Missile Trajectory Research Articles

Dynamics of the gas-dust cloud observed in the upper atmosphere on October 26, 2017

The results of the study of the gas-dust cloud of solid fuel combustion products dynamics formed under a rocket stages separation are presented. The sequence of the digital images obtained in the twilight condition at a distance of ∼1500 km from the missile trajectory was analyzed. The height of the cloud center reaches up to ∼900 km, and its diameter is ∼2000 km. The glow of the cloud is determined by the scattering of sunlight on dispersed particles of the combustion products. The obtained data allow to specify the dispersed composition of the cloud and dynamic parameters of its development. The proposed methodology can be used to clarify the physical picture of the interaction of the combustion products of solid propellant with the environment, as well as environmental conditions and processes in the upper atmosphere.

A Hybrid Control with PID⁻Improved Sliding Mode for Flat-Top of Missile Electromechanical Actuator Systems.

Electromechanical actuator (EMA) systems are widely employed in missiles. Due to the influence of the nonlinearities, there is a flat-top of about 64 ms when tracking the small-angle sinusoidal signals, which significantly reduces the performance of the EMA system and even causes the missile trajectory to oscillate. Aiming to solve these problems, this paper presents a hybrid control for flat-top situations. In contrast to the traditional PID or sliding mode controllers that missiles usually use, this paper utilizes improved sliding mode control based on a novel reaching law to eliminate the flat-top during the steering of the input signal, and utilizes the PID control to replace discontinuous control and improve the performance of EMA system. In addition, boundary layer and switching function are employed to solve the high-frequency chattering problem caused by traditional sliding mode control. Experiments indicate that the hybrid control can evidently reduce the flat-top time from 64 ms to 12 ms and eliminate the trajectory limit cycle oscillation. Compared with PID controllers, the proposed controller provides better performance—less chattering, less flat-top, higher precision, and no oscillation.

Data Analysis and Validation of Acquired Temperature Data on Underwater Platform

<p class="western" style="margin-left: -2.25cm; margin-bottom: 0.35cm; line-height: 115%;">Underwater missiles are launched from canister by hot gasses produced by a gas generator. Hot gasses eject the missile out of canister, positioned on an underwater platform in high seas at a depth of 50 m to 70 m. During development phase of submarine launched missile, maximum number of physical parameters related to platform and launching mechanism are acquired on a data acquisition system on-board platform and selected critical parameters are transmitted to control station in real time through an optical data communication link. Missile parameters are recorded on-board and transmitted to the control station by delayed transmission technique once the missile is out of water. Exit velocity of missile is very important parameter for the missile trajectory and range, which depends upon the heat loss in canister and annular gap pressure between missile and canister during the ejection process. Prediction of exit velocity is validated by heat loss calculation by measured temperature at different stations during the test. Temperature measurement is carried out by sensors mounted on the inner wall of canister and also by jumping type of temperature sensor, which measures canister gas temperature. In spite of all efforts, few sensors do not work as expected. It is important to measure various parameters according to instrumentation measurement plan. In case of temperature measurement, sometimes, it is required to predict temperature at location, where sensor was originally not mounted. To validate the recorded test data, another set of data is needed for which one has to wait till next test is conducted that may take years and practically impossible to ensure identical test setup and environmental condition. A mathematical approach to predict temperature at required location and to validate the recorded test data is presented.</p><p class="western" style="margin-left: -2.25cm; margin-bottom: 0.35cm; line-height: 115%;"> </p><p class="western" style="margin-left: -2.25cm; margin-bottom: 0.35cm; line-height: 115%;"> </p>

Switching Multiple Model Filter for Boost-Phase Missile Tracking

This paper introduces a filter for tracking a ballistic missile during its boost phase. This filter includes a new switching algorithm and a modified interacting multiple model unscented filter (IMMUF), where the Markov transition matrix is time variable. Position, velocity, and all unknown parameters of a medium-range ballistic missile model are reconstructed. Simulations demonstrate that the new filter is able to consistently estimate a missile's trajectory and all unknown parameters and to outperform the previous forms of the IMMUF.

Cooperative time-varying formation guidance for leader-following missiles to intercept a maneuvering target with switching topologies

This study investigates the cooperative time-varying formation guidance (CTFG) problem for leader-following missiles to intercept a maneuvering target with switching communication topologies. Multiple missiles are classified into a leader missile and multiple follower missiles. The leader missile intercepts the maneuvering target under the modified proportional navigation guidance law. The follower missiles are expected to form a predefined time-varying formation and track the trajectory of the leader missile. Multiple missiles intercept the maneuvering target simultaneously and then form a many-to-one engagement. A four-step approach to determine the parameters in the CTFG law is given. The convergence of the approach is discussed. A numerical example for multiple missiles intercepting a maneuvering target subjected to switching communication topologies is presented.

Guidance Laws against Towed Decoy Based on Adaptive Back-stepping Sliding Mode and Anti-saturation Methods

In order to meet the needs of high-precision guidance for missile-guided maneuvering targets in the presence of towed bait interference, this paper proposes a new guidance strategy based on heading angle method and parallel approaching method. Its main idea: a suitable angle is determined by heading angle method which of the missile trajectory is above that of the towing bait. Meanwhile, the accurate interception of missiles to targets is guaranteed by parallel approaching method. Firstly, system models of missile and target with towed decoy are established. Then, considering unknown bounded system disturbances, a controller is given based on sliding mode, back-stepping method. Furthermore, to solve the input saturation problem, an anti-saturation controller is given using adaptive and back-stepping sliding mode methods. Finally, strict proofs of the two controllers are given using Lyapunov stability theory, and simulations are carried out to verify the effectiveness of the two controllers.

6DOF Missile Trajectory Simulation Using Reusable Frame and Models

A reusable frame and appropriate models are designed for six degree of freedom (6DOF) missile trajectory simulation. The importance of establishing trajectory simulation model in missile design and experiment is described at first. Guidance Navigation and Control (GNC) loop as the core component in missile is discussed with emphasis on performance limitations. Design Patterns (DP) in software engineering are utilized to accomplish module partition. Reusable design is conducted in a two-step process: frame design and models design. This method can improve design productivity and shorten design circle as its reusable frame and relevant models can applied to many kinds of missiles without major revisions. An air defense scenario is designed to validate the proposed model frame. The 6DOF trajectory simulation results are obtained. Results show that the method offers an effective and practical way to design parameters and evaluate performance of missile.

6DOF Missile Trajectory Simulation Using Reusable Frame and Models

6DOF Missile Trajectory Simulation Using Reusable Frame and Models

Traumatic Brain Injury Caused by Missile Wounds in the North of Palestine: A Single Institution's Experience with 520 Consecutive Civilian Patients

Literature about traumatic brain injury caused by missile wounds is scanty. We shed some light on this field. This retrospective study was carried out, between September 2000 and September 2010, on 520 civilian patients who sustained traumatic brain injury from missiles in the north of Palestine. Thorough detailed analyses were made of patients' admission Glasgow Coma Scale (GCS) scores, pupillary reactivity to light, site and mode of injuries, type of injurious agents, missile trajectory, method of treatment, radiologic manifestations, complications, and outcome. The GCS score was used to assess the level of consciousness, whereas the Glasgow Outcome Scale score was used to evaluate the outcome. Patients' age ranged from 6 months to 75 years. Only 50 (9.6%) patients were female. Patients injured by metallic bullets, rubber bullets, and shrapnel from bomb explosions numbered 351, 139, and 30, respectively. Of 384 patients who were treated conservatively, no mortality was detected, whereas of 136 surgically treated patients, 66 (48.5%) died of their injuries. Although our management of patients was not optimal because of many factors, the overall mortality was 12.7% (n= 66). The promptness of transport to hospital was a decisive factor with a major bearing on decreasing mortality. Brain computed tomography was invaluable in the diagnosis and follow-up of our patients. In addition, age, pupillary reactivity, admission GCS score, missile trajectory, ventricular involvement, and site and mode of injury were important prognostic factors.

Evaluation of Critical Geometrical Parameters and Alignment Corrections of Large Size Aerospace Systems

Metrological assessment of geometrical, form parameters plays an important role in development of quality hardware of aerospace systems such as missiles. These parameters are critical for mission performance and system evaluation studies. High precision CNC Coordinate Measuring Machines (CMMs) are extensively used for evaluating geometrical, form parameters in alignment checks of large missile subsystems, assemblies and tooling. These high precision metrological tools can also be used for geometrical and alignment corrections of critical missile subsystems. Alignment check of integrated missile is an important activity carried out during development of missile system. The critical aerodynamic parameters viz. nose tip deviation, cant angle and orthogonality of wings & fins and propulsion parameters such as thrust axis misalignment are evaluated using geometrical features available on integrated missile. These aerodynamic and propulsion parameters are used for aerodynamic studies and predicting missile trajectory during pre-flight simulation analysis. The deviation in these values directly affects the missile performance during flight. In case of high deviations, the above parameters are corrected mechanically in order to meet the design requirements. This paper brings out the applications and methodologies developed for evaluation and correction of geometrical and form parameters in alignment checks of integrated missiles

A Two-Phased Guidance Law for Impact Angle Control with Seeker’s Field-of-View Limit

A two-phased guidance problem with terminal impact angle constraints and seeker’s field-of-view limit is addressed in this paper for a missile against a nonmaneuvering incoming target. From the conventional PN guidance without any constraints, it is found that satisfying the impact angle constraint causes a more curved missile trajectory requiring a large look angle. To avoid the look angle exceeding the seeker’s physical limit, a two-phased look angle control guidance scheme with the terminal constraint is introduced. The PN-typed guidance law is designed for each guidance phase with a specific switching condition of line-of-sight. The proposed guidance law is comprised of two types of acceleration commands: the one in the initial phase which aims at controlling the missile’s look angle to reach the limit and the other for final phase which is produced by switching the navigation gain. The monotonicity of the line-of-sight angle and look angle is analyzed and proved to support the proposed method. To evaluate the specific navigation gains for both initial and final phases, the scaling coefficient between them is discussed by solving a quadratic equation with respect to the initial navigation gain. To avoid a great abrupt acceleration change at the switching instant, a minimum coefficient is chosen. Extensive simulations are performed to validate the efficiency of the proposed approach.

Application and Determination of Defended Footprint Using a Simulation Model for Ballastic Missile Trajectory

Application and Determination of Defended Footprint Using a Simulation Model for Ballastic Missile Trajectory

Multiple Model Ballistic Missile Tracking With State-Dependent Transitions and Gaussian Particle Filtering

This paper proposes a new method for tracking the entire trajectory of a ballistic missile from launch to impact on the ground. Multiple state models are used to represent the different ballistic missile dynamics in three flight phases: boost, coast, and re-entry. In particular, the transition probabilities between state models are represented in a state-dependent way by utilizing domain knowledge. Based on this modeling system and radar measurements, a state-dependent interacting multiple model approach based on Gaussian particle filtering is developed to accurately estimate information describing the ballistic missile such as the phase of flight, position, velocity, and relevant missile parameters. Comprehensive numerical simulation studies show that the proposed method outperforms the traditional multiple model approaches for ballistic missile tracking.

Application of methods of conditional multidimensional minimization to the ballistic trajectory calculation problem

The paper focuses on the problem of calculating the approximate ballistic missile trajectory, the calculation ensuring that the missile travels from a given launch point to the finish point and covering the entire range rate for the missiles of the type considered. The missile trajectory is defined by a system of nonlinear differential equations. A different range is achieved by changing the initial values of the flight-path angle and the operating time of the missile stages. Due to the physical significance, these variables are constrained. The problem of multidimensional conditional minimization by the method of barrier functions with minimization of Nelder - Meed method

Weaving Guidance for Missile Observability Enhancement

This paper proposes a new optimal guidance law to enhance the target observability. Based on the observability criteria with respect to the line-of-sight rate, a weaving maneuver is suggested to increase the variation of the line-of-sight angle and to intercept the target. The proposed guidance law is derived analytically in the optimal framework with augmenting virtual states to induce the weaving maneuver. The role of virtual states is investigated by obtaining the closed-form solution of the missile trajectory and by analyzing the effect of the number and intitial values of the virtual states. Improvements in the observability are also validated by the performance of estimation.

A Study on the Tube-exit Cavity Surrounding Submarine-launched Missile

The gas-steam ejection dynamic system is usually employed by submarine launched missile. In the separating process of missile tail and canister outlet, cavity formed by Interaction between gas and water has influence on the load of launch platform and missile trajectory. The mixture multiphase flow model, RNG k-ε turbulence model combined with the dynamic mesh model were adopted to simulate the tube-exit cavity and missile trajectory. The results show that in the process of missile bottom leaving tube, the high pressure gas pours out and forms cavity in missile bottom. With the missile moving and hydrostatic pressure impacting, the cavity will expand, shrink and break and its effects on trajectory of missile and loads on deck are presented. In addition, the natural cavitation of missile shoulder because of high speed movement of missile is analyzed.

State dependent multiple model-based particle filtering for ballistic missile tracking in a low-observable environment

This paper proposes a new method for tracking the whole trajectory of a ballistic missile (BM), in a low-observable environment with ‘imperfect’ sensor measurement incorporating both miss detection and false alarms. A hybrid system with state dependent transition probabilities is proposed where multiple state models represent the ballistic missile movement during different phases; and domain knowledge is exploited to model the transition probabilities between different flight phases in a state-dependent way. The random finite set (RFS) is adopted to model radar sensor measurements which include both miss detection and false alarms. Based on the proposed hybrid modeling system and the RFS represented sensor measurements, a state dependent interacting multiple model particle filtering method integrated with a generalized measurement likelihood function is developed for the BM tracking. Comprehensive simulation studies show that the proposed method outperforms the traditional ones for the BM tracking, with more accurate estimations of flight mode probabilities, positions and velocities.

Общий интеграл для одного класса нестационарных атмосферных летательных аппаратов и приложения для анализа траекторий

A complete analytical integration of the aircraft kinematic and dynamic equations of motion is presented. Different applications of defined integrals to trajectory analysis are considered. The dynamic equations are obtained under the assumptions, that acceleration due to aerodynamic lift, the difference between the accelerations due to propulsive thrust and aerodynamic drag are not changed, the aircraft body rate about the velocity axis is zero and the sideslip angle is zero. The general integral of these equations consists of six independent first integrals of motion and describes a class of non-steady flight trajectories in a maneuver plane. It will be shown that the dynamic equations can be derived and completely integrated in a closed-form for more general assumptions. The problem of computing thrust for a given trajectory has been considered. The trajectory is defined by constraint equation. Constraints stabilization equations, which have asymptotically stable trivial solution, are constructed. Explicitness can make the integrals applicable to modeling the trajectories of spacecraft, re-entry vehicles and missiles, and to the design of on-board targeting and guidance. An illustrative example is presented.

The Trajectory Controller Design and Implementation of a Certain Vehicular Missile Virtual Mark

To solve the trajectory control problem of vehicular missile virtual mark ,we design a kind of stepping motor control system based on single chip microcomputer, according to the generation principle of missile control instruction, single chip microcomputer generates longitudinal direction and horizontal direction control signal, realizes simulation of missile flight trajectory on the graphic. This design adopts to 8051 single chip microcomputer, study and explore missile trajectory operation rule, and combine with control theory, establish stepper motor control system based on single-chip, design hardware and software structure, simulate actual missile trajectory, finally realizes a vehicle-mounted striker anti-tank missile training simulation system of trajectory control.

DESIGN AND SIMULATION OF RADIO FREQUENCY SEEKER ANTENNA STABILIZATION

Abstract Present day guided weapon systems, especially tactical class missiles use RF seeker, for target tracking towards terminal engagement. The seeker system including its antenna assembly will be onboard the missile. Due to the missile trajectory corrections, the seeker antenna pointing to the target may get disturbed resulting in track loss. To avoid this track loss, it becomes necessary to stabilize the antenna system in two planes. The fundamental role of stabilization loop in seeker application is to precisely follow the angular rate of the target. In order to achieve this requirement, it is essential to highly isolate the gimbaled antenna from the missile body motion due to the maneuvering of target or low frequency vibration during flight. However, the isolation ratio and stability margin of stabilization loop adopting the gimbaled platform with both low stiffness and heavy inertia are limited by mechanical characteristic such as low resonance frequency and its high magnitude. The selection of proper feedback sensors, modeling of the total system are key features of this project. In the end, the performance and the stability of designed stabilization loop are demonstrated using simulation in both frequency and time domain. The Hardware for the system is under realization by the Industry. The whole scheme is simulated in MATLAB off-line for this project.