Proportional navigation

About: Proportional navigation is a research topic. Over the lifetime, 1426 publications have been published within this topic receiving 26098 citations.

Tactical and strategic missile guidance

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.

Missile Guidance and Control Systems

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

Differential games and optimal pursuit-evasion strategies

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.

Homing Guidance Law for Cooperative Attack of Multiple Missiles

Abstract: OVER the past few years, there have been significant efforts devoted to the research and development of cooperative unmannedsystems [1–3].The formationflyingofmultipleunmanned aerial vehicles (UAVs) has been studied for radar deception, reconnaissance, surveillance, and surface-to-air-missile jamming in military operations. An example of a cooperative operational scenario of multiple vehicles is that of a small UAV flying over an urban area, dispensingmultiplemicro aerial vehicles to examinepointsof interest fromclosedistances [4].Agroupofwell-organized low-costmultiple vehicles can be far superior to a single high-technology and high-cost UAV in effectiveness. Tactical missile systems as well as UAVs provide more capabilities when they are organized as a coordinated group than when they are operated independently. Modern antiship missiles need to be able to penetrate the formidable defensive systems of battleships such as antiair defense missile systems and close-in weapon system (CIWS). CIWS is a naval shipboard weapon system for detecting and destroying incoming antiship missiles and enemy aircraft at short range. These defensive weapons with powerful fire capability and various strategies seriously intimidate the survivability of the conventional antiship missiles. Hence, antiship missile developers have made great efforts to develop a high-performance missile system with ultimate sea-skimming flight and terminal evasive maneuvering capabilities despite a huge cost. On the other hand, cooperative attack strategies have been studied to enhance survivability of the conventional ones. Here, a cooperative attack means that multiple missiles attack a single target or multiple targets cooperatively or, in a specific case, simultaneously [5,6]. Clearly, it is difficult to defend a group of attackers bursting into sight at the same time, even though each member is the conventional one in performance. So the simultaneous attack ofmultiple missiles is a cost-effective and efficient cooperative attack strategy. A simultaneous attack of a group of missiles against a single common target can be achieved by two ways. The first approach is individual homing, inwhich a common impact time is commanded to all members in advance, and thereafter each missile tries to home on the target on time independently. The second is cooperative homing, inwhich themissiles communicate among themselves to synchronize the arrival times. In other words, the missiles with larger times-to-go try to take shortcuts, whereas others with shorter times-to-go take detours to delay the arrival times. The first concept requires determination of a suitable common impact time before homing, but the second needs online data links throughout the engagement. Despite a number of studies on guidance problems related to timeto-go [7–10], studies on guidance laws to control impact time for a simultaneous attack are rare, except a few recent works by the authors. An impact-time-control guidance law (ITCG) for antiship missiles was developed in [5] and, as an extension of this study, a guidance law to control both impact time and angle (ITACG) was presented in [11]. These individual homing methods are based on optimal control theory, providing analytical closed-loop guidance laws. Herein, the desired impact time is assumed to be prescribed before the homing phase starts. Alternatively, this Note is concerned with a new guidance law based on the second approach, cooperative homing, for a simultaneous attack of multiple missiles. Proportional navigation (PN) is a well-known homing guidance method in which the rate of turn of the interceptor is made proportional with a navigation ratio N to the rate of turn of the line of sight (LOS) between the interceptor and the target. The navigation constant N is a unitless gain chosen in the range from 3 to 5 [12]. Although PNwithN 3 is known to be energy-optimal, an arbitrary N > 3 is also optimal if a time-varying weighting function is included into the cost function of the linear quadratic energy-optimal problem [13,14]. In general, the navigation ratio is held fixed. In some cases, however, it can be considered as a control parameter to achieve a desired terminal heading angle [15].Although PN results in successful intercepts under a wide range of engagement conditions, its control-efficiency is not optimal, in general, especially for the case of maneuvering targets [16]. Augmented proportional navigation, a variant of PN, is useful in cases in which target maneuvers are significant [12]. Biased proportional navigation is also commonly used to compensate for target accelerations and sensor noises or to achieve a desired attitude angle at impact [17]. Even if PN and its variants are alreadywell known andwidely used, they are not directly applicable to many-to-one engagements. This Note proposes a homing guidance law called cooperative proportional navigation (CPN) for many-to-one engagements: CPN has the same structure as conventional PN except that it has a time-varying navigation gain that is adjusted based on the onboard time-to-go and the times-to-go of the other missiles. CPN uses the time-varying navigation gain as a control parameter for reducing the variance of times-on-target of multiple missiles. This Note begins with the formulation of the homing problem of multiple missiles against a single target, subject to constraints on the impact time. Next, preliminary concepts such as the relative time-togo error and the variance of times-to-go of multiple missiles are introduced and a new guidance law is proposed. Then the major property of the law is investigated and the characteristics of the law for the case of twomissiles are examined in detail. Finally, numerical simulation results illustrate the performances of the proposed law.