Tactical and strategic missile guidance

Title:

Personal Author:

Zarchan, Paul

Series:

Progress in astronautics and aeronautics ; v. 219

Edition:

5th ed.

Publication Information:

Reston, Va. : American Institute of Aeronautics and Astronautics, c2007

Physical Description:

888 p. : ill. ; 24 cm.

ISBN:

9781563478741

Subject Term:

Guided missiles -- Guidance systems

Ballistic missiles -- Guidance systems

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010263466	TL507 Z37 2007	Open Access Book	Book	Searching... Unknown

The fifth edition of this best-selling title has three new chapters on important topics related to improving missile guidance performance and several important new concepts in the Appendix. The first new chapter presents several alternative ways of developing guidance laws numerically. These techniques can be used to derive more advanced guidance laws when the missile guidance system dynamics become very complex. An example is presented showing the advantages of a new advanced guidance law over more conventional guidance laws. Previous editions of the text have shown that intentional or unintentional spiraling maneuvers on the part of a tactical ballistic missile can also make it particularly difficult for a pursuing missile to hit. Estimating the target weave frequency is a critical component in advanced guidance laws that can be used to counter these spiraling threats. The second new chapter presents a linear Kalman filter bank approach, originally introduced in the 1960's, for accurately estimating the target weave frequency and improving missile guidance system performance.So far, all of the engagement simulations presented in this text have either been in one or two dimensions. This was done to make it easier for the reader to more easily understand all of the concepts presented in the text. The third new chapter provides several examples on how to convert previous engagement simulation code to three dimensions in both the tactical and strategic worlds. A simplified mapping database is included with the text in order to demonstrate how geographical context can be provided in three dimensional strategic engagement simulations. An example of one of the new concepts presented in the Appendix is the use of the discrete Fourier Transform for calculating the miss due to weaving targets. Together with numerous new examples and easy-to-understand graphs and explanations, readers with varied learning styles will find ""Tactical and Strategic Missile Guidance"" a staple for any aerospace engineer's library. Companion software, in both Macintosh and IBM-compatible versions, contains source code listings in FORTRAN, C, and MATLAB[registered] languages.A detailed set of appendices not only serves as a user's guide but also explains how the text's FORTRAN source can easily be converted to either C or MATLAB. The conversion technique plus detailed source code examples will be tools of interest to all engineers, regardless of whether you specialize in missile guidance or other aerospace-related fields.

Author Notes

Paul Zarchan is currently a member of the technical staff at MIT Lincoln Laboratory

Acknowledgments	p. xvii
Preface to the Fifth Edition	p. xix
Introduction	p. xxi
Chapter 1 Numerical Techniques	p. 1
Introduction	p. 1
Laplace Transforms and Differential Equations	p. 1
Numerical Integration of Differential Equations	p. 3
Z Transforms and Difference Equations	p. 6
References	p. 10
Chapter 2 Fundamentals of Tactical Missile Guidance	p. 11
Introduction	p. 11
What Is Proportional Navigation?	p. 12
Simulation of Proportional Navigation in Two Dimensions	p. 12
Two-Dimensional Engagement Simulation	p. 15
Linearization	p. 20
Linearized Engagement Simulation	p. 22
Important Closed-Form Solutions	p. 24
Proportional Navigation and Zero Effort Miss	p. 27
Summary	p. 28
References	p. 28
Chapter 3 Method of Adjoints and the Homing Loop	p. 31
Introduction	p. 31
Homing Loop	p. 31
Single Time Constant Guidance System	p. 32
How to Construct an Adjoint	p. 34
Adjoint Mathematics	p. 37
Adjoints for Deterministic Systems	p. 38
Deterministic Adjoint Example	p. 40
Adjoint Closed-Form Solutions	p. 43
Normalization	p. 48
Summary	p. 50
References	p. 50
Chapter 4 Noise Analysis	p. 51
Introduction	p. 51
Basic Definitions	p. 51
Gaussian Noise Example	p. 54
Computational Issues	p. 58
More Basic Definitions	p. 60
Response of Linear System to White Noise	p. 61
Low-Pass-Filter Example	p. 61
Adjoints for Noise-Driven Systems	p. 65
Shaping Filters and Random Processes	p. 66
Example of a Stochastic Adjoint	p. 70
Closed-Form Solution for Random Target Maneuver	p. 75
Summary	p. 76
References	p. 77
Chapter 5 Covariance Analysis and the Homing Loop	p. 79
Background	p. 79
Theory	p. 79
Low-Pass Filter Example	p. 80
Numerical Considerations	p. 81
Homing Loop Example	p. 82
Acceleration Adjoint	p. 91
Summary	p. 94
References	p. 94
Chapter 6 Proportional Navigation and Miss Distance	p. 95
Introduction	p. 95
System Order	p. 95
Design Relationships	p. 96
Optimal Target Evasive Maneuvers	p. 104
Practical Evasive Maneuvers	p. 106
Saturation	p. 108
Parasitic Effects	p. 110
Thrust Vector Control	p. 116
Summary	p. 118
References	p. 118
Chapter 7 Digital Fading Memory Noise Filters in the Homing Loop	p. 119
Introduction	p. 119
Fading Memory Filters	p. 119
Fading Memory Filter in Homing Loop	p. 120
Mixed Continuous Discrete Adjoint Theory	p. 127
Replace n by N - n in the Arguments of All Variable Coefficients	p. 127
Using Adjoints to Evaluate Filter Performance	p. 130
Some Properties of Fading Memory Filters	p. 134
Estimating Target Maneuver	p. 136
Summary	p. 140
References	p. 140
Chapter 8 Advanced Guidance Laws	p. 143
Introduction	p. 143
Review of Proportional Navigation	p. 143
Augmented Proportional Navigation	p. 145
Derivation of Augmented Proportional Navigation	p. 149
Influence of Time Constants	p. 152
Optimal Guidance	p. 155
Summary	p. 161
References	p. 161
Chapter 9 Kalman Filters and the Homing Loop	p. 163
Introduction	p. 163
Theoretical Equations	p. 163
Application to Homing Loop	p. 164
Kalman Gains	p. 167
Numerical Examples	p. 168
Experiments with Optimal Guidance	p. 178
Summary	p. 183
References	p. 183
Chapter 10 Other Forms of Tactical Guidance	p. 185
Introduction	p. 185
Proportional Navigation Command Guidance	p. 185
Beam Rider Guidance	p. 193
Command to Line-of-Sight Guidance	p. 201
Summary	p. 204
References	p. 205
Chapter 11 Tactical Zones	p. 207
Introduction	p. 207
Velocity Computation	p. 207
Drag	p. 210
Acceleration	p. 214
Gravity	p. 216
Summary	p. 219
References	p. 219
Chapter 12 Strategic Considerations	p. 221
Introduction	p. 221
Background	p. 221
Gravitational Model	p. 221
Polar Coordinate System	p. 228
Closed-Form Solutions	p. 233
Hit Equation	p. 239
Flight Time	p. 243
Summary	p. 244
References	p. 245
Chapter 13 Boosters	p. 247
Introduction	p. 247
Review	p. 247
Staging	p. 249
Booster Numerical Example	p. 251
Gravity Turn	p. 255
Summary	p. 261
Reference	p. 261
Chapter 14 Lambert Guidance	p. 263
Introduction	p. 263
Statement of Lambert's Problem	p. 263
Solution to Lambert's Problem	p. 264
Numerical Example	p. 267
Speeding Up Lambert Routine	p. 270
Booster Steering	p. 274
General Energy Management (GEM) Steering	p. 281
Summary	p. 289
References	p. 289
Chapter 15 Strategic Intercepts	p. 291
Introduction	p. 291
Guidance Review	p. 291
Ballistic Engagement Simulation	p. 293
Boosting Target Considerations	p. 305
Summary	p. 316
Reference	p. 316
Chapter 16 Miscellaneous Topics	p. 317
Introduction	p. 317
Gravity Compensation	p. 317
Predictive Guidance	p. 320
Booster Estimation with Range and Angle Measurements	p. 330
Pulsed Guidance	p. 342
Chapter 17 Ballistic Target Properties	p. 353
Introduction	p. 353
Ballistic Target Model	p. 353
Ballistic Target Experiments	p. 354
Closed-Form Solutions for Ballistic Targets	p. 359
Missile Aerodynamics	p. 362
Intercepting a Ballistic Target	p. 364
Summary	p. 371
References	p. 372
Chapter 18 Extended Kalman Filtering and Ballistic Coefficient Estimation	p. 373
Introduction	p. 373
Theoretical Equations	p. 373
Differential Equation for One-Dimensional Ballistic Target	p. 375
Extended Kalman Filter for One-Dimensional Ballistic Target	p. 376
Numerical Example	p. 379
Summary	p. 387
References	p. 387
Chapter 19 Ballistic Target Challenges	p. 389
Introduction	p. 389
Miss Distance Due to Noise	p. 389
Fifth-Order Binomial Guidance System Miss Distances	p. 393
Minimum Guidance System Time Constant	p. 397
Missile Turning Rate Time Constant	p. 397
Checking Minimum Guidance System Time Constant Constraints	p. 399
Miss Due to Noise for Aircraft and Ballistic Targets	p. 403
Summary	p. 405
References	p. 405
Chapter 20 Multiple Targets	p. 407
Introduction and Background	p. 407
Development of a Linear Model	p. 407
Single Time Constant Guidance System	p. 415
Higher-Order Guidance System Dynamics	p. 422
Acceleration Saturation	p. 426
Summary	p. 431
References	p. 431
Chapter 21 Weaving Targets	p. 433
Introduction and Background	p. 433
Weave Maneuver in Single Time Constant Guidance System	p. 433
Closed-Form Solutions for Miss Distance	p. 440
Higher-Order Guidance System Dynamics	p. 444
Acceleration Saturation	p. 448
Reducing the Time Constant to Improve Performance	p. 451
Advanced Guidance Techniques to Improve Performance	p. 453
Summary	p. 460
References	p. 460
Chapter 22 Representing Missile Airframe with Transfer Functions	p. 461
Introduction	p. 461
Force and Moment Equations	p. 461
Airframe Simulation	p. 465
Linearization of the Airframe	p. 469
Numerical Example	p. 472
Experiments	p. 478
Summary	p. 482
References	p. 482
Chapter 23 Introduction to Flight Control Besign	p. 483
Introduction	p. 483
Open-Loop Flight-Control System	p. 483
Guidance System Interactions	p. 489
Rate Gyro Flight-Control System	p. 490
Open-Loop Transfer Function	p. 496
Time Domain Verification of Open-Loop Results	p. 500
Simplified Expression for Open-Loop Crossover Frequency	p. 504
Summary	p. 506
References	p. 506
Chapter 24 Three-Loop Autopilot	p. 507
Introduction	p. 507
Three-Loop Autopilot Configuration	p. 507
Open-Loop Analysis	p. 507
Closed-Loop Analysis	p. 510
Experiments with Flight Condition	p. 523
Guidance System Analysis	p. 527
Summary	p. 539
References	p. 539
Chapter 25 Trajectory Shaping Guidance	p. 541
Introduction	p. 541
Problem Setup	p. 541
Using the Schwartz Inequality for Trajectory Shaping Guidance	p. 543
Alternate Form of Trajectory Shaping Guidance Law	p. 547
Testing Trajectory Shaping Guidance in the Linear World	p. 548
Closed-Form Solutions	p. 554
Nonlinear Results	p. 560
Summary	p. 568
References	p. 569
Chapter 26 Filtering and Weaving Targets	p. 571
Introduction	p. 571
Review of Original Three-State Linear Kalman Filter	p. 571
Four-State Weave Kalman Filter	p. 579
Miss Distance Analysis	p. 592
Extended Kalman Filter	p. 595
Summary	p. 612
References	p. 612
Chapter 27 Predictor-Corrector Guidance	p. 613
Introduction	p. 613
Surface-to-Surface Missile Problem	p. 613
Predictor-Corrector Guidance With Surface-to-Surface Intercept Problem	p. 620
Roll Angle or Rate Guidance Problem	p. 627
Predictor-Corrector Guidance With Roll-Rate Problem	p. 631
Summary	p. 641
References	p. 641
Chapter 28 Alternative Approaches to Guidance Law Development	p. 643
Introduction	p. 643
Optimal Control	p. 643
Using Optimal Control to Derive Guidance Law for Single-Lag Flight Control System	p. 645
Deriving Guidance Law for Weaving Target Using Optimal Control	p. 652
Guidance Portion due to Maneuvering Targets	p. 658
Alternative Numerical Approach as a Result of due to Flight Control System Dynamics	p. 660
Deriving New Guidance Law for Cubic Flight Control System	p. 664
Alternative Approach to Cubic Flight-Control-System Guidance Law	p. 670
Performance Comparison of Guidance Laws in Presence of Cubic Flight Control System	p. 670
Summary	p. 682
References	p. 682
Chapter 29 Filter Bank Approach to Weaving Target Problem	p. 683
Introduction	p. 683
Review of Five-State Extended-Kalman-Filter Performance	p. 683
Review of Four-State Linear Weave Kalman-Filter Performance	p. 685
Filter Bank Methodology	p. 688
Three Filter Bank Example	p. 690
Twelve-Filter Bank	p. 704
Summary	p. 718
References	p. 719
Chapter 30 Engagement Simulations in Three Dimensions	p. 721
Introduction	p. 721
Weaving Targets in Three Dimensions	p. 721
Mapping	p. 731
Ballistic Target Trajectory Generator in Three Dimensions	p. 731
Intercept Point Prediction for Ballistic Targets	p. 742
Strategic Missile-Target Engagement Simulation	p. 746
Orthographic Projections	p. 762
Summary	p. 767
References	p. 768
Appendix A Tactical and Strategic Missile Guidance Software	p. 769
Introduction	p. 769
Software Details	p. 769
Integration Example	p. 770
Pursuit Guidance	p. 771
Sensitivity of Optimal Guidance to Time to Go Errors	p. 775
Alternative Formulation of Radome Effects	p. 778
Another Way of Generating Random Numbers	p. 780
Simulating an Impulse	p. 781
Different Guidance System Distributions	p. 785
Fading Memory Filters for Booster Estimation	p. 789
Adjoint of Discrete Inputs	p. 798
Sampling Experiments	p. 801
Brute Force Frequency Response	p. 804
Why Stability Margins Are Important	p. 809
Minimum Energy Trajectories	p. 815
Trajectory Shaping Guidance in Three Dimensions	p. 821
Using the Discrete Fourier Transform to Find Miss Caused by Weaving Target	p. 828
Minimum Energy Trajectories for Shorter and Longer Flights	p. 831
Using Modified Lambert Subroutine to Partially Solve Kepler's Problem	p. 833
Modeling Poisson Target Maneuver	p. 838
Traveling Long Way	p. 846
References	p. 852
Appendix B Converting Programs to C	p. 855
Appendix C Converting Programs to MATLAB	p. 861
Appendix D True Basic	p. 873
Reference	p. 878
Appendix E Units	p. 879
Listing Index	p. 881
Index	p. 885
Supporting Materials	p. 889

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