Proportional navigation

Abstract: Numerical Techniques Fundamentals of Tactical Missile Guidance Method of Adjoints and the Homing Loop Noise Analysis Convariance Analysis and the Homing Loop Proportional Navigation and Miss Distance Digital Fading Memory Noise Filters in the Homing Loop Advanced Guidance Laws Kalman Filters and the Homing Loop Other Forms of Tactical Guidance Tactical Zones Strategic Considerations Boosters Lambert Guidance Strategic Intercepts Miscellaneous Topics Ballistic Target Properties Extended Kalman Filtering and Ballistic Coefficient Estimation Ballistic Target Challenges Multiple Targets Weaving Targets Representing Missile Airframe with Transfer Functions Introduction to Flight Control Design Three-Loop Autopilot. Appendices: Tactical and Strategic Missile Guidance Software Converting Programmes to C Converting Programmes to MATLAB Units.

Abstract: A new smooth second-order sliding mode control is proposed and proved using homogeneity-based technique for a system driven by sufficiently smooth uncertain disturbances. The main target application of this technique-the missile-interceptor guidance system against targets performing evasive maneuvers is considered. The smooth second-order sliding mode control-based guidance law is designed and compared with augmented proportional navigation guidance law via computer simulations of a guided missile intercepting a maneuvering ballistic target.

Abstract: Contents 1 Introduction References 2 The Generalized Missile Equations of Motion 2.1 Coordinate Systems 2.1.1 Transformation Properties of Vectors 2.1.2 Linear Vector Functions 2.1.3 Tensors 2.1.4 Coordinate Transformations 2.2 Rigid-Body Equations of Motion 2.3 D'Alembert's Principle 2.4 Lagrange's Equations for Rotating Coordinate Systems References 3 Aerodynamic Forces and Coefficients 3.1 Aerodynamic Forces Relative to the Wind Axis System 3.2 Aerodynamic Moment Representation 3.2.1 Airframe Characteristics and Criteria 3.3 System Design and Missile Mathematical Model 3.3.1 System Design 3.3.2 The Missile Mathematical Model 3.4 The Missile Guidance System Model 3.4.1 The Missile Seeker Subsystem 3.4.2 Missile Noise Inputs 3.4.3 Radar Target Tracking Signal 3.4.4 Infrared Tracking Systems 3.5 Autopilots 3.5.1 Control Surfaces and Actuators 3.6 English Bias References 4 Tactical Missile Guidance Laws 4.1 Introduction 4.2 Tactical Guidance Intercept Techniques 4.2.1 Homing Guidance 4.2.2 Command and Other Types of Guidance 4.3 Missile Equations of Motion 4.4 Derivation of the Fundamental Guidance Equations 4.5 Proportional Navigation 4.6 Augmented Proportional Navigation 4.7 Three-Dimensional Proportional Navigation 4.8 Application of Optimal Control of Linear Feedback Systems with Quadratic Performance Criteria in Missile Guidance 4.8.1 Introduction 4.8.2 Optimal Filtering 4.8.3 Optimal Control of Linear Feedback Systems with Quadratic Performance Criteria 4.8.4 Optimal Control for Intercept Guidance 4.9 End Game References 5 Weapon Delivery Systems 5.1 Introduction 5.2 Definitions and Acronyms Used in Weapon Delivery 5.2.1 Definitions 5.2.2 Acronyms 5.3 Weapon Delivery Requirements 5.3.1 Tactics and Maneuvers 5.3.2 Aircraft Sensors 5.4 The Navigation/Weapon Delivery System 5.4.1 The Fire Control Computer 5.5 Factors In.uencing Weapon Delivery Accuracy 5.5.1 Error Sensitivities 5.5.2 Aircraft Delivery Modes 5.6 Unguided Weapons 5.6.1 Types of Weapon Delivery 5.6.2 Unguided Free-Fall Weapon Delivery 5.6.3 Release Point Computation for Unguided Bombs 5.7 The Bombing Problem 5.7.1 Conversion of Ground Plane Miss Distance into Aiming Plane Miss Distance 5.7.2 Multiple Impacts 5.7.3 Relationship Among REP, DEP, and CEP 5.8 Equations of Motion 5.9 Covariance Analysis 5.10 Three-Degree-of-Freedom Trajectory Equations and Error Analysis 5.10.1 Error Analysis 5.11 Guided Weapons 5.12 Integrated Flight Control in Weapon Delivery 5.12.1 Situational Awareness/Situation Assessment (SA/SA) 5.12.2 Weapon Delivery Targeting Systems 5.13 Air-to-Ground Attack Component 5.14 Bomb Steering 5.15 Earth Curvature 5.16 Missile Launch Envelope 5.17 Mathematical Considerations Pertaining to the Accuracy of Weapon Delivery Computations References 6 Strategic Missiles 6.1 Introduction 6.2 The Two-Body Problem 6.3 Lambert's Theorem 6.4 First-Order Motion of a Ballistic Missile 6.4.1 Application of the Newtonian Inverse-Square Field Solution to Ballistic Missile Flight 6.4.2 The Spherical Hit Equation 6.4.3 Ballistic Error Coef.cients 6.4.4 Effect of the Rotation of the Earth 6.5 The Correlated Velocity and Velocity-to-Be-Gained Concepts 6.5.1 Correlated Velocity 6.5.2 Velocity-to-Be-Gained 6.5.3 The Missile Control System 6.5.4 Control During the Atmospheric Phase 6.5.5 Guidance Techniques 6.6 Derivation of the Force Equation for Ballistic Missiles 6.6.1 Equations of Motion 6.6.2 Missile Dynamics 6.7 Atmospheric Reentry 6.8 Missile Flight Model 6.9 Ballistic Missile Intercept 6.9.1 Introduction 6.9.2 Missile Tracking Equations of Motion References 7 Cruise Missiles 7.1 Introduction 7.2 System Description<7.2.1 System Functional Operation and Requirements 7.2.2 Missile Navigation System Description 7.3 Cruise Missile Navigation System Error Analysis 7.3.1 Navigation Coordinate System 7.4 Terrain Contour Matching (TERCOM) 7.4.1 Introduction 7.4.2 De.nitions 7.4.3 The Terrain-Contour Matching (TERCOM) Concept 7.4.4 Data Correlation Techniques 7.4.5 Terrain Roughness Characteristics 7.4.6 TERCOM System Error Sources 7.4.7 TERCOM Position Updating 7.5 The NAVSTAR/GPS Navigation System 7.5.1 GPS/INS Integration References A Fundamental Constants B Glossary of Terms C List of Acronyms D The Standard Atmospheric Model References E Missile Classi.cation F Past and Present Tactical/Strategic Missile Systems F.1 Historical Background F.2 Unpowered Precision-Guided Munitions (PGM) References G Properties of Conics G.1 Preliminaries G.2 General Conic Trajectories References H Radar Frequency Bands I Selected Conversion Factors Index

Abstract: In this paper it is shown that variational techniques can be applied to solve differential games. Conditions for capture and for optimality are derived for a class of optimal pursuit-evasion problems. Results are used to demonstrate that the well-known proportional navigation law is actually an optimal intercept strategy.

Abstract: Optimal guidance laws providing the specified impact angle as well as zero terminal miss distance are generalized for arbitrary missile dynamics. The optimal guidance command is represented by a linear combination of the ramp and the step responses of the missile’s lateral acceleration. Optimal guidance laws in the form of the state feedback for the lag-free and the first-order lag system are derived, and their characteristics are investigated. Practical timeto-go calculation methods, which are important for the implementation of the optimal guidance laws, are proposed to consider the path curvature. Nonlinear and adjoint simulations are performed to investigate the performance of the proposed laws.