Tactical and Strategic Missile Guidance, Fifth Edition / Edition 5

Tactical and Strategic Missile Guidance, Fifth Edition / Edition 5

by Paul Zarchan

ISBN-10: 1563478749

ISBN-13: 9781563478741

Pub. Date: 01/01/2007

Publisher: American Institute of Aeronautics & Astronautics

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


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 by a tactical ballistic missile can 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 counter these problems. The second new chapter presents a linear Kalman filter bank approach, originally introduced in the 1960s, for accurately estimating the target weave frequency and improving missile guidance system performance.

The engagement simulations presented in this text have previously been in one or two dimensions, to make it easier for the reader to understand 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 to demonstrate how geographical context can be provided in three dimensional strategic engagement simulations.

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. With numerous new examples and easy-to-understand graphs and explanations, Tactical and Strategic Missile Guidance is a staple for any aerospace engineer's library. Companion software, in both Macintosh and PC versions, contains source code listings in FORTRAN, C, and MATLAB® languages. A detailed set of appendices not only serves as a user's guide but also explains how the text's FORTRAN source code 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 specializing in missile guidance or other aerospace-related fields.

Product Details

American Institute of Aeronautics & Astronautics
Publication date:
Progress in Astronautics and Aeronautics Series
Edition description:
New Edition
Product dimensions:
6.20(w) x 9.20(h) x 2.10(d)

Table of Contents

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

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