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     

Accurate solution of proportional navigation for maneuveringtargets

An accurate solution is presented of the nonlinear differential equations describing motion under proportional navigation when the target is laterally maneuvering. A quasilinearization (QL) approach is used, followed by a perturbation technique to obtain closed-form solutions for trajectory parameters. An explicit expression for the pursuer lateral acceleration is derived and shown to contain contributions due to initial heading error and target maneuver, with a coupling between the two effects. The solution is shown to be a substantial and consistent generalization or an earlier accurate solution for nonmaneuvering targets and also of classical linear solutions for maneuvering targets. The generalized QL solution presented provides very accurate estimates of pursuer lateral acceleration over a much broader range of engagement geometries and target maneuvers than presently available closed-form solutions     

Estimating matched filter amplitude probability functions byfailure rate analysis

Performance analysis of echolocation systems requires knowledge of the probability density function (pdf) or cumulative distribution function (cdf) of a matched filter output. A method is presented to estimate these and other probability functions from data by estimating the failure rate function, a function employed in reliability theory. The method can also be used to derive approximations to closed-form probability functions. The method is demonstrated using experimental sonar and radar clutter data and a closed-form radar clutter model     

A Closed-Form Solution for Doppler Satellite Navigation

Doppler satellite navigation relies on an initial position estimate with an iterative solution. A closed-form solution of this problem, which forms the basis of a complete analytic treatment, is presented. The solution is exact for arbitrary satellite orbits with an ellipsoid Earth model.     

Closed-Form Solution of a Recursive Tracking Filter with a Priori Velocity Initialization

A closed-form solution is presented for the transient gains and covariances of a two-state tracking filter which is initialized with a finite a priori velocity error variance. The formulas are applied to long-range tracking and fire control problems, and are shown to agree (in the limit) with classical formulas for a least-squares line estimator and a bias-in-noise estimator.     

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.     

Distributed computation in linear networks: closed-form solutions

A linear network of communicating processors is analyzed. The processors in the network may or may not be equipped with front-end processors. The processing load originates either at the boundary or at the interior of the network. Closed-form solutions and computational techniques are presented for the above situations, to obtain time optimal distribution of processing loads on the processors. Some important results are proved analytically using the closed-form expressions     

Dual-Spin Spacecraft Nutation Control Using Articulated Payloads

A technique is presented for achieving active control of nutation on a dual-spin spacecraft with an articulated payload through use of the payload's control system. Using the Orbiting Solar Observatory (OSO)-8 as an illustration, the closed-form solution to the nutation/control system dynamic interaction is presented. Control system design criteria are developed which establish the basic stability of the interaction. Design procedures are described to achieve the most effective nutation damping. Limitations on the amount of damping which can be achieved are characterized as functions of spacecraft and payload mass properties and servodesign parameters. The design techniques presented are verified through a series of on-orbit tests recently conducted on the OSO-8 spacecraft.     

模态密集柔性空间结构二阶内平衡降阶

 给出一种针对二阶线性系统方程直接进行降阶的二阶系统内平衡降阶方法。大型柔性空间结构动力学方程采用二阶线性微分方程描述,采用传统的一阶内平衡降阶方法降阶后的状态方程是一阶形式,破坏了原系统的二阶结构和物理意义。采用新方法降阶后的系统可以保持原系统二阶结构,同时可以进一步保持原系统的对称和正定特性。柔性空间结构系统级降阶的柔性模态方程通常为对角形式,针对这种特殊形式,系统可控和可观Gramian矩阵存在闭合解析解,给出了闭合解的具体表达形式。数值仿真结果表明,二阶内平衡降阶方法可以达到一阶内平衡方法一样的降阶精度,Gramian矩阵的闭合解析解可以大幅度提高Lyapunov方程求解速度。     

柔性空间结构选频二阶保结构平衡降阶

利用传统的一阶选频内平衡降阶方法进行降阶时,不但破坏了原二阶系统动力学结构,而且降阶过程中的选频Gramian矩阵的求解计算量大、数值稳定性差.利用解耦模态坐标的二阶柔性空间结构(FSS)方程的特殊性,给出了可控和可观Gramian矩阵的选频闭合解析解.为了将FSS动力学模型在指定频段进行降阶并保留原系统的二阶动力学结...     

基于欧拉角的炮弹位姿参数光学测量解析算法

炮弹空间位置和姿态参数的解算是研究其飞行弹道特性和弹道控制的非常重要的内容。利用4个已知空间坐标的非共面控制点,通过建立控制点的过渡坐标系,提出了一种基于单目视觉,采用欧拉角直接参与计算的炮弹位姿参数的测量方法,建立了位姿参数测量的误差修正模型。最后对该算法进行了完整的数学仿真。仿真结果表明,该算法简单有效且稳定,能满足位姿参数测量的精度要求。     

Steady state analysis for discrete tracking filters

An analysis of a discrete constant-gain α-β-γ tracking filter is presented. Steady-state tracking filter gains are determined without solving a discrete matrix Ricatti equation. Explicit closed-form gain solutions are found as a function of the roots to a cubic equation. Gain variations as a function of process noise, measurement noise, and sampling time are investigated     

Buckling of composite panels: A criterion for optimum stiffener design

In this paper a linear, closed-form analysis of the buckling behavior of an orthotropic plate with elastic clamping and edge reinforcement under uniform compressive load is presented. This is a typical structural situation found in aerospace engineering for instance as stiffeners in wings or the fuselage. All governing equations are transformed in a dimensionless system using common characteristic quantities to gain good analytical access. The buckling behavior is analyzed and generic buckling diagrams are presented. The solutions show excellent agreement with results from literature and numerical analyses.The minimum bending stiffness of the edge reinforcement needed to withstand buckling is examined and a minimum stiffness criterion is presented. Furthermore an absolute minimum bending stiffness is found which is sufficient to enable the reinforcement to act as a near-rigid support for arbitrarily long plates. These criteria are of interest for optimized lightweight design of stringers and stiffeners.     

Closed-form solution of hyperbolic geolocation equations

A 3-dimensional (3D), closed-form solution for the time difference of arrival (TDOA) problem that does not depend on range data is given. Such a solution did not exist previously in the literature. For aerospace and military applications, the solution is precise. For civilian cellular phone applications, however, the solution is susceptible to unrelated errors from the phenomenon of multipath delays in the channels. This phenomenon is factored in mathematically in the solution and a simulation that characterizes its error bounds is presented     

Composite Bound on Arrival Time Estimation Errors

Time of arrival (TOA) estimation of narrowband signals is a problem of considerable practical interest in radar and sonar applications. A new technique is presented to analyze the mean square error (MSE) performance of TOA estimation schemes, based on recently developed lower bound. We obtain a complete characterization of the MSE as a function of the signal and noise parameters. The results are given in a simple closed-form analytical expression.     

Analysis of generalized guidance laws for homing missiles

It is shown that the optimal guidance problem can be handled as a Bolza-type problem which can be solved by straightforward calculation. The solution proves to be different from that given by Yang, et al. (1989) and is verified to be a minimum performance index solution. Also presented is an alternate unified approach to the solution of the nonlinear system of differential equation of the generalized proportional navigation law discussed earlier by Yang, et al. This unified equation has been solved for all the different cases of proportional navigation for which closed-form solutions have been published by earlier authors     

Divisible load scheduling on single-level tree networks with buffer constraints

Scheduling a divisible load on a heterogeneous single-level tree network with processors having finite-size buffers is addressed. We first present the closed-form solutions for the case when the available buffer size at each site is assumed to be infinite. Then we analyze the case when these buffer sizes are of finite size. For the first time in the domain of DLT (divisible load theory) literature, the problem of scheduling with finite-size buffers is addressed. For this case, we present a novel algorithm, referred to as incremental balancing strategy, to obtain an optimal load distribution. Algorithm IBS adopts a strategy to feed the divisible load in a step-by-step incremental balancing fashion by taking advantage of the available closed-form solutions of the optimal scheduling for the case without buffer size constraints. Based on the rigorous mathematical analysis, a number of interesting and useful properties exhibited by the algorithm are proven. We present a very useful discussion on the implications of this problem on the effect of sequencing discussed in the literature. Also, the impact of Rule A, a rule that obtains a reduced optimal network to achieve optimal processing time by eliminating a redundant set of processor-link pairs, is also discussed. Numerical examples are presented.     

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     

Emitter localization using clustering-based bearing association

A closed-form emitter location estimator using time difference of arrival (TDOA) measurements is developed based on triangulation of hyperbolic asymptotes. The problem of associating the asymptotes with the emitter is solved by clustering the bearing angles of the linear asymptotes using a kernel density estimate. A closed-form estimate of the emitter location is obtained from triangulation of the clustered bearings using a weighted version of the pseudolinear estimator. By way of simulation examples, the proposed closed-form estimator is shown to outperform the computationally demanding and divergence-prone maximum likelihood (ML) estimator at moderate TDOA noise levels.     

Digital Communication Systems in Impulsive Atmospheric Radio Noise

Analyses are presented of the performance of binary and M-ary coherent and noncoherent communication systems operating in the impulsive atmospheric radio noise environment. The receiver is usually a maximum likelihood detector for white Gaussian interference and therefore has the form of a parallel bank of matched filters followed by decision circuitry. By employing a Poisson or generalized Shot noise model for the impulsive noise with a suitable probability density function (pdf), closed-form expressions and bounds of error probabilities for M-ary noncoherent and coherent amplitude-shift keying (ASK), phase-shift keying (PSK), and frequency-shift keying (FSK) systems are obtained and the results discussed.