This best-selling title provides an in-depth look into tactical and strategic missile guidance, considering proven guidance methods from various points of view. The Sixth Edition includes six new chapters on topics related to improving missile guidance system performance and understanding key design concepts and tradeoffs. In addition, the original FORTRAN source code has now been converted into the widely used MATLAB programming language. The book aims to lay the foundation for meeting today’s new challenges facing guidance engineers. In this latest edition, the new chapters feature two new applications of the method of adjoints for mixed continuous-discrete systems; a new guidance law that can be used to shape the interceptor trajectory against a stationary target; an introduction of the differential game guidance law with bounded controls; techniques for graphically presenting strategic information on successful intercepts of an impulsive ballistic target being pursued by an impulsive interceptor; an examination of two filtering options for the boost-phase intercept of a strategic target; and a look into some of the guidance and control issues involved in enabling an air-launched interceptor carrying a highly maneuverable kinetic kill vehicle to perform an exoatmospheric intercept of a boosting threat target. With numerous new examples and easy-to-understand graphs and explanations, this is an indispensable guide for both the expert and the novice.
- Data and information appearing in this book are for informational purposes only. AIAA and the author are not responsible for any injury or damage resulting from use or reliance, nor do AIAA and the author warrant that use or reliance will be free from privately owned rights.
Author(s): Zarchan Paul
Edition: 6
Publisher: American Institute of Aeronautics and Astronautics
Year: 2012
Language: English
Commentary: Progress in Astronautics and Aeronautics
Pages: 1098
Tactical and Strategic Guidance 1600868940 (AIAA, 2012)......Page 1
Table of Contents......Page 6
Index......Page 0
1.2 Laplace Transforms and Differential Equations......Page 16
1.3 Numerical Integration of Differential Equations......Page 19
1.4 Z Transforms and Difference Equations......Page 23
References......Page 26
2.1 Introduction......Page 27
2.3 Simulation of Proportional Navigation in Two Dimensions......Page 28
2.4 Two-Dimensional Engagement Simulation......Page 32
2.5 Linearization......Page 38
2.6 Linearized Engagement Simulation......Page 39
2.7 Important Closed-Form Solutions......Page 43
2.8 Proportional Navigation and Zero Effort Miss......Page 46
2.9 Summary......Page 47
References......Page 48
3.2 Homing Loop......Page 49
3.3 Single Time Constant Guidance System......Page 51
3.4.2 Rule 2: Replace t by t_F - t in the Arguments of All Time-Varying Coefficients......Page 53
3.4.3 Rule 3: Reverse All Signal Flow, Redefining Nodes as Summing Junctions and Vice Versa......Page 54
3.5 Adjoint Mathematics......Page 56
3.6 Adjoints for Deterministic Systems......Page 58
3.7 Deterministic Adjoint Example......Page 60
3.8 Adjoint Closed-Form Solutions......Page 63
3.9 Normalization......Page 69
3.10 Summary......Page 71
References......Page 72
4.2 Basic Definitions......Page 73
4.3 Gaussian Noise Example......Page 76
4.4 Computational Issues......Page 81
4.6 Response of Linear System to White Noise......Page 84
4.7 Low-Pass-Filter Example......Page 85
4.8 Adjoints for Noise-Driven Systems......Page 89
4.9 Shaping Filters and Random Processes......Page 90
4.10 Example of a Stochastic Adjoint......Page 94
4.11 Closed-Form Solution for Random Target Maneuver......Page 100
4.12 Summary......Page 101
References......Page 102
5.2 Theory......Page 103
5.3 Low-Pass Filter Example......Page 104
5.4 Numerical Considerations......Page 105
5.5 Homing Loop Example......Page 107
5.6 Acceleration Adjoint......Page 114
5.7 Summary......Page 118
References......Page 119
6.2 System Order......Page 120
6.3 Design Relationships......Page 122
6.4 Optimal Target Evasive Maneuvers......Page 130
6.5 Practical Evasive Maneuvers......Page 133
6.6 Saturation......Page 135
6.7 Parasitic Effects......Page 139
6.8 Thrust Vector Control......Page 145
References......Page 147
7.2 Fading Memory Filters......Page 149
7.3 Fading Memory Filter in Homing Loop......Page 150
7.5 Replace n by N - n in the Arguments of All Variable Coefficients......Page 158
7.6 Using Adjoints to Evaluate Filter Performance......Page 160
7.7 Some Properties of Fading Memory Filters......Page 167
7.8 Estimating Target Maneuver......Page 170
References......Page 174
8.2 Review of Proportional Navigation......Page 175
8.3 Augmented Proportional Navigation......Page 177
8.4 Derivation of Augmented Proportional Navigation......Page 183
8.5 Influence of Time Constants......Page 186
8.6 Optimal Guidance......Page 189
References......Page 196
9.2 Theoretical Equations......Page 198
9.3 Application to Homing Loop......Page 200
9.4 Kalman Gains......Page 203
9.5 Numerical Examples......Page 204
9.6 Experiments with Optimal Guidance......Page 215
References......Page 222
10.2 Velocity Computation......Page 223
10.3 Drag......Page 226
10.4 Acceleration......Page 231
10.5 Gravity......Page 233
References......Page 237
11.2 Background......Page 238
11.3 Gravitational Model......Page 239
11.4 Polar Coordinate System......Page 246
11.5 Closed-Form Solutions......Page 251
11.6 Hit Equation......Page 258
11.7 Flight Time......Page 263
References......Page 264
12.2 Review......Page 266
12.3 Staging......Page 268
12.4 Booster Numerical Example......Page 271
12.5 Gravity Turn......Page 275
Reference......Page 281
13.2 Statement of Lambert's Problem......Page 282
13.3 Solution to Lambert's Problem......Page 283
13.4 Numerical Example......Page 286
13.5 Speeding Up Lambert Routine......Page 290
13.6 Booster Steering......Page 293
13.7 General Energy Management (GEM) Steering......Page 299
References......Page 307
14.2 Guidance Review......Page 308
14.3 Ballistic Engagement Simulation......Page 310
14.4 Boosting Target Considerations......Page 321
Reference......Page 332
15.2 Gravity Compensation......Page 333
15.3 Predictive Guidance......Page 337
15.4 Pulsed Guidance......Page 346
16.2 Ballistic Target Model......Page 356
16.3 Ballistic Target Experiments......Page 358
16.4 Closed-Form Solutions for Ballistic Targets......Page 363
16.5 Missile Aerodynamics......Page 366
16.6 Intercepting a Ballistic Target......Page 369
16.7 Summary......Page 377
References......Page 378
17.2 Theoretical Equations......Page 379
17.3 Differential Equation for One-Dimensional Ballistic Target......Page 381
17.4 Extended Kalman Filter for One-Dimensional Ballistic Target......Page 382
17.5 Numerical Example......Page 385
Reference......Page 393
18.2 Miss Distance due to Noise......Page 394
18.3 Fifth-Order Binomial Guidance System Miss Distances......Page 399
18.4 Minimum Guidance System Time Constant......Page 404
18.5 Missile Turning Rate Time Constant......Page 405
18.6 Checking Minimum Guidance System Time Constant Constraints......Page 406
18.7 Miss due to Noise for Aircraft and Ballistic Targets......Page 411
References......Page 414
19.2 Development of a Linear Model......Page 415
19.3 Single Time Constant Guidance System......Page 424
19.4 Higher-Order Guidance System Dynamics......Page 434
19.5 Acceleration Saturation......Page 438
References......Page 442
20.2 Weave Maneuver in Single Time Constant Guidance System......Page 443
20.3 Closed-Form Solutions for Miss Distance......Page 451
20.4 Higher-Order Guidance System Dynamics......Page 456
20.5 Acceleration Saturation......Page 461
20.6 Reducing the Time Constant to Improve Performance......Page 464
20.7 Advanced Guidance Techniques to Improve Performance......Page 467
References......Page 475
21.1 Introduction......Page 476
21.2 Force and Moment Equations......Page 477
21.3 Airframe Simulation......Page 481
21.4 Linearization of the Airframe......Page 485
21.5 Numerical Example......Page 490
21.6 Experiments......Page 495
References......Page 501
22.2 Open-Loop Flight-Control System......Page 502
22.3 Guidance System Interactions......Page 509
22.4 Rate Gyro Flight-Control System......Page 511
22.5 Open-Loop Transfer Function......Page 518
22.6 Time Domain Verification of Open-Loop Results......Page 523
22.7 Simplified Expression for Open-Loop Crossover Frequency......Page 528
References......Page 530
23.2 Three-Loop Autopilot Configuration......Page 531
23.3 Open-Loop Analysis......Page 532
23.4 Closed-Loop Analysis......Page 534
23.5 Experiments with Flight Condition......Page 551
23.6 Guidance System Analysis......Page 554
References......Page 568
24.2 Problem Setup......Page 570
24.3 Using the Schwartz Inequality for Trajectory Shaping Guidance......Page 572
24.4 Alternate Form of Trajectory Shaping Guidance Law......Page 576
24.5 Testing Trajectory Shaping Guidance in the Linear World......Page 577
24.6 Closed-Form Solutions......Page 584
24.7 Nonlinear Results......Page 591
24.8 Summary......Page 601
References......Page 602
25.2 Review of Original Three-State Linear Kalman Filter......Page 603
25.3 Four-State Weave Kalman Filter......Page 611
25.4 Miss Distance Analysis......Page 626
25.5 Extended Kalman Filter......Page 630
References......Page 647
26.2 Optimal Control......Page 648
26.3 Using Optimal Control to Derive Guidance Law for Single-Lag Flight Control System......Page 651
26.4 Deriving Guidance Law for Weaving Target Using Optimal Control......Page 657
26.5 Guidance Portion due to Maneuvering Targets......Page 663
26.6 Alternative Numerical Approach as a Result of Flight Control System Dynamics......Page 666
26.7 Deriving New Guidance Law for Cubic Flight Control System......Page 670
26.8 Alternative Approach to Cubic Flight-Control-System Guidance Law......Page 676
26.9 Performance Comparison of Guidance Laws in Presence of Cubic Flight Control System......Page 681
References......Page 688
27.2 Review of Five-State Extended-Kalman-Filter Performance......Page 690
27.3 Review of Four-State Linear Weave Kalman-Filter Performance......Page 692
27.4 Filter Bank Methodology......Page 696
27.5 Three Filter Bank Example......Page 698
References......Page 712
28.2 Weaving Targets in Three Dimensions......Page 714
28.3 Ballistic Target Trajectory Generator in Three Dimensions......Page 725
28.4 Intercept Point Prediction for Ballistic Targets......Page 735
28.5 Strategic Missile-Target Engagement Simulation......Page 740
References......Page 749
29.2 Multiple Sampling Rate Adjoint......Page 750
29.3 Adjoint of Discrete Linear Kalman Filter......Page 761
Reference......Page 775
30.2 Biased Proportional Navigation for Trajectory Shaping against Stationary Targets......Page 776
30.3 Smallest Possible Miss Distance for a Radar Homing Missile......Page 787
References......Page 804
31.1 Introduction......Page 805
31.2 Traditional Guidance Law Review......Page 806
31.3 Differential Game Guidance Law......Page 808
31.4 Target Maneuvers......Page 809
31.5 Guidance Law Comparison......Page 811
31.6 Making Differential Game Guidance More Practical......Page 824
31.7 Target Dynamics......Page 827
References......Page 830
32. Kinematics of Intercepting a Ballistic Target......Page 832
32.1 Operational Area......Page 845
32.2 Launch Area Denied......Page 850
32.3 Defended Area......Page 854
32.4 Summary......Page 858
33.1 Introduction......Page 859
33.3 ICBM Guidance......Page 860
33.4 Filtering Options......Page 867
33.5 Two-State Templated Based Filter......Page 869
33.6 Three-State Filter......Page 870
References......Page 886
34.2 Background......Page 888
34.3 Air-Launched Interceptor Approach......Page 889
34.5 One-Dimensional Model for Understanding Guidance......Page 890
34.6 Developing Formulas for Divert due to Boosting Target and PIP Errors......Page 896
34.7 Interceptor-IRBM Engagements......Page 898
34.8 Interceptor-ICBM Engagements......Page 918
34.9 Noise and Filtering......Page 922
34.10 Interceptor Engagements with Noise and Filtering......Page 938
References......Page 942
A.3 Sensitivity of Optimal Guidance to Time to Go Errors......Page 943
A.4 Simulating an Impulse......Page 946
A.5 Different Guidance System Distributions......Page 950
A.6 Sampling Experiments......Page 954
A.7 Brute Force Frequency Response......Page 956
A.8 Minimum Energy Trajectories......Page 962
A.9 Trajectory Shaping Guidance in Three Dimensions......Page 966
A.10 Modeling Poisson Target Maneuver......Page 973
References......Page 983
A......Page 984
B......Page 998
C......Page 1004
D......Page 1008
E......Page 1013
F......Page 1017
G......Page 1025
H......Page 1031
I......Page 1033
K......Page 1037
L......Page 1040
M......Page 1045
N......Page 1053
O......Page 1058
P......Page 1062
R......Page 1067
S......Page 1070
T......Page 1078
V......Page 1091
W......Page 1093
Z......Page 1096
Supporting Materials......Page 1098
