Line Of Sight Angle Research Articles

Cooperative Guidance Law with Predefined-Time Convergence for Multimissile Systems

To intercept the maneuvering target through multimissile cooperation, predefined-time cooperative guidance (PTCG) law is presented with constraints including the impact time and the line-of-sight (LOS) angle. In order to achieve simultaneous interception, we propose a PTCG law in the LOS direction based on a predefined-time consensus protocol, which guarantees the achievement of consensus on each missile’s impact time within the predefined time. Furthermore, to ensure the predefined-time convergence of the LOS angle and the predefined-time convergence of the LOS angular rate, a PTCG law with a fixed-time disturbance observer (FxTDO) is presented in the normal direction of the LOS. Compared with the traditional finite-time or fixed-time cooperative guidance laws, the proposed PTCG law predefines the upper bound of the settling time as an explicit parameter. Finally, the simulation results of the PTCG law verify the efficiency of the proposed method.

Cooperative guidance laws against highly maneuvering target with impact time and angle

To address the issue that multiple missiles intercepting a highly maneuvering target simultaneously with desired angles, a novel cooperative guidance law based on the decoupled model in the line-of-sight (LOS) and normal LOS direction is proposed in LOS frame. However, there is control coupling in the two directions of the cooperative guidance model. In this article, we first decouple the guidance model and then separately design estimation decouple cooperative guidance law in two directions based on the decoupled model. The guidance law component in the LOS direction is designed with the integral sliding mode control and multi-agent consensus theory, where the combining disturbance is compensated by an adaptively estimated term. The guidance law component in the normal LOS direction is designed based on nonsingular terminal sliding mode control with fast power reaching law, and a nonlinear disturbance observer is introduced to estimate the combining disturbance. Then, the finite time convergence of time-to-go and LOS angle is proved. Finally, numerical simulation results demonstrate the effectiveness and superiority of the proposed cooperative guidance law.

Line-of-sight rates extraction of roll-pitch seeker under anti-infrared decoy state

In this paper, the method of extracting guidance information such as the line-of-sight (LOS) rates under the anti-infrared decoy state for the roll-pitch seeker is researched. Co-ordinate systems which are used to describe the angles transform are defined. The LOS angles reconstruction model of the roll-pitch seeker in inertial space is established. A Kalman filter model for extracting LOS rates of the roll-pitch seeker is proposed. In this model, the target performs constant acceleration (CA) model maneuvers. The error model of LOS rates extraction under infrared decoy state is established. Several existing methods of extracting LOS rates under anti-infrared decoy state are listed in this paper. Different from the existing methods, a novel method that uses extrapolated values of target accelerations as filter measurements is proposed to solve the guidance information extraction problem under the anti-infrared decoy state. Numerical simulations are conducted to verify the effectiveness of the proposed method under different target maneuvering models such as the CA model, the CA extended model and the singer model. The simulation results show that the proposed method of extracting guidance information such as LOS rates for the roll-pitch seeker under the anti-infrared decoy state is effective.

Three-dimensional fixed-time robust cooperative guidance law for simultaneous attack with impact angle constraint

This paper proposes a three-dimensional (3-D) robust nonlinear cooperative guidance law for multiple missiles to simultaneously attack a maneuvering target at desired impact angles. Since the flight time of terminal guidance is very short, the fast convergence of guidance errors is a vital demand, especially when the initial errors are huge and the target is maneuvering. By utilizing the theory of fixed time convergence, a distributed sliding surface that only utilizes the information from adjacent missiles is first designed, whose convergence time is independent of initial conditions. In order to avoid the performance degradation due to the estimation error of time-to-go, the consensus variables of the fixed-time sliding surface are chosen as range-to-go and radial relative velocity. Then, a robust cooperative guidance law along the line-of-sight (LOS) direction is proposed to bring the multi-missile system to reach the sliding surface in finite time. Thus, the simultaneous attack to a maneuvering target can be guaranteed. Next, the guidance laws in the elevation and azimuth direction of LOS are developed to ensure the fixed-time convergence of LOS angles. The fixed-time stability is proved through the Lyapunov theory and bi-homogenous property. Simulation results indicate that the impact time of each missile under the proposed guidance law is the same, without any deviation. Compared with the state-of-the-art methods, the convergence time of LOS angles is shortened by about 30%. In addition, the miss distance and errors of LOS angles can be reduced by more than 80%.

Robust Head-Pursuit Guidance Accounting for Hit-to-Kill and Angle Constraints

In this paper, the hit-to-kill strategy is introduced to solve the three-dimensional (3D) robust head-pursuit (HP) interception problem considering the line-of-sight (LOS) angle constraints. Firstly, a target based relative dynamic model is proposed to be the nominal model for designing the robust HP guidance laws, where the HP interception problem is formulated as a target passively chases after the interceptor missile. Secondly, the 3D retro-proportional navigation (RPN) guidance law is reinterpreted from the point of control theory, which forces the corresponding guidance system asymptotically stable. Meanwhile, the concept of nullifying the LOS angular rates is successfully introduced to solve the 3D robust HP guidance problem via the sliding mode control. Thirdly, the LOS angles constrained robust HP guidance law is proposed based on the nonsingular terminal sliding mode control. The stabilities of the presented guidance laws are analyzed via the Lyapunov approach. The simulation results are in agreement with the theoretical statements.

Finite-Time Cooperative Guidance Strategy for Impact Angle and Time Control

In this article, two cooperative guidance schemes with impact angle and time constraints are proposed for multiple missiles cooperatively intercepting a maneuvering target in the presence or absence of a leader missile. First, cooperative interception with impact angle constraint is formulated based on the relative motion equation between the interceptors. Subsequently, the design of the guidance law is divided into two stages. In the first stage, based on finite-time consensus theory and the super-twisting control algorithm, the cooperative guidance law in the direction of the line of sight (LOS) is derived to control the impact time so that all missiles can simultaneously intercept the target in finite time. Then, based on finite-time sliding mode control and the super-twisting control algorithm, a finite-time convergence cooperative guidance law in the normal direction to the LOS is developed to control the intercept angle and the LOS angle rate so that each missile can accurately hit the target at a desired angle. Finally, by controlling the consensus error of flight time in the presence of a leader missile, a finite-time cooperative guidance method in the “leader–follower” scenario is derived for simultaneous arrival at the target. The proposed methods can effectively suppress chattering and ensure fast convergence in finite time. Simulation experiments are conducted to verify the effectiveness of the proposed cooperative guidance schemes.

Accurate estimation of line-of-sight rate under strong impact interference effect

In the process of the terminal guidance of a kinetic kill vehicle (KKV), it is very important to accurately estimate the line-of-sight (LOS) rate via the measurements of a target seeker onboard the KKV. The strong impact interference caused by the large lateral thrust produced by the thrusters on the KKV is a main factor that affects the measurements on the LOS angle. A method to estimate the impact interference and the LOS rate together via a Kalman filter is proposed to improve the estimation precision of the LOS rate. The observability of the system describing the missile-target relative motion model and the impact interference model is proved, and then a Kalman filter is designed. In the Kalman filter design, the continuous-discrete and two-stage filtering techniques are used because the system model is time-variant and high-order. Numerical simulation results show that by estimating the impact interference, the estimation precision of the LOS rate is increased, and so the miss distance of the KKV under the strong impact interference is reduced. The proposed continuous-discrete two-stage Kalman filter shows higher estimation precision and lower computational cost than the naive discrete augmented state Kalman filter.

Forward modelling of MHD waves in braided magnetic fields

Aims. We investigate synthetic observational signatures generated from numerical models of transverse waves propagating in complex (braided) magnetic fields. Methods. We consider two simulations with different levels of magnetic field braiding and impose periodic, transverse velocity perturbations at the lower boundary. As the waves reflect off the top boundary, a complex pattern of wave interference occurs. We applied the forward modelling code FoMo and analysed the synthetic emission data. We examined the line intensity, Doppler shifts, and kinetic energy along several line-of-sight (LOS) angles. Results. The Doppler shift perturbations clearly show the presence of the transverse (Alfvénic) waves. However, in the total intensity, and running difference, the waves are less easily observed for more complex magnetic fields and may be indistinguishable from background noise. Depending on the LOS angle, the observable signatures of the waves reflect some of the magnetic field braiding, particularly when multiple emission lines are available, although it is not possible to deduce the actual level of complexity. In the more braided simulation, signatures of phase mixing can be identified. We highlight possible ambiguities in the interpretation of the wave modes based on the synthetic emission signatures. Conclusions. Most of the observables discussed in this article behave in the manner expected, given knowledge of the evolution of the parameters in the 3D simulations. Nevertheless, some intriguing observational signatures are present. Identifying regions of magnetic field complexity is somewhat possible when waves are present; although, even then, simultaneous spectroscopic imaging from different lines is important in order to identify these locations. Care needs to be taken when interpreting intensity and Doppler velocity signatures as torsional motions, as is done in our setup. These types of signatures are a consequence of the complex nature of the magnetic field, rather than real torsional waves. Finally, we investigate the kinetic energy, which was estimated from the Doppler velocities and is highly dependent on the polarisation of the wave, the complexity of the background field, and the LOS angles.

Adaptive Leader–Follower Formation for Unmanned Surface Vehicles Subject to Output Constraints

This paper addresses the leader–follower formation control strategy for unmanned surface vehicles with model uncertainties. First, to achieve the desired formation configuration, the line-of-sight (LOS) scheme is incorporated in the guidance design. The constraints of LOS range and angle are required to meet the connectivity maintenance and collision avoidance. Tan-type time-varying Barrier Lyapunov function (BLF) is applied to address the output constraints. Next, in the formation control design, bioinspired models are combined with backstepping techniques to achieve less calculation. Adaptive fuzzy control approach is developed to deal with the uncertainties of marine vessels due to their superior approximation capability. Finally, the uniform ultimate boundedness of all signals can be guaranteed via stability analysis. Simulation examples are carried out to demonstrate the feasibility of the theoretical results.

Integrated guidance and control for missile with narrow field-of-view strapdown seeker

Due to the removal of the mechanically stable platform in the conventional gimbaled seeker, the strapdown seeker’s measurement is coupled with the missile body attitude motion, such that the inertial line-of-sight (LOS) angular rate required to implement traditional guidance laws cannot be measured, and the field-of-view (FOV) limit must be considered when designing guidance and control systems for a strapdown homing missile. To address these practical problems, an integrated guidance and control (IGC) scheme with considering the FOV limit is proposed in this paper. A novel IGC model is first derived based on the body-LOS (BLOS) angle that a strapdown seeker can directly measure, and then an IGC controller is designed using the dynamic surface control technique. A great merit of this design is that the inertial LOS angle and its angular rate are not needed, and thus the filters/estimators required to extract this guidance information in previous studies can be canceled. Next, by using the output to input saturation transformation (OIST) technique, the FOV limit, which is always considered as a state/output constraint, is transformed to a time-varying boundary limitation on the control input, and then is handled simultaneously with the actuator saturation constraint. Finally, extensive numerical simulations against both stationary and moving targets are performed to fully demonstrate the efficiency of the proposed IGC law.

Nonlinear Suboptimal Guidance Law With Impact Angle Constraint: An SDRE-Based Approach

In this article, a guidance law with impact angle constraint is developed using the state-dependent Riccati equation (SDRE) technique. First, the nonlinear guidance dynamics consisting of line-of-sight (LOS) angle rate and error is formulated under a planar engagement scenario. After the state-dependent coefficient parameterization, a nonlinear regulator problem is formed to concurrently zero LOS angle rate and error. Second, a preliminary guidance law is directly developed under the framework of the SDRE technique. By applying the Lyapunov stability analysis, a nonlinear suboptimal guidance law is obtained through further parameter modifications. Then, the proposed guidance law is extended to attack maneuvering targets. Finally, the effectiveness of the proposed guidance law is demonstrated through numerical simulations.

Estimation of Full Strap-down Rotating Bomb Guidance Information Based on Unscented Kalman Filter

In this paper, the full strap-down seeker of rotating bomb is taken as the research object, and the method of extracting the LOS (line-of-sight) angle and angular rate of the full strap-down seeker of the rotating bomb is studied. The structure of the full strap-down seeker is quite different from that of the conventional rate gyro seeker. The measurement system of full strap-down seeker is fixed to the missile, the seeker can only obtain the measurement information in the projectile coordinate system, and the measurement information is coupled with the body posture information, so it cannot be directly used for the control guidance of the rotating projectile. First, based on the conversion relationship between coordinate systems, the mathematical model of the inertial LOS angle of the rotating bomb is established, and the mathematical model of the extraction of the inertial LOS angle and angular rate of the rotating bomb is further established. Then, the Kalman filter is designed by using the unscented Kalman filter method (UKF), and the extracted LOS angle containing noise information is filtered. Finally, the mathematical simulation is carried out to verify the validity of the mathematical model of LOS angle and angular rate extraction. Compared with the Extended Kalman filter method (EKF), the UKF has a higher accuracy for estimating the navigation information of the full strap-down rotating projectile.

Analytical Solution for Nonlinear Three-Dimensional Guidance With Impact Angle and Field-of-View Constraints

An analytical 3-D guidance law with impact angle and field-of-view (FOV) constraints considering nonlinear coupled dynamics is proposed. As a stepping stone, the guidance model is transformed to a set of nonlinear differential equations in terms of the relative range variable. To meet the desired impact angles in the pitch and yaw planes, two cubic polynomials including eight coefficients are developed with respect to the relative range for creating reference line-of-sight (LOS) profiles. The unknown coefficients are explicitly solved by initial and terminal conditions on the LOS angles and LOS rates in the mutually orthogonal planes. Then, the analytical 3-D impact angle guidance (IAG) law is derived via formulating the second-order LOS dynamics of the transformed model. Moreover, the relation between the seeker's look angle and the reference LOS profiles is developed, such that the achievable impact angle set can be obtained to handle the FOV limit. Numerical simulations with comparison study and a realistic model are conducted to verify effectiveness and robustness of the guidance law. Its feasibility is additionally validated by applying it to the guidance of unmanned aerial vehicles landing on surface moving carriers.

Bioinspired neurodynamics based formation control for unmanned surface vehicles with line-of-sight range and angle constraints

In this work, a leader–follower formation control for a group of waterjet unmanned marine surface vehicles (USV) is proposed under the consideration of formation tracking errors constraints. To guarantee line-of-sight (LOS) range and angle tracking errors constraints, a time-varying tan-type barrier Lyapunov function (BLF) is used. In addition, the bioinspired neurodynamics is introduced to solve the traditional differential explosion problem which can not only avoid the differential of the virtual control but can limit the output in a certain range. Further, an observer is involved to overcome the leader’s velocity unavailable problem and decrease the communication burden. Simulation results verify that under the proposed method, the LOS range and angle errors can converge into an arbitrary small neighborhood around 0, while the requirements of the constraints are never violated during the maneuver.

Two‐UAV trajectory planning for cooperative target locating based on airborne visual tracking platform

Two-unmanned-aerial-vehicle (UAV) cooperative target locating based on airborne visual tracking platform is a common UAV reconnaissance mode. In the process of two-UAV cooperative target locating, the performance of target locating is highly dependent on UAV trajectory. In this Letter, a trajectory planning method for two-UAV cooperative target locating is presented. Using the line-of-sight (LOS) targeting property of the airborne visual tracking platform, in combination with the azimuth angle and elevation angle of the measured LOS, a locating error model is established, which can reflect the correlation between the target locating error and LOS angle error. Then an objective function based on minimising the target locating error is built, which is used as an index of two-UAV trajectory planning. This method can be applied in two-UAV trajectory planning for cooperative target locating and the simulated results confirm that it works effectively.

The Microvariable Activity of BL Lacertae

We report on seven nights of optical observation taken over a two-week period, and the resultant analysis of the intermediate-frequency peaked BL Lac object (IBL), BL Lac itself, at redshift z = 0.069. The microvariable behavior can be confirmed over the course of minutes for each night. A relativistic beaming model was used in our analysis, to infer changes to the line of sight angles for the motion of the different relativistic components. This model has very few free parameters. The light curves we generated show both high and moderate frequency cadence to the variable behavior of BL Lac itself, in addition to the well documented long-term variability.

Simple adaptive trajectory tracking control of underactuated autonomous underwater vehicles under LOS range and angle constraints

In this study, the authors propose a simple adaptive trajectory tracking control scheme for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and disturbances under asymmetric time-varying line-of-sight (LOS) range and angle constraints. A simple error mapping function is constructed to transform the LOS range and angle constraint problems of AUVs trajectory tracking into the problem of the boundedness of transform variable, such that any constraint boundaries of LOS range and angle can be handled. The compounded uncertain item caused by the unknown dynamic parameters and disturbances is transformed into a linear parametric form with only three unknown parameters called virtual parameters. Based on the above, a simple adaptive trajectory tracking control law is developed using dynamic surface control technique, where the adaptive laws online provide the estimations of virtual parameters. As a result, the proposed trajectory tracking control scheme is simple to compute and easy to implement in engineering applications. Strict stability analysis indicates that the designed control law makes AUVs track the desired trajectory within the LOS range and angle constraints and guarantees the boundedness of all signals of the closed-loop control system. Simulation results and comparison verify the effectiveness of the designed control scheme.

Dynamic modeling, control and experimental validation of gimballed sensor system for precision pointing applications

Gimballed sensor system is a precision electromechanical assembly designed primarily to isolate the optical system from disturbances induced by the operating environment. This paper gives an insight to the design and development of gimballed sensor system for Line of Sight (LOS) stabilization of an electro-optical tracking and pointing system. Initially kinematic equations are formulated to establish a relationship between LOS angle and applied torque. This relationship is used to obtain nested loop transfer function model. First, the parameters of the proposed assembly are determined through experimentation & rigorous analysis process, and then conventional control design methodology is adopted for controller configuration design for current and rate loop. The frequency response analysis of the designed LOS stabilization model with conventional controller is done in simulation and the obtained results are verified experimentally against angular disturbances in real time scenario. Further, Based on prior qualitative information about system dynamics and linguistic performance criteria, a fuzzy logic controller of mamdani type with simplified rule set is developed with an objective to improve the disturbance attenuation and command response performance of designed system irrespective of angular disturbances due to platform vibrations, model uncertainties and mass imbalance in gimbal assembly. Both the Fuzzy logic simulation model and conventional model are tested based on critical performance characteristics such as stability of the loop, responsiveness of the loop and insensitivity to disturbances. Finally, the comparative analysis suggests that, although both the control configuration satisfies the required accuracy, Fuzzy logic control certainly improvised the performance of the gimballed sensor system and hence can be very effective for more precise pointing, tracking and stabilization application.

Fixed-Time Cooperative Guidance Law With Angle Constraint for Multiple Missiles Against Maneuvering Target

This paper addresses the problem of the fixed-time cooperative guidance (FxTCG) law for multi-missiles against a single maneuvering target with constraints of both the interception time and the line-of-sight (LOS) angle. Firstly, by utilizing the consensus protocol and the fixed-time consensus theory, a new FxTCG in the LOS direction is presented to guarantee that the multiple missiles intercept the incoming target synchronously. Moreover, the acceleration of the target causes disturbance, so a simple fixed-time disturbance observer (FxTDO) is introduced to compensate FxTCG with the disturbance estimation. Subsequently, the FxTCG in the normal direction of the LOS is designed based on an adaptive fixed-time convergence reaching law and the proposed FxTDO, which ensures the fixed-time convergence of the LOS angular velocity and LOS angle between each missile and the maneuvering target. Finally, numerical simulations and adequate analyses are carried out to illustrate the accuracy, effectiveness, and robustness of the proposed FxTCG scheme.

Integrated Guidance and Control Design of Rolling-Guided Projectile Based on Adaptive Fuzzy Control with Multiple Constraints

In the terminal guidance section of large caliber naval gun-guided projectile while striking nearshore maneuvering target, an integrated guidance and control (IGC) method based on an adaptive fuzzy and block dynamic surface sliding mode (AFCBDSM) was proposed with multiple constraints, including the impact angle, control limitations, and limited measurement of the line of sight (LOS) angle rate. The strict feedback cascade model of rolling-guided projectile IGC in space was constructed, and the extended state observer (ESO) was used to estimate the LOS angle rate and uncertain disturbances inside and outside the system, such as target maneuvering, model errors, and wind. A nonsingular terminal sliding mode (NTSM) was designed to zero the LOS angle tracking errors and LOS angle rate in finite time, with the adaptive exponential reaching law. The cascade system was effectively stabilized by the block dynamic surface sliding mode, which prevented differential explosions. To compensate for the saturated nonlinearity of canard control constraints, an adaptive Nussbaum gain function was adopted. The switching chatter of the block dynamic surface sliding mode was reduced through adaptive fuzzy control. Proven by Lyapunov theory, the LOS angle tracking error and LOS angle rate were convergent in finite time, the closed-loop system was uniformly ultimately bounded (UUB), and the system states could be made arbitrarily small at the steady state. Hardware-in-the-loop simulation (HILS) experiments showed that the AFCBDSM provided the guided projectile with good guidance performance while striking targets with different maneuvering forms.