Optimal guidance of extended trajectory shaping

To control missile＇s miss distance as well as terminal impact angle, by involving the timeto-go-nth power in the cost function, an extended optimal guidance law against a constant maneuvering target or a stationary target is proposed using the linear quadratic optimal control theory.An extended trajectory shaping guidance（ETSG） law is then proposed under the assumption that the missile-target relative velocity is constant and the line of sight angle is small. For a lag-free ETSG system, closed-form solutions for the missile＇s acceleration command are derived by the method of Schwartz inequality and linear simulations are performed to verify the closed-form results. Normalized adjoint systems for miss distance and terminal impact angle error are presented independently for stationary targets and constant maneuvering targets, respectively. Detailed discussions about the terminal misses and impact angle errors induced by terminal impact angle constraint, initial heading error, seeker zero position errors and target maneuvering, are performed.     

Generalized linear solution of proportional navigation

Proportional navigation (PN) equations are not solvable in closed form. Linearized solutions have been widely used for PN system analysis and design, but these are based on overly restrictive assumptions regarding the initial geometry, and are valid only for near-tail-chase pursuits. A generalization of the linearized approach is presented which yields more-accurate estimates of pursuer lateral acceleration than the classical linear solutions as verified by comparison with `exact' numerical solutions. Further, the solution is applicable over a much wider range of engagement geometries. The treatment is based on a closed-form quasilinearized solution of the PN equations followed by the small-angle approximation only to line-of-sight (LOS) angle rate     

Generalized guidance law for homing missiles

The concept of a generalized guidance law is presented, and the closed-form solution for a homing missile pursuing a maneuvering target according to generalized guidance laws is given. It is shown that the guidance laws appearing in the literature are merely special cases of the one proposed by the authors. The derived generalized forms of capture area, missile acceleration, and homing time duration that are derived provide insight into the performance of the guidance laws being considered and lead to the discovery of new ones. The problem of finding a nonlinear optimal guidance law for a homing missile with controlled acceleration, applied so as to capture a maneuvering target with a predetermined trajectory while minimizing a weighted linear combination of time of capture and energy expenditures, is solved in closed form. The derived optimal control law is equal to the LOS (line of sight) rate multiplied by a trigonometric function of the aspect angle. Numerical simulation shows that the resulting guidance law appears to yield a significant advantage over true proportional navigation     

Discrete optimal guidance for high-order missile and maneuvering target

An explicit closed-form formula of a discrete guidance law for a linear time-invariant, acceleration commanded, arbitrary-order missile and a linear, time-invariant arbitrary-order, maneuvering target is derived. The formula is given in terms of the missile and target transfer functions and responses to initial conditions. Examples are explicitly solved for zero-lag and a first-order missile. As an example, it is shown that the discrete proportional navigation ratio is higher than 3 and time varying in contrast to the continuous case.<>     

Simple Tracking Filters: Closed-Form Solutions

A closed-form steady-state solution is presented for a three-state tracking filter with continuous position measurements and exponentially correlated target acceleration. Some other related closed-form solutions are discussed, and some comparative performance data is presented for the discrete measurement case.     

A Gaussian Mixture PHD Filter for Jump Markov System Models

The probability hypothesis density (PHD) filter is an attractive approach to tracking an unknown and time-varying number of targets in the presence of data association uncertainty, clutter, noise, and detection uncertainty. The PHD filter admits a closed-form solution for a linear Gaussian multi-target model. However, this model is not general enough to accommodate maneuvering targets that switch between several models. In this paper, we generalize the notion of linear jump Markov systems to the multiple target case to accommodate births, deaths, and switching dynamics. We then derive a closed-form solution to the PHD recursion for the proposed linear Gaussian jump Markov multi-target model. Based on this an efficient method for tracking multiple maneuvering targets that switch between a set of linear Gaussian models is developed. An analytic implementation of the PHD filter using statistical linear regression technique is also proposed for targets that switch between a set of nonlinear models. We demonstrate through simulations that the proposed PHD filters are effective in tracking multiple maneuvering targets.     

机动目标“当前”统计模型与自适应跟踪算法

本文提出机动目标“当前”统计模型的概念并建议用修正的瑞利-马尔科夫过程描述目标随机加速机动的统计特性。文中指出了在机动目标运动模型中状态（机动加速度）估值与状态噪声之间的内在联系。在此基础上提出了具有机动加速度均值及方差自适应的卡尔曼滤波算法。对一维和三维的情形进行了计算机模拟。计算结果表明,在仅对目标位置进行观测的情况下,这类自适应估值算法无论对高度机动或无机动的目标均可绘出较好的位置、速度及加速度估值。     

Multisensor tracking of a maneuvering target in clutter

An algorithm is presented for tracking a highly maneuvering target using two different sensors, a radar and an infrared sensor, assumed to operate in a cluttered environment. The nonparametric probabilist data association filter (PDAF) has been adapted for the multisensor (MS) case, yielding the MSPDAF. To accommodate the fact that the target can be highly maneuvering, the interacting multiple model (IMM) approach is used. The results of single-model-based filters and of the IMM/MSPDAF algorithm with two and three models are presented and compared. The IMM has been shown to be able to adapt itself to the type of motion exhibited by the target in the presence of heavy clutter. It yielded high accuracy in the absence of acceleration and kept the target in track during the high acceleration periods     

三维空间中目标机动加速度的估值问题

建立了描述目标在三维空间中进行切向与法向机动的非线性状态模型。目标切向与法向机动加速度的幅值表示为修正的瑞利-马尔可夫随机过程;法向加速度的方向角则假定在2π区间内具有均匀的概率密度。在仅有含噪声位置观察数据的情况下,发展了一种推广的卡尔曼滤波和自适应算法,并由此获得一种机动目标切向与法向加速度估值的直接方法。提供了某些计算结果以证实方法的有效性。     

A simple smoother: closed-form solution and analytical results

A closed-form solid-state solution for a simple one-dimensional smoother is presented. The target position-velocity dynamics are modeled as a linear discrete Gauss-Markov process: the discrete position measurements are assumed to be independent and identically normally distributed. Analytical results derived from estimating optimum steady-state position and velocity are given as well as the improvement provided by smoothing relative to pure filtering estimates. Analytical results, including appropriate limiting cases, show that the ratios of the RMS smoothing to the RMS filtering error are from 1/2 to 1 in position and from 1/2 to 1/√2 in velocity. As a numerical example a highly maneuvering target characterized by an acceleration width of 30 m/s² is considered     

机动多目标跟踪问题中关联区域的研究

 本文研究了跟踪多个机动目标时,由滤波算法所获得的新息向量范数的统计性质,关联区域的大小以及接收正确回波的概率。借助拉蒙特卡洛方法,考察了不同的目标状态模型、目标机动加速度及状态噪声方差等因素对所研究的问题的影响。研究表明,文献[1]所提出的机动目标状态模型及相应的自适应算法具有较好的适应目标机动的能力,关联区域的大小及接收正确回波的概率均较为稳定。     

Distributed online mission planning for multi-player space pursuit and evasion

There are three important roles in evasion conflict: pursuer, target and defender. Pur-suers’ mission is to access targets;targets’ mission is to escape from pursuers’ capture;defenders’ mission is to intercept pursuers who are potentially dangerous to targets. In this paper, a distributed online mission plan (DOMP) algorithm for pursuers is proposed based on fuzzy evaluation and Nash equilibrium. First, an integrated effectiveness evaluation model is given. Then, the details of collaborative mission planning which includes the co-optimization of task distributing, trajectory and corresponding maneuvering scheme are presented. Finally, the convergence and steadiness of DOMP are discussed with simulation results. Compared with centralized mission planning, DOMP is more robust and can greatly improve the effectiveness of pursuing. It can be applied to dynamic scenario due to its distributed architecture.     

Ideal proportional navigation for exoatmospheric interception

Ideal proportional navigation (IPN) is a natural choice for exoatmospheric interception for its mighty capture capability and ease of implementation. The closed-form solution of two- dimensional ideal proportional navigation was conducted in previous public literature, whereas the practical interception happens in the three-dimensional space. A novel set of relative dynamic equations is adopted in this paper, which is with the advantage of decoupling relative motion in the instantaneous rotation plane of the line of sight from the rotation of this plane. The dimension-reduced IPN is constructed in this instantaneous plane, which functions as a three-dimensional guidance law. The trajectory features of dimension-reduced IPN are explored, and the capture regions of dimension-reduced IPN with limited acceleration against nonmaneuvering and maneuvering targets are analyzed by using phase plane method. It is proved that the capture capability of IPN is much stronger than true proportional navigation (TPN), no matter the target maneuvers or not. Finally, simulation results indicate that IPN is more effective than TPN in exoatmospheric interception scenarios.     

Extended solution to multiple maneuvering target tracking

An improved algorithm for tracking multiple maneuvering targets is presented. This approach is implemented with an approximate adaptive filter consisting of the one-step conditional maximum-likelihood technique together with the extended Kalman filter and an adaptive maneuvering compensator. In order to avoid the extra computational burden of considering events with negligible probability, a validation matrix is defined in the tracking structure. With this approach, data-association and target maneuvering problems can be solved simultaneously. Detailed Monte Carlo simulations of the algorithm for many tracking situations are described. Computer simulation results indicate that this approach successfully tracks multiple maneuvering targets over a wide range of conditions     

机动目标三维空间导引运动建模及导引律研究

给出了导弹—目标追逃运动的空间矢量方程，在此基础上推导了三维导引运动模型。对机动目标应用李雅普诺夫稳定性分析方法提出了一种自适应变结构制导算法。六自由度数学仿真结果表明了模型的正确性和制导算法的有效性。     

自寻的导弹攻击机动目标的最优制导规律的研究及实现

提出一种适用于红外和雷达自寻的制导导弹的适应性强、制导精度高、易实现的最优制导规律。为解决工程实现的关键问题,提出了目标机动加速度模型。根据该模型并利用导弹导引头的AGC信号或雷达测距信号,给出了目标机动加速度、导弹与目标相对距离和距离变化率的估计算法。     

Saturated super-twisting sliding mode missile guidance

This paper concentrates on developing a missile terminal guidance law against a highly maneuvering target whose maneuvering acceleration is very close to that of the missile or even exceeds the missile normal acceleration in a finite period of time. A new saturated super-twisting algorithm is proposed and applied to the design of missile guidance law. The proposed algorithm has the advantages of simple structure, easy parameter tuning rules and a full utilization of the limit control input. The designed saturated super-twisting sliding mode guidance law is then employed in a missile guidance system. Simulation and its superior performance against strong maneuvering targets is demonstrated.     

Closed-form solution for the Kalman filter gains of time-varyingsystems

A method for derivation of closed-form solutions for the differential Riccati matrix equation for specific time-varying systems is presented. It allows more insight into the nature of the solution. It reduces the on-line computation requirements, since it does not require on-line solution of a differential equation. Sufficient conditions for the existence of the closed-form solution are given. The method is applied to a target tracking problem     

三维制导的几何方法与鲁棒控制方法

 在考虑导弹速度和目标速度均为时变的情况下,将微分几何方法与李雅普诺夫稳定理论结合起来,提出了一种导弹三维导引规律设计新方法。对机动目标,PPNG方法的主要问题是在导引末段,它要求导弹在俯仰和偏航通道上具有较大的加速度,为了解决这一问题,本文应用基于李雅普诺夫稳定理论的鲁棒控制方法,提出了一种三维鲁棒制导算法。这种方法在导引末段不需要过大的加速度命令,不需要知道目标精确的加速度和速度方位信息。     

Optimal predictive sliding-mode guidance law for intercepting near-space hypersonic maneuvering target

The design of optimal guidance law for intercepting a near-space hypersonic maneuvering target with bounded inputs is considered. Firstly, a maneuvering model for near-space hypersonic aircraft is given. Then, the aircraft acceleration prediction can be obtained using this model with two neural networks. By using the target acceleration prediction, which is taken into account when calculating the Zero Effort Miss(ZEM), an optimal sliding-mode guidance law is proposed to fulfill the guidance task...