Observability analysis of two closed-loop guidance systems with bearings-only measurements

The implementation of missile guidance laws on collision course trajectories with bearings-only measurements may result in bad range observability. This in turn may result in poor engagement performance for those guidance algorithms that exploit range information in their steering law. Maneuvering away from the collision course trajectory improves range observability. To propose a sizing criterion for this maneuver, this work presents a new guidance strategy that exploits the information from the error covariance matrix of the homing loop integrated Kalman filter in the framework of a pursuit-evasion game. The new strategy has been tested in several scenarios against other guidance laws, such as the classical formulation of the pursuit-evasion game and proportional navigation. Numerical simulations on a set of Monte Carlo samples show that the proposed solution is able to improve engagement performance in terms of both miss distance and range observability.

Deep reinforcement learning-based impact time control guidance law with constraints on the field-of-view

In this work, design of three-dimensional (3D) proportional navigation guidance law based on input-output linearization (IOL) for tactical missiles is proposed. For the three-dimensional nonlinear missile-target engagement dynamics, the line-of-sight (LOS) rates in pitch and yaw planes are taken as outputs and the IOL theory is used to derive the guidance laws without ignoring the cross-coupling terms. Simulations are carried out by considering maneuvering target, and the results are presented to showcase the efficacy of the proposed design. Further, comparison of the performance of the proposed guidance law with augmented proportional navigation guidance(APNG) laws is carried out and the related results are presented. Lastly, implementation issues of the proposed guidance law are discussed.

Cooperative pursuit―evasion strategies are derived for a team composed of two agents. The specific problem of interest is that of protecting a target aircraft from a homing missile. The target aircraft performs evasive maneuvers and launches a defending missile to intercept the homing missile. The problem is analyzed using a linear quadratic differential game formulation for arbitrary-order linear players' dynamics in the continuous and discrete domains. Perfect information is assumed. The analytic continuous and numeric discrete solutions are presented for zero-lag adversaries' dynamics. The solution of the game provides 1) the optimal cooperative evasion strategy for the target aircraft, 2) the optimal cooperative pursuit strategy for the defending missile, and 3) the optimal strategy of the homing missile for pursuing the target aircraft and for evading the defender missile. The obtained guidance laws are dependent on the zero-effort miss distances of two pursuer―evader pairs: homing missile with target aircraft and defender missile with homing missile. Conditions for the existence of a saddle-point solution are derived and the navigation gains are analyzed for various limiting cases. Nonlinear two-dimensional simulation results are used to validate the theoretical analysis. The advantages of cooperation are shown. Compared with a conventional one-on-one guidance law, cooperation significantly reduces the maneuverability requirements from the defending missile.

Adaptive Impact Time Control Via Look-Angle Shaping Under Varying Velocity

Two new guidance laws for short range homing missiles are developed by invoking the sliding mode control (SMC) theory. Guidance law 1 as structured around the basic proportional navigation (PN), with an additive switching term, which is a function of the line of sight (LOS) rate alone. An adaptive procedure is suggested to select the gain of the switching term, in order to reduce chattering. This guidance law is nearly as simple to implement as the PN itself and does not require any explicit target maneuver estimation. Guidance law 2, based on a first order sliding surface, is designed such that it results in a continuous acceleration law, thereby reducing the chattering problem. While explicitly taking into account the effect of aerodynamic drag, it requires the second derivatives of LOS angle and range, which are not directly measured. An estimation scheme, again based on sliding mode theory, is presented to estimate these quantities. Simulation results clearly demonstrate the superior performance of these schemes. >

Implementation of Linear Homing Guidance Law on a Two-Part Homing Missile

The extra-atmospheric aircraft model is established, and then the control system is designed. The control system consist of attitude control system and orbit control system, the attitude control system used PID controller and the orbit control system used augmented proportional navigation method. The traditional Proportional Navigation (PN) guidance law has higher accuracy. But for highly maneuvering targets, the accuracy of traditional PN guidance law is still not enough. An Augmented Proportional Navigation (APN) guidance law is designed, an acceleration compensation of the target is introduced on the basis of PN guidance law to overcome the effect of the acceleration on the guidance accuracy. And the engine control method is designed based on the fixed engine thrust. Simulation results indicated that, for homing against maneuverable targets, the APN guidance law is better than the PN guidance law in the following aspects: guidance accuracy is higher, miss distance is lower, interception time is shorter. And the new guidance law provides significant performance improvements over the commonly used classical proportional navigation law.

In this paper, distributed three‐dimensional (3D) cooperative guidance laws are designed for leader–follower multiple missiles to achieve simultaneous attack at a specified time. The guidance laws are derived from the biased proportional navigation guidance (PNG) law. Two fixed‐time distributed algorithms with time‐varying coefficients are proposed to track the state of the leader under undirected and directed topologies, respectively. The upper bounds of convergence times for the tracking algorithms are obtained. The biased guidance terms of followers are designed to track the leader with the proposed algorithms and the biased guidance term of the leader is designed to achieve specified impact time. Then, an auxiliary function is included into the biased guidance terms to meet the field‐of‐view (FOV) constraints. The leading angles' properties and convergence times under the proposed guidance laws are further analyzed. Numerical simulations are given to verify the effectiveness of the proposed cooperative guidance laws.

Most underwater target tracking algorithms are based on noisy bearing-only measurements. The bearing measurements are actually bearing estimates obtained from acoustic field measurements made by an array of sensors placed on a manoeuvrable platform. In this paper, we investigate the problem of tracking a manoeuvring target in the ocean directly from the acoustic field measurements. The use of acoustic field measurements eliminates the need for the use of a manoeuvrable platform, and also eliminates the intermediate step of bearing estimation. We consider the vector acoustic field measurements by an array of acoustic vector sensors (AVS), which are more informative than the scalar acoustic field measurements by an array of acoustic pressure sensors (APS). We model the target dynamics by a piecewise-constant turn rate model. The resultant nonlinear estimation problem is solved using the Gaussian approximation filtering approach. Within this framework, we consider the quasi-Monte Carlo Kalman filtering (QMC-KF) algorithm that employs an advanced numerical integration procedure to solve the multi-dimensional integrals appearing in the filtering process. We also derive the posterior Cramer-Rao lower bound (PCRLB) on the root mean square error (RMSE) of the sequential Bayesian estimator, and show that the PCRLB for acoustic field measurements is lower than that for bearing-only measurements. Simulation results indicate that acoustic field measurements yield a significantly better performance than bearing-only measurements, the QMCKF performs better than other deterministic filters, and an AVS array provides a much better performance than an APS array.

By combining the Lyapunov stability theorem with the proportional navigation guidance (PNG) law, a novel guidance law which can control the impact time is proposed. This paper treats the impact time control problem as the impact time error regulation problem. The impact time error is defined by the difference between the desired time and the estimated time-to-go.The Lyapunov candidate function is introduced concerning the impact time error, and the control parameter is proposed to satisfy the Lyapunov stability theorem. The impact time error will go to zero before the desired time, and the singularity issue of the acceleration command has been analyzed. Numerical simulations are carried out to prove the effectiveness of the proposed guidance law.

The implementation of advanced guidance laws with bearings-only measurements requires estimation of the range information. To improve estimation accuracy and satisfy the impact angle constraint, this paper proposes a two-phase optimal guidance law consisting of an observing phase and an attacking phase. In the observing phase, the determinant of Fisher information matrix is maximized to achieve the optimal observability and a suboptimal solution expressed by leading angle is derived analytically. Then, a terminal sliding-mode guidance law is designed to track the desired leading angle. In the followed attacking phase, an optimal guidance law is integrated with a switching term to satisfy both the impact angle constraint and the field-of-view constraint. Finally, comparison studies of the proposed guidance law and a traditional optimal guidance law are conducted on stationary targets and maneuvering targets cases. Simulation results demonstrate that the proposed guidance law is able to improve the range observability and achieve better terminal performances including impact angle accuracy and miss distance.

In this paper, the three-dimensional terminal guidance problem of a missile intercepting a maneuvering target is studied. Augmented proportional navigation (PN) guidance laws based on Lyapunov stability theory are presented. Augmented terms are target accelerations such that proposed guidance laws have the ability to track the target maneuver. But, target accelerations cannot be accurately obtained in practice. To solve this problem, the nonlinear disturbance observer (NDOB) technology is introduced to estimate target accelerations. Estimated target accelerations will be employed as compensation terms in the proposed augmented PN guidance laws. Composite guidance laws combining augmented PN guidance laws with NDOB are proposed. Finally, simulation comparison results are provided to demonstrate the effectiveness of the presented guidance laws.

This paper presents a three-dimensional (3D) piecewise guidance scheme for multiple UAVs) guaranteeing simultaneous arrival even under the field-of-view (FOV) constraint. The guidance law does not require to consider the estimation of the time-to-go and can be divided into two stages: cooperative stage and proportional navigation guidance (PNG) stage. In the cooperative stage, a decentralized consensus control approach is proposed for multi-UAV systems and does not rely on global information about the communication topography. Moreover, the neighbors’ new auxiliary states are introduced to ensure the states achieving consensus under FOV constrain. The guidance strategy transfers to the PNG stage while the UAV formation is close enough to the target and the simultaneous arrival to hit the target is guaranteed for UAVs via the PNG guidance law. Numerical simulation results demonstrate the effectiveness of the proposed cooperative guidance law.

Two new algorithms for homing missile guidance and estimation in the two-dimensional intercept problem are proposed based on the assumption that certain targets execute evasive maneuvers orthogonal to their velocity vectors. The objectives of both algorithms are to estimate the engagement states in the presence of unknown target accelerations and guide the interceptor to hit the target based on these state estimates. Both algorithms are the integration of a fllter in cascade with a guidance law but constructed using difierent philosophies. One algorithm constructs the fllter that estimates the target acceleration and the guidance law based on a target model in which the magnitude of the target acceleration vector is assumed to be a sinusoidal function. The other algorithm constructs the fllter by blocking the dynamic efiect of the target acceleration and constructs the guidance law based on the anticipated worst possible target acceleration. These two algorithms form an interesting design trade between the inherent estimation lag and increased estimation uncertainty.