Contents
Aircraft System Identification: Theory and Practice
by
Preface xiii
Chapter 1 Introduction 1
1.1 System Identification Applied to Aircraft 2
1.2 Outline of the Text 4
References 6
Chapter 2 Elements of System Theory 9
2.1 Mathematical Modeling 9
2.2 System Identification and Parameter Estimation 17
2.3 Aircraft System Identification 19
2.4 Summary and Concluding Remarks 24
References 25
Chapter 3 Mathematical Model of an Aircraft 27
3.1 Reference Frames and Sign Conventions 28
3.2 Rigid Body Equations of Motion 31
3.3 Rotational Kinematic Equations 36
3.4 Navigation Equations 37
3.5 Force Equations in Wind Axes 38
3.6 Collected Equations of Motion 40
3.7 Output Equations 42
3.8 Aerodynamic Model Equations 45
3.9 Simplifying the Equations of Motion 60
3.10 Summary and Concluding Remarks 71
References 72
Chapter 4 Outline of Estimation Theory 75
4.1 Properties of Estimators 77
4.2 Parameter Estimation 79
4.3 State Estimation 83
4.4 Summary and Concluding Remarks 92
References 94
Chapter 5 Regression Methods 95
5.1 Ordinary Least Squares 97
5.2 Generalized Least Squares 132
5.3 Nonlinear Least Squares 137
5.4 Model Structure Determination 138
5.5 Data Collinearity 158
5.6 Data Partitioning 174
5.7 Summary and Concluding Remarks 176
References 179
Chapter 6 Maximum Likelihood Methods 181
6.1 Dynamic System with Process Noise 182
6.2 Output-Error Method 191
6.3 Computational Aspects 195
6.4 Equation-Error Method 216
6.5 Summary and Concluding Remarks 220
References 221
Chapter 7 Frequency Domain Methods 225
7.1 Transforming Measured Data to the Frequency Domain 226
7.2 Frequency Response 228
7.3 Maximum Likelihood Estimator 232
7.4 Output-Error Method 237
7.5 Equation-Error Method 240
7.6 Complex Linear Regression 243
7.7 Low Order Equivalent System Identification 250
7.8 Summary and Concluding Remarks 258
References 259
Chapter 8 Real-Time Parameter Estimation 261
8.1 Recursive Least Squares 264
8.2 Time-Varying Parameters 270
8.3 Regularization 273
8.4 Frequency-Domain Sequential Least Squares 275
8.5 Extended Kalman Filter 282
8.6 Summary and Concluding Remarks 285
References 287
Chapter 9 Experiment Design 289
9.1 Data Acquisition System 290
9.2 Instrumentation 297
9.3 Input Design 299
9.4 Recommendations 323
9.5 Open-loop Parameter Estimation from Closed-Loop Data 327
9.6 Summary and Concluding Remarks 329
References 329
Chapter 10 Data Compatibility 333
10.1 Kinematic Equations 333
10.2 Data Reconstruction 336
10.3 Aircraft Instrumentation Errors 338
10.4 Model Equations for Data Compatibility Check 340
10.5 Instrumentation Error Estimation Methods 344
10.6 Summary and Concluding Remarks 348
References 349
Chapter 11 Data Analysis 351
11.1 Filtering 351
11.2 Smoothing 352
11.3 Interpolation 366
11.4 Numerical Differentiation 367
11.5 Signal Comparisons 369
11.6 Finite Fourier Transform 370
11.7 Power Spectrum Estimation 376
11.8 Maneuver Visualization 380
11.9 Summary and Concluding Remarks 381
References 382
Chapter 12 MATLAB® Software 383
12.1 Overview 383
12.2 Linear Regression 388
12.3 Model Structure Determination 390
12.4 Output-Error Parameter Estimation 395
12.5 Frequency Domain 399
12.6 Real-Time Parameter Estimation 403
12.7 Input Design 406
12.8 Data Compatibility 411
12.9 Data Analysis 415
References 422
Appendices 423
A. Mathematical Background 423
A.1 Linear Algebra 423
A.2 Complex Numbers 432
A.3 Calculus 434
A.4 Polynomial Splines 437
B. Probability, Statistics, and Random Variables 439
B.1 Random Variables 439
B.2 Statistics 444
B.3 Random Process Theory 451
References 454
C. Reference Information 455
C.1 Properties of Air and the Atmosphere 455
C.2 Elementary Aerodynamics 456
C.3 Mass / Inertia Properties 459
C.4 Greek Alphabet and Conversion Factors 461
References 461
D. F-16 Nonlinear Simulation 463
D.1 F-16 Aircraft 463
D.2 Equations of Motion 463
D.3 Engine Model 468
D.4 Aerodynamic Model 469
D.5 Atmosphere Model 470
D.6 Mass / Inertia Properties 471
D.7 Analysis Tools 471
References 476
Index 479
Supporting Materials 485