Missile Guidance and Control Systems: Missile Guidance and Control Systems.jpg

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 The Generalized Missile Equations of Motion . . . . . . . . . . . . 15
2.1 Coordinate Systems . . . . . . . . . . . . . . . . . . . . . . . . 15
2.1.1 Transformation Properties of Vectors . . . . . . . . . . . 15
2.1.2 Linear Vector Functions . . . . . . . . . . . . . . . . . . 16
2.1.3 Tensors . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.4 Coordinate Transformations . . . . . . . . . . . . . . . . 18
2.2 Rigid-Body Equations of Motion . . . . . . . . . . . . . . . . . 22
2.3 D’Alembert’s Principle . . . . . . . . . . . . . . . . . . . . . . 45
2.4 Lagrange’s Equations for Rotating Coordinate Systems . . . . . 46
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3 Aerodynamic Forces and Coefficients . . . . . . . . . . . . . . . . 53
3.1 Aerodynamic Forces Relative to the Wind Axis System . . . . . 53
3.2 Aerodynamic Moment Representation . . . . . . . . . . . . . . 62
3.2.1 Airframe Characteristics and Criteria . . . . . . . . . . . 77
3.3 System Design and Missile Mathematical Model . . . . . . . . . 85
3.3.1 System Design . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.2 The Missile Mathematical Model . . . . . . . . . . . . . 91
3.4 The Missile Guidance System Model . . . . . . . . . . . . . . . 99
3.4.1 The Missile Seeker Subsystem . . . . . . . . . . . . . . 102
3.4.2 Missile Noise Inputs . . . . . . . . . . . . . . . . . . . . 113
3.4.3 Radar Target Tracking Signal . . . . . . . . . . . . . . . 119
3.4.4 Infrared Tracking Systems . . . . . . . . . . . . . . . . . 125
3.5 Autopilots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.5.1 Control Surfaces and Actuators . . . . . . . . . . . . . . 144
3.6 English Bias . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
xii Contents
4 Tactical Missile Guidance Laws . . . . . . . . . . . . . . . . . . . . 155
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.2 Tactical Guidance Intercept Techniques . . . . . . . . . . . . . . 158
4.2.1 Homing Guidance . . . . . . . . . . . . . . . . . . . . . 158
4.2.2 Command and Other Types of Guidance . . . . . . . . . 162
4.3 Missile Equations of Motion . . . . . . . . . . . . . . . . . . . . 174
4.4 Derivation of the Fundamental Guidance Equations . . . . . . . 181
4.5 Proportional Navigation . . . . . . . . . . . . . . . . . . . . . . 194
4.6 Augmented Proportional Navigation . . . . . . . . . . . . . . . 225
4.7 Three-Dimensional Proportional Navigation . . . . . . . . . . . 228
4.8 Application of Optimal Control of Linear Feedback Systems
with Quadratic Performance Criteria in Missile Guidance . . . . 235
4.8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 235
4.8.2 Optimal Filtering . . . . . . . . . . . . . . . . . . . . . 237
4.8.3 Optimal Control of Linear Feedback Systems with
Quadratic Performance Criteria . . . . . . . . . . . . . . 242
4.8.4 Optimal Control for Intercept Guidance . . . . . . . . . . 248
4.9 End Game . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
5 Weapon Delivery Systems . . . . . . . . . . . . . . . . . . . . . . . 269
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
5.2 Definitions and Acronyms Used in Weapon Delivery . . . . . . . 270
5.2.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 271
5.2.2 Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . 279
5.3 Weapon Delivery Requirements . . . . . . . . . . . . . . . . . . 284
5.3.1 Tactics and Maneuvers . . . . . . . . . . . . . . . . . . . 286
5.3.2 Aircraft Sensors . . . . . . . . . . . . . . . . . . . . . . 289
5.4 The Navigation/Weapon Delivery System . . . . . . . . . . . . . 290
5.4.1 The Fire Control Computer . . . . . . . . . . . . . . . . 292
5.5 Factors Influencing Weapon Delivery Accuracy . . . . . . . . . 293
5.5.1 Error Sensitivities . . . . . . . . . . . . . . . . . . . . . 294
5.5.2 Aircraft Delivery Modes . . . . . . . . . . . . . . . . . . 297
5.6 Unguided Weapons . . . . . . . . . . . . . . . . . . . . . . . . 299
5.6.1 Types of Weapon Delivery . . . . . . . . . . . . . . . . . 300
5.6.2 Unguided Free-Fall Weapon Delivery . . . . . . . . . . . 302
5.6.3 Release Point Computation for Unguided Bombs . . . . . 304
5.7 The Bombing Problem . . . . . . . . . . . . . . . . . . . . . . . 305
5.7.1 Conversion of Ground Plane Miss Distance into Aiming
Plane Miss Distance . . . . . . . . . . . . . . . . . . . . 308
5.7.2 Multiple Impacts . . . . . . . . . . . . . . . . . . . . . . 312
5.7.3 Relationship Among REP, DEP, and CEP . . . . . . . . 314
5.8 Equations of Motion . . . . . . . . . . . . . . . . . . . . . . . . 314
5.9 Covariance Analysis . . . . . . . . . . . . . . . . . . . . . . . . 320
Contents xiii
5.10 Three-Degree-of-Freedom Trajectory Equations and
Error Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
5.10.1 Error Analysis . . . . . . . . . . . . . . . . . . . . . . . 326
5.11 Guided Weapons . . . . . . . . . . . . . . . . . . . . . . . . . . 328
5.12 Integrated Flight Control in Weapon Delivery . . . . . . . . . . . 332
5.12.1 Situational Awareness/Situation
Assessment (SA/SA) . . . . . . . . . . . . . . . . . . . . 334
5.12.2 Weapon Delivery Targeting Systems . . . . . . . . . . . 336
5.13 Air-to-Ground Attack Component . . . . . . . . . . . . . . . . . 339
5.14 Bomb Steering . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
5.15 Earth Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . 351
5.16 Missile Launch Envelope . . . . . . . . . . . . . . . . . . . . . 353
5.17 Mathematical Considerations Pertaining to the Accuracy of
Weapon Delivery Computations . . . . . . . . . . . . . . . . . . 360
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364
6 Strategic Missiles . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
6.2 The Two-Body Problem . . . . . . . . . . . . . . . . . . . . . . 366
6.3 Lambert’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . 382
6.4 First-Order Motion of a Ballistic Missile . . . . . . . . . . . . . 389
6.4.1 Application of the Newtonian Inverse-Square Field Solution
to Ballistic Missile Flight . . . . . . . . . . . . . . . . . 389
6.4.2 The Spherical Hit Equation . . . . . . . . . . . . . . . . 392
6.4.3 Ballistic Error Coefficients . . . . . . . . . . . . . . . . 418
6.4.4 Effect of the Rotation of the Earth . . . . . . . . . . . . . 440
6.5 The Correlated Velocity and Velocity-to-Be-Gained Concepts . . 443
6.5.1 Correlated Velocity . . . . . . . . . . . . . . . . . . . . 443
6.5.2 Velocity-to-Be-Gained . . . . . . . . . . . . . . . . . . . 449
6.5.3 The Missile Control System . . . . . . . . . . . . . . . . 457
6.5.4 Control During the Atmospheric Phase . . . . . . . . . . 462
6.5.5 Guidance Techniques . . . . . . . . . . . . . . . . . . . 466
6.6 Derivation of the Force Equation for Ballistic Missiles . . . . . . 472
6.6.1 Equations of Motion . . . . . . . . . . . . . . . . . . . . 477
6.6.2 Missile Dynamics . . . . . . . . . . . . . . . . . . . . . 480
6.7 Atmospheric Reentry . . . . . . . . . . . . . . . . . . . . . . . 482
6.8 Missile Flight Model . . . . . . . . . . . . . . . . . . . . . . . . 490
6.9 Ballistic Missile Intercept . . . . . . . . . . . . . . . . . . . . . 504
6.9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 504
6.9.2 Missile Tracking Equations of Motion . . . . . . . . . . 515
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
xiv Contents
7 Cruise Missiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 521
7.2 System Description . . . . . . . . . . . . . . . . . . . . . . . . 527
7.2.1 System Functional Operation and Requirements . . . . . 532
7.2.2 Missile Navigation System Description . . . . . . . . . . 534
7.3 Cruise Missile Navigation System Error Analysis . . . . . . . . 543
7.3.1 Navigation Coordinate System . . . . . . . . . . . . . . 548
7.4 Terrain Contour Matching (TERCOM) . . . . . . . . . . . . . . 551
7.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . 551
7.4.2 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . 555
7.4.3 The Terrain-Contour Matching (TERCOM) Concept . . . 557
7.4.4 Data Correlation Techniques . . . . . . . . . . . . . . . 563
7.4.5 Terrain Roughness Characteristics . . . . . . . . . . . . 568
7.4.6 TERCOM System Error Sources . . . . . . . . . . . . . 570
7.4.7 TERCOM Position Updating . . . . . . . . . . . . . . . 571
7.5 The NAVSTAR/GPS Navigation System . . . . . . . . . . . . . 576
7.5.1 GPS/INS Integration . . . . . . . . . . . . . . . . . . . . 583
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
A Fundamental Constants . . . . . . . . . . . . . . . . . . . . . . . . 589
B Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . 591
C List of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . 595
D The Standard Atmospheric Model . . . . . . . . . . . . . . . . . . 605
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 609
E Missile Classification . . . . . . . . . . . . . . . . . . . . . . . . . 611
F Past and Present Tactical/Strategic Missile Systems . . . . . . . . . 625
F.1 Historical Background . . . . . . . . . . . . . . . . . . . . . . . 625
F.2 Unpowered Precision-Guided Munitions (PGM) . . . . . . . . . 644
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 650
G Properties of Conics . . . . . . . . . . . . . . . . . . . . . . . . . . 651
G.1 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651
G.2 General Conic Trajectories . . . . . . . . . . . . . . . . . . . . 653
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
H Radar Frequency Bands . . . . . . . . . . . . . . . . . . . . . . . 659
I Selected Conversion Factors . . . . . . . . . . . . . . . . . . . . . 661
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

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Multiple Hypothesis Tracking System Design and Applcation

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