a Stationary Model
245(6)
4.3 Parameter Estimation of Stationary Time Series Models
251(9)
4.3.1 Estimation of Autocovariance Functions and Autocorrelation Functions
251(2)
4.3.2 Parameter Estimation of AR(p) Models
253(2)
4.3.2.1 Moment Estimation of Parameters in AR Models
253(1)
4.3.2.2 Least Squares Estimation of Parameters in AR Models
254(1)
4.3.3 Parameter Estimation of MA(g) Models
255(3)
4.3.3.1 Linear Iteration Method
256(1)
4.3.3.2 Newton-Raphson Algorithm
256(2)
4.3.4 Parameter Estimation of ARMA(p,q) Models
258(2)
4.3.4.1 Moment Estimation
258(1)
4.3.4.2 Nonlinear Least Squares Estimation
259(1)
4.4 Tests of Observational Data from a Time Series
260(6)
4.4.1 Normality Test
261(1)
4.4.2 Independence Test
262(1)
4.4.3 Stationarity Test: Reverse Method
263(3)
4.4.3.1 Testing the Mean Stationarity
265(1)
4.4.3.2 Testing the Variance Stationarity
265(1)
4.5 Modeling Stationary Time Series
266(4)
4.5.1 Model Selection: Box-Jenkins Method
266(1)
4.5.2 AIC Criterion for Model Order Determination
267(1)
4.5.2.1 AIC for AR Models
268(1)
4.5.2.2 AIC for MA and ARMA Models
268(1)
4.5.3 Model Testing
268(2)
4.5.3.1 AR Models Testing
269(1)
4.5.3.2 MA Models Testing
269(1)
4.5.3.3 ARMA Models Testing
269(1)
4.6 Nonstationary Time Series
270(20)
4.6.1 Nonstationarity of Time Series
270(1)
4.6.1.1 Processing Variance Nonstationarity
270(1)
4.6.1.2 Processing Mean Nonstationarity
271(1)
4.6.2 ARIMA Model
271(2)
4.6.2.1 Definition of ARIMA Model
271(2)
4.6.2.2 ARIMA Model Fitting for Time Series Data
273(1)
4.6.3 RARMA Model
273(3)
4.6.4 PAR Model
276(6)
4.6.4.1 Model and Parameter Estimation
276(2)
4.6.4.2 PAR Model Fitting
278(1)
4.6.4.3 Further Discussions
279(3)
4.6.5 Parameter Estimation of RAR Model
282(5)
4.6.6 Parameter Estimation of RMA Model
287(1)
4.6.7 Parameter Estimation of RARMA Model
288(2)
4.7 Mathematical Modeling of CW Radar Measurement Noise
290(6)
References
296(3)
Chapter 5 Discrete-Time Kalman Filter 299(48)
5.1 Introduction
299(2)
5.2 Random Vector and Estimation
301(9)
5.2.1 Random Vector and Its Process
301(4)
5.2.1.1 Mean Vector and Variance Matrix
301(2)
5.2.1.2 Conditional Mean Vector and Conditional Variance Matrix
303(1)
5.2.1.3 Vector Random Process
304(1)
5.2.2 Estimate of the State Vector
305(5)
5.2.2.1 Minimum Mean Square Error Estimate
305(3)
5.2.2.2 Linear Minimum Mean Square Error Estimate (LMMSEE)
308(2)
5.2.2.3 The Relation between MMSEE and LMMSEE
310(1)
5.3 Discrete Time Kalman Filter
310(11)
5.3.1 Orthogonal Projection
310(4)
5.3.2 The Formula of Kalman Filter
314(3)
5.3.3 Examples
317(4)
5.4 Kalman Filter with Colored Noise
321(4)
5.4.1 Kalman Filter with Colored State Noise
321(1)
5.4.2 Kalman Filtering with Colored Measurement Noise
322(2)
5.4.3 Kalman Filtering with Both Colored State Noise and Measurement Noise
324(1)
5.5 Divergence of Kalman Filter
325(7)
5.6 Kalman Filter with Noises of Unknown Statistical Characteristics
332(13)
5.6.1 Selection of Correlation Matrix Qk of the Dynamic Noise
333(1)
5.6.2 Extracting Statistical Features of Measurement Noises
333(12)
References
345(2)
Chapter 6 Processing Data From Radar Measurements 347(102)
6.1 Introduction
347(14)
6.1.1 Space Measurements
347(1)
6.1.2 Tracking Measurements and Trajectory Determination Principle
348(5)
6.1.2.1 Optical Measurements
348(2)
6.1.2.2 Radar Measurements
350(3)
6.1.3 Precision Appraisal and Calibration of Measurement Equipments
353(3)
6.1.3.1 Precision Appraisal
353(1)
6.1.3.2 Precision Calibration
354(2)
6.1.4 Systematic Error Model of CW Radar
356(1)
6.1.5 Mathematical Processing for Radar Measurement Data
357(4)
6.2 Parametric Representation of the Trajectory
361(9)
6.2.1 Equation Representation of Trajectory
361(2)
6.2.2 Polynomial Representation of Trajectory
363(2)
6.2.3 Matching Principle
365(1)
6.2.4 Spline Representation of Trajectory
366(4)
6.3 Trajectory Calculation
370(13)
6.3.1 Mathematical Method for MISTRAM System Trajectory Determination
371(5)
6.3.1.1 Problem Introduction
371(1)
6.3.1.2 Mathematical Model for the MISTRAM System Measurement Data
372(1)
6.3.1.3 Mathematical Method for Trajectory Determination
372(3)
6.3.1.4 Error Propagation Relationship
375(1)
6.3.2 Nonlinear Regression Analysis Method for Trajectory Determination
376(7)
6.3.2.1 Introduction
376(1)
6.3.2.2 Mathematical Model Establishment
377(2)
6.3.2.3 Algorithm and Error Analysis
379(3)
6.3.3.4 Simulation Calculation Results
382(1)
6.4 Composite Model of Systematic Error and Trajectory Parameters
383(4)
6.4.1 Measurement Data Models
383(1)
6.4.2 Matched Systematic Error and Unmatched Systematic Error
384(3)
6.4.3 Summary
387(1)
6.5 Time Alignment of CW Radar Multistation Tracking Data
387(14)
6.5.1 Introduction
387(1)
6.5.2 Velocity Measurement Mechanism of CW Radars
388(3)
6.5.3 Mathematical Model of the Multistation Measurement Data
391(2)
6.5.4 Solving Method and Error Analysis
393(5)
6.5.5 Time Alignment between the Distance Sum and Its Change Rate
398(3)
6.6 Estimation for Constant Systematic Error of CW Radars
401(15)
6.6.1 Mathematical Model of Measurement Data
401(2)
6.6.2 EMBET Method Analysis
403(2)
6.6.3 Nonlinear Modeling Method
405(7)
6.6.4 Algorithm and Numerical Examples
412(3)
6.6.5 Conclusions
415(1)
6.7 Systematic Error Estimation for the Free Flight Phase
416(10)
6.7.1 Trajectory Equations in the Free Flight Phase
417(3)
6.7.2 Nonlinear Model of the Measurement Data
420(3)
6.7.3 Parameter Estimation Method
423(3)
6.7.4 Numerical Example and Analysis
426(1)
6.8 Estimation of Slow Drift Error in Range Rate Measurement
426(12)
6.8.1 Mathematical Model of Measurement Data
426(3)
6.8.2 Selection of the Spline Nodes
429(7)
6.8.3 Estimation of the Slow Drift Errors
436(2)
6.9 Summary of Radar Measurement Data Processing
438(9)
6.9.1 Data Processing Procedures
438(6)
6.9.1.1 Analysis of Abnormal Data
439(1)
6.9.1.2 Analysis of the Measurement Principle and the Measurement Data
440(1)
6.9.1.3 Measurement Data Modeling.
441(1)
6.9.1.4 Estimation of Statistical Features of Random Errors
442(1)
6.9.1.5 Estimation of True Signal and Systematic Error
443(1)
6.9.1.6 Engineering Analysis for Data Processing Results
443(1)
6.9.2 Basic Conclusions
444(3)
References
447(2)
Chapter 7 Precise Orbit Determination Of Leo Satellites Based On Dual-Frequency Gps 449(48)
7.1 Introduction
449(2)
7.2 Spaceborne Dual-Frequency GPS Data Preprocessing
451(16)
7.2.1 Basic Observation Equations
452(1)
7.2.2 Pseudocode Outliers Removal
452(9)
7.2.2.1 Threshold Method of Signal-to-Noise Ratio
453(1)
7.2.2.2 Threshold Method of Ionospheric Delay
453(1)
7.2.2.3 Fitting Residual Method of Ionospheric Delay
453(5)
7.2.2.4 Method of Monitoring Receiver Autonomous Integrity
458(3)
7.2.3 Carrier Phase Outliers Removal and Cycle Slip Detection
461(5)
7.2.3.1 M-W Combination Epoch Difference Method
462(1)
7.2.3.2 Ionosphere-Free Ambiguity Epoch Difference Method
463(1)
7.2.3.3 Cumulative Sum Method
464(2)
7.2.4 Data Preprocessing Flow
466(1)
7.3 Orbit Determination by Zero-Difference Reduced Dynamics
467(27)
7.3.1 Observational Equations and Error Correction
469(4)
7.3.1.1 Relativity Adjustments
470(1)
7.3.1.2 Antenna Offset Corrections for GPS Satellites
470(2)
7.3.1.3 Antenna Offsets for LEO Satellites
472(1)
7.3.2 Parameter Estimation of Orbit Models
473(4)
7.3.3 Dynamic Orbit Models and Parameter Selections
477(8)
7.3.3.1 Earth Nonspherical Perturbation
478(2)
7.3.3.2 Third Body Gravitational Perturbations
480(1)
7.3.3.3 Tide Perturbations
481(1)
7.3.3.4 Atmospheric Drag Forces
481(1)
7.3.3.5 Solar Radiation Pressures
482(1)
7.3.3.6 Relativity Perturbations
483(1)
7.3.3.7 Empirical Forces
483(1)
7.3.3.8 Dynamic Orbit Models and Parameter Selections
484(1)
7.3.4 Re-Editing Observational Data
485(1)
7.3.4.1 Re-Editing Pseudocode Data
485(1)
7.3.4.2 Re-Editing Phase Data
485(1)
7.3.5 The Flow of Zero-Difference Reduced Dynamic Orbit Determination
486(1)
7.3.6 Analysis of Results from Orbit Determination
487(7)
References
494(3)
Appendix 1 Matrix Formulas In Common Use 497(6)
A1.1 Trace of a Matrix
497(1)
A1.2 Inverse of a Block Matrix
498(2)
A1.3 Positive Definite Character of a Matrix
500(1)
A1.4 Idempotent Matrix
501(1)
A1.5 Derivative of a Quadratic Form
501(2)
Appendix 2 Distributions In Common Use 503(14)
A2.1 x2-Distribution
503(2)
A2.2 Noncentral x2-Distribution
505(1)
A2.3 t-Distribution
506(2)
A2.4 F-Distribution
508(9)
Index 517
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