Midcourse Phase Research Articles

Launch Envelope Optimization of Virtual Sliding Target Guidance Scheme

This paper presents an optimization of the performance of a recently proposed virtual sliding target (VST) guidance scheme in terms of maximization of its launch envelope for three-dimensional (3-D) engagements. The objective is to obtain the launch envelope of the missile using the VST guidance scheme for different lateral launch angles with respect to the line of sight (LOS) and demonstrate its superiority over kinematics-based guidance laws like proportional navigation (PN). The VST scheme uses PN as its basic guidance scheme and exploits the relation between the atmospheric properties, missile aerodynamic characteristics, and the optimal trajectory of the missile. The missile trajectory is shaped by controlling the instantaneous position and the speed of a virtual target which the missile pursues during the midcourse phase. In the proposed method it is shown that an appropriate value of initial position for the virtual target in 3-D, combined with optimized virtual target parameters, can significantly improve the launch envelope performance. The paper presents the formulation of the optimization problem, obtains the approximate models used to make the optimization problem more tractable, and finally presents the optimized performance of the missile in terms of launch envelope and shows significant improvement over kinematic-based guidance laws. The paper also proposes modification to the basic VST scheme. Some simulations using the full-fledged six degrees-of-freedom (6-DOF) models are also presented to validate the models and technique used.

A fuzzy guidance law for vertical launch interceptors

A fuzzy logic-based guidance design for longer engagement in time and beneficial interception attitudes is investigated and proposed here. The integrated fuzzy logic-based guidance scheme consisting of vertical, midcourse and terminal guidance phases can intercept the target from diverse aspects. The engagement strategy in the vertical guidance phase includes general vertical launch to handle the case of longer engagement ranges, and vertical launch with back turn (BT) to handle shorter engagement ranges. Numerical experimental results show excellent engagement performance and defensible volumes.

Gauss meets Newton again: How to make Gauss orbit determination from two position vectors more efficient and robust with Newton–Raphson iterations

Gauss’s method for determining the six classical idealized Keplerian two-body orbital parameters from two position vectors and two times is elegantly formulated. It first reduces the three-dimensional velocity determination problem to two equation in two variables x, y. These two equations take the form: (i) x = F( y; l, m), (ii) y = G( x; l). Here l and m are parameters that are functions of the two position vectors and the corresponding time span between them. Gauss’s approach was to form a functional iteration ( y-iteration) by substituting (i) into (ii) An alternate second functional iteration ( x-iteration) is formed by substituting (ii) into (i). In either case a further reduction of dimension from two to one is obtained. The method first appeared in the early-19th century and is ubiquitous in the astronomy and astro-dynamics literature. However, it could not exploited until the mid 20th century advent of powerful radars. These can provide initial elliptical orbital positional observations of such natural space objects as the moon, comets, asteroids, and meteors as well as man-made objects such as satellites and ballistic missile in the mid-course phase of their trajectories. There are, however, three basic problems with the classical approach: (1) it breaks down when the angular difference in true anomaly between the two position vectors grows larger than π/4, (2) the classical first guess, y 0 = 1, may not lie in the convergence region of the method’s functional iteration, and (3) the functional iteration, when it works, is slowly linearly convergent. In this paper we show that applying a Newton–Raphson iteration to the fixed-point equation that defines the functional iteration, in y when the angular spread is sufficiently small, or in x when the spread is large, together with trivial first guesses solves all three problems at once. Moreover, we prove a theorem on a simple necessary and sufficient condition for the existence of unique solutions and put forth a conjecture on the concavity of the two fixed-point equation graphs. This Newton–Raphson iteration approach extends the range of algorithm applicability to a true anomaly angular spread close to π, a basic singularity of the Gauss method.

BTT 유도탄의 하중계수 분배논리 연구

본 논문은 느리거나 정지된 표적을 요격할 수 있는 Bank-to-turn(BTT) 유도탄의 하중계 수 분배논리 (PCL) 에 대해 기술하였다. BTT 제어를 위해서는 직각 좌표계에서 표현된 유도 명령을 극좌표 형태로 변환시켜야만 한다. 이러한 극좌표 변환은 비선형성이 심하고 불연속적인 함수를 포함하고 있어 피치 가속도명령이 0인 경우 가제어성을 상실하는 문제점도 발생한다. 또한 2축 탐색기를 포함하는 BTT 유도탄의 호밍 유도시 롤 상관에 의해 불안정 성이 나타나는 문제점이었다. 본 논문에서는 중기유도 단계에서 그러한 가제어성 상실을 완화시키고 유도명령 추종성능을 향상시킬 수 있도록 linear homotopy 관계식을 도입하였다. 또한, 호밍유도루프의 안정성을 향상시키기 위하여 피지 가속도명령에 대한 민감도를 감소시킬 수 있는 PCL을 구성하였다. 제안한 논리의 타당성은 전산모의시험을 통해 검증 하였다. This paper presents polar converting logic(PCL) of BTT missiles against slowly moving or stationary targets. A guidance commands expressed in rectangular coordinates must be converted in the form of polar coordinates for BTT control. Since conventional PCL has nonlinear and discontinuous function, the missiles may lose controllability when pitch acceleration command equals to zero. Further, roll coupling may have a serious unstabilizing influence on homing guidance with two gimbals seeker. In this paper, a linear homotopy equation is introduced to improve the controllability and a command following performance at midcourse phase. We also design a PCL which is less sensitive to pitch acceleration command so that it may improve the stability of the homing loop. To substantiate our conclusion, results of the computer simulation have been illustrated.

Empirical virtual sliding target guidance law design: an aerodynamic approach

We present a novel empirical virtual sliding target (VST) guidance law for the midcourse phase of a long range surface-to-air missile that uses the simplicity of the conventional proportional navigation (PN) guidance law while exploiting the aerodynamic characteristics of a missile's flight through the atmosphere to enable the missile to achieve superior performance than that achieved by conventional PN guidance laws. The missile trajectory emulates the trajectory of an optimal control based guidance law formulated on a realistic aerodynamic model of the missile-target engagement. The trajectory of the missile is controlled by controlling the speed of a virtual target that slides towards a predicted intercept point during the midcourse phase. Several sliding schemes, both linear and nonlinear, are proposed and the effect of the variation of the sliding parameters, which control the sliding speed of the virtual target, on the missile performance, are examined through extensive simulations that take into account the atmospheric characteristics as well as limitations on the missile in terms of the energy available and lateral acceleration limits. Launch envelopes for these sliding schemes for approaching and receding targets are also obtained. These results amply demonstrate the superiority of the proposed guidance law over the conventional PN law.

Design of Fuzzy Logic Guidance Law Against High-Speed Target

An advanced guidance law is developed against very high-speed targets. Preliminary studies have shown that the aspect angle of the interceptor at lock-on near 180 deg is a fundamental requirement for achieving small miss distance against a very high-speed target. To meet this requirement, a fuzzy guidance law in midcourse phase that is more similar to human decision making is designed. In terminal phase, a proportional and derivative-type fuzzy terminal guidance law is explored. It is shown that the integrated guidance scheme offers a near head-on homing condition before the missile enters terminal phase and provides better e nal results (smaller miss distance and wider defensible volume ) than the conventional guidance law. A complete simulation study is performed to show the effects of the proposed design. Nomenclature CD = drag coefe cient CD0 = zero drag coefe cient CL = lift coefe cient CLa = @CL/@a D = drag h = vertical coordinate L = lift m = mass Q = dynamic pressure Stref = reference area of ballistic target s = reference area T = thrust v = missile speed vt = target speed W = target weight x = horizontal coordinate a = angle of attack b = ballistic coefe cient c = e ight-path angle c t = reentry angle of target d = velocity angle error h = inertial line-of-sight angle l = induced drag coefe cient q = atmospheric density r = heading error angle

Student monitoring procedures for competency-based programs

A diverse set of techniques for monitoring the progress of students within competency-based programs of a public community college are discussed and evaluated. Groupings of monitoring procedures are delineated for the entry, midcourse, and exit phases of several operational programs. Those specific approaches considered are placement testing, entry self-testing, computer-generated entry surveying and test generation, computer records management, student manuals, and competency-based transcripts.

MONTE CARLO SIMULATION OF THE MIDCOURSE GUIDANCE FOR LUNAR FLIGHTS

Description and numerical results of a monte carlo simulation to determine fuel requirements and final accuracy of the midcourse phase of the lunar missions

Trends in Space Navigation

The theme of this paper is based on the growing use of self-contained navigational systems in space navigation. A figure of merit, called the self-containment index (SCI), is defined in order to define quantitatively the degree of autonomy for which a system design is directed. The navigational problem of spacecraft is divided into problems of point-dynamics and rigid-body dynamics and the major factors are defined which deserve consideration in the understanding of the space navigational problem. Consistent with the requirements for low size, weight and power allocations and for very high accuracy and reliability tolerances, optical techniques are found ideally suited for space navigation. Open-loop and closed-loop methods of earth satellite navigation are presented and extended to the lunar navigation problem. Some advanced navigational concepts are given using nonrotating and track-while-scan instruments. The importance is emphasized of the increase in data-processing requirements and their part in accuracy enhancement through statistical techniques. A review of optical Doppler and lasers for measurement of distance and velocity is given. The concept of guidance management is proposed for consolidation of all the launch, orbital, midcourse, return and other guidance phases of a future multistage spacecraft into a single, integrated, selfcontained navigation system within the final upper stage.