The GPS equations and the Problem of Apollonius

By relating the Global Positioning System (GPS) problem of location to the ancient Problem of Apollonius, this work presents a closed solution to the pseudorange positioning problem for two and three dimensions The positioning problem, given by a set of nonlinear equations, has been reduced to the solution of a quadratic equation. The resulting expressions yield either two or one physically meaningful solutions for both the two- and three-dimensional problems. Expressions for the boundary curves and surfaces that separate the one-solution domain from the two-solution domains are also given. Asymptotic lines and planes for the boundary curves and surfaces have also been derived     

电动力绳系周期解求解及稳定性控制

电动力绳系姿态摆动动力学方程具有非线性特点,且姿态摆动状态直接影响着空间任务能否正常进行。首先,基于哑铃模型及偶极子地磁场模型假设,推导了在倾斜圆轨道上运行的电动力绳系姿态动力学方程。其次,给出了利用摄动法和不动点迭代法相互配合的数值方法求解该非线性方程周期解的过程及解的稳定性判断准则,并针对不稳定周期解提出了相应的稳定性控制策略。最后,通过数值仿真分析,得到了姿态摆动运动的周期解图像,验证了周期解求解算法的有效性,并对不稳定周期解实现了稳定性控制。     

导航星座的自主导航技术--卫星自主时间同步

基于星载原子时钟频率稳定性的Allan方差表达,建立系统状态方程,并以星间双向测量伪距差作为基本观测量,组成系统测量方程,从而可以设计适用于导航星座卫星时间同步的Kalman滤波算法。系统仿真结果表明：通过对星间双向测量数据的滤波处理,能够实现星座卫星时间精密同步。     

Existence and uniqueness of GPS solutions

The existence and uniqueness of positions computed from global positioning system (GPS) pseudorange measurements is studied. Contrary to the claims of S. Bancroft (1985) and L.O. Krause (1987), in the case of n=4 satellites a fix may not exist, and, if a fix exists, it is not guaranteed to be unique. In the case of n>or=5 satellites, a unique fix is assured, except in certain degenerate cases such as coplanar satellites. An alternate formulation of the direct n=4 pseudorange to three-space position solutions of Bancroft and Krause is presented, and simple tests for existence and uniqueness are derived.<>     

Geometric Approach in Solving Inverse Kinematics of PUMA Robots

A geometric approach for deriving a consistent joint solution of a six-point PUMA1 robot is presented. The approach calls for the definition of various possible arm configurations based on the link coordinate systems and human arm geometry. These arm configurations are then expressed in an exact mathematical way to allow the construction of arm configuration indicators and their corresponding decision equations. The arm configuration indicators are prespecified by a user for finding the joint solution. These indicators enable one to find a solution from the possible four solutions for the first three joints, a solution from the possible two solutions for the last three joints. The solution is calculated in two stages. First a position vector pointing from the shoulder to the wrist is derived. This is used to derive the solution of the first three joints by looking at the projection of the position vector onto the xi-1-yi-1(i = 1,2,3) plane. The last three joints are solved using the calculated joint solution from the first three joints, the orientation matrices, and the projection of the link coordinate frames onto the xi-1-yi-1 (i = 4,5,6) plane. From the geometry, one can easily find the arm solution consistently. A computer simulation study conducted on a VAX-11/780 computer demonstrated the validity of the arm solution.     

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     

欺骗环境下GNSS信号估计与定位修正技术

欺骗信号以其极强的隐蔽性使卫星导航接收机难以察觉并迅速定位到错误位置,严重影响了卫星导航的安全性。现有抗欺骗技术需要其他导航系统辅助来修正受欺骗影响的定位解算,针对该问题,本文提出了一种GNSS欺骗信号参数估计与辨识方法,能够在欺骗干扰环境下估计并辨识出真实信号所对应的伪距,进而解算出接收机真实位置。该方法通过研究欺骗干扰下接收机相关值模型,在信号跟踪阶段建立真实与欺骗双信号状态模型与基于九路相关器输出的观测模型,利用扩展卡尔曼滤波（EKF）估计真实信号与欺骗信号的伪码延时与信号相关幅值,进而获得真实与欺骗伪距,在定位解算阶段利用改进观测量残差检测方法辨识出真实与欺骗伪距,最终使用真实伪距定位获得真实位置。仿真结果表明对相对码延时介于0.3~0.9 chip之间且欺骗/真实信号幅度比介于1~5之间的隐蔽欺骗攻击,所提方法的码延时估计误差约0.1 chip,可有效估计真实信号与欺骗信号参数,辨识出真实伪距,并使被欺骗的定位结果重新回到真实位置结果,改善GNSS接收机抗欺骗能力,提高卫星导航安全性。     

轴对称弯道流动的N—S方程数值解

利用涡量—流函数方法求解离心压气机进气弯道中的轴对称粘性流场。本文推导出了q—τ湍流模型方程在正交曲线坐标系下的表达式,并用以预测湍流流场。文中在涡量方程及q—τ方程中引进非定常项,采用时间推进法求解。通过对二维直通道及复杂边界的轴对称弯道内的层流、湍流流动的计算,获得了令人满意的结果。      

叶轮机械气动声学频域分析

得到中弧线小弯度薄叶片叶轮机械声场的详细结果。讨论适用于近声场, 叶片的弯、掠等几何特征及运行条件也都在频域解中显式地表示出来。      

An Algebraic Solution of the GPS Equations

The global positioning system (GPS) equations are usually solved with an application of Newton's method or a variant thereof: Xn+1 = xn + H-1(t - f(xn)). (1) Here x is a vector comprising the user position coordinates together with clock offset, t is a vector of tour pseudorange measurements, and H is a measurement matrix of partial derivatives H = fx· In fact the first fix of a Kalman filter provides a solution of this type. If more than four pseudoranges are available for extended batch processing, H-1 may be replaced by a generalized inverse (HTWH)-1HTW, where W is a positive definite weighting matrix (usually taken to be the inverse of the measurement covariance matrix). This paper introduces a new method of solution that is algebraic and noniterative in nature, computationally efficient and numerically stable, admits extended batch processing, improves accuracy in bad geometric dilution of precision (GDOP) situations, and allows a "cold start" in deep space applications.     

Evaluation and reduction of multipath-induced bias on GPS time-of-arrival

New expressions are presented for the multipath-induced pseudorange error (i.e. bias) and variance introduced by multipath onto the time-of-arrival estimate obtained using a noncoherent early-late gate discriminator. The results include the effect of front-end bandwidth and early-late gate spacing. We also investigate a blind method for cancelling the multipath, in order to improve the time-of-arrival estimate. Our approach uses early-late gate processing on an objective function derived from an adaptive finite impulse response (FIR) filter that attempts to match the crosscorrelation of the received signal with a multipath-free replica of the desired crosscorrelation. This method performs reasonably well, and decreases the multipath-induced pseudorange error by approximately a factor of 2, even in very stressing multipath environments.     

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     

变比热激波关系式及其在高超声速进气道计算中的应用

本文根据空气热力性质表建立了空气热力性质的解析表达式,从气动热力学基本方程和激波前后比热比不同出发建立并推导出完全变比热激波方程组及其解法。对分别使用变比热激波关系式与定比热激波和等熵流关系式计算结果进行的比较表明,使用变比热激波关系式进行高超声速进气道气动热力学分析计算,能够减少定比热假定产生的偏差,提高计算准确性。      

层合双曲率厚壳的状态方程及其半解析法

采用正交曲线坐标导出了角铺设层合双曲率厚壳的状态方程及其半解析法。该方法在α－β曲面内采用通常的有限元离散,而沿壳厚（ｒ）方向采用状态空间法给出解析解,从而计入了剪切效应的影响,且通过状态转移矩阵的建立,保证了层界面之间层间位移和应力的连续,减少了计算中未知量数目。     

一种无条件稳定的时域推进法与有限元混合分析瞬态热传导问题

本文将一种新的无条件稳定的时域推进法与有限元结合,用于分析瞬态热传导问题。根据微-积分型热传导控制方程,对时间变量在小区闻内插值积分,变初-边值问题为一系列离散时刻的边界值问题,再应用有限元法求解之。由于推进中的每一时刻的解,都严格满足原给定的初始条件,就消除了累积误差的影响。此外,这种时域推进法对时间变量的数值积分也优于数值微分。因而,与现行的基于微分型控制方程,采用时-空有限元模型同时离散,再逐步求解的直接积分算法相比,计算精度可大大提高。不难预料,当求解较长时间后的瞬态值时,本算法的优越性会更加明显。     

求解Euler／Navier—Stokes方程的有限体积龙格库塔方法

提出了一个求解定常Ｅｕｌｅｒ／Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程的计算方法,求解的主管方程是积分形式的Ｅｕｌｅｒ方程或雷诺平均的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程,计算方法是有限体积多步龙格库塔方法,通过在格式中加入自适应的二阶加四阶人工粘性项以保证数值计算的稳定性,用空间变时间步长、焓阻尼来加速定常问题的收敛速度。     

考虑预应力和液体影响的圆柱壳颤振分析

 为了研究预应力和液体对圆柱壳颤振的影响,采用杂交元方法,建立了圆柱壳的气动弹性方程。由Sanders薄壳理论和经典有限元理论,从壳的精确解推导节点位移函数入手,并由一阶活塞理论得到结构的气动阻尼矩阵和刚度矩阵,最终推导出考虑预应力和内部液体影响的圆柱壳的混合有限元公式和气动弹性方程。通过特征值法验证了此种有限元方法的正确性,并重点研究了预应力和内部注有液体对圆柱壳稳定性的影响。计算结果表明:预应力和液体对圆柱壳的颤振特性有显著的影响。     

导电圆柱壳体磁弹性二阶谐波共振响应分析

 研究了磁场环境中受机械载荷作用圆柱壳体的二阶谐波共振响应问题。首先给出了电磁场环境中导电圆柱壳体的非线性磁弹性振动方程和电磁场方程,并应用伽辽金积分法导出了相应的无量纲化非线性振动微分方程。然后采用多尺度法对系统的二阶超谐波和亚谐波共振问题进行求解,得到了稳态运动下关于定常解的幅值响应方程及解的稳定性判别式。最后通过数值算例,给出了共振幅值随磁感应强度和外激励力等参量变化的特征曲线图,分析了解的稳定性、奇点性态及分岔特性。结果表明,通过电磁或机械参数的适当选取,能够达到激发或抑制系统共振现象的目的。     

拟压缩性方法数值模拟绕弹体的不可压缩层流脱体涡流动

本文应用在连续生方程中增加压力对时间导数项的拟压缩性方法，数值求解三维定常不可压缩Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程。数值求解过程采用隐式的Ｂｅａｍ－Ｗａｒｍｉｎｇ近似因式分解格式。计算绕尖头旋成柱体的大迎角脱体涡流动，得到与实验相符的结果。     

北斗二号伪距偏差特性分析及其对定位的影响

伪距偏差是指因卫星下行导航信号非理想状态,导致不同技术状态的终端在接收同一卫星导航信号时产生不同的测距偏差,而现有伪距改正手段尚未考虑该偏差,甚至在双频定位时还会被进一步放大.基于Curtin GNSS研究中心设置的零基线接收机,使用接收机零基线差分解算多组观测终端下北斗二号卫星的伪距偏差,分析其特性,并采用标准单点定...