Measuring Rotational Motion with Linear Accelerometers

Inertial navigation systems usually use gyroscopes to sense angular motion and use accelerometers to sense linear acceleration. It is feasible, however, using only linear accelerometers as sensors, to determine both the angular velocity and the linear acceleration of a vehicle. This paper presents and compares five configurations of linear accelerometers which may be used to determine both the angular motion and the linear motion of a vehicle.     

Interlaced Kalman filtering of 3D angular motion based on Euler'snonlinear equations

A novel Kalman filtering technique is presented that reduces the mean-square-error (MSE) between three-dimensional (3D) actual angular velocity values and estimated ones by an order of magnitude (when compared with the MSE resulting from direct measurements) even under extremely low signal-to-noise ratio conditions. The filtering problem is nonlinear in nature because the dynamics of 3D angular motion are described by Euler's equations. This nonlinear set of differential equations state that the angular acceleration in one axis is proportional to the torque applied to that axis, and to the products of angular velocity components in the other two axes of rotation. Instead of using extended Kalman filtering techniques to solve this complex problem, the authors developed a new approach where the nonlinear Euler's model is decomposed into two pseudolinear models (primary and secondary). The first model describes the time progression of the state vector containing the linear terms, while the other characterizes the propagation of the state vector containing the nonlinearities. This makes it possible to run two interlaced discrete-linear Kalman filters simultaneously. One filter estimates the values of the state vector containing the linear terms, while the other estimates the values of the state vector containing the nonlinear terms in the system. These estimates are then recombined, solving the nonlinear estimation process without linearizing the system. Thus, the new approach takes advantage of the simplicity, computational efficiency and higher convergence speed of the linear Kalman filter form and it overcomes many of the drawbacks typical of conventional extended Kalman filtering techniques. The high performance and effectiveness of this method is demonstrated through a computer simulation case study     

Extension of Euler's theorem to n-dimensional spaces

Euler's theorem states that any sequence of finite rotations of a rigid body can be described as a single rotation of the body about a fixed axis in three-dimensional Euclidean space. The usual statement of the theorem in the literature cannot be extended to Euclidean spaces of other dimensions. Equivalent formulations of the theorem are given and proved in a way which does not limit them to the three-dimensional Euclidean space. Thus, the equivalent theorems hold in other dimensions. The proof of one formulation presents an algorithm which shows how to compute an angular-difference matrix that represents a single rotation which is equivalent to the sequence of rotations that have generated the final n-D orientation. This algorithm results also in a constant angular velocity which, when applied to the initial orientation, eventually yields the final orientation regardless of what angular velocity generated the latter. The extension of the theorem is demonstrated in a four-dimensional numerical example. The issue of the correct n-D representation of angular velocity is discussed     

无陀螺捷联惯导系统捷联方案研究

提出了无陀螺捷联惯导系统的惯性测量单元沿单轴相对载体旋转的捷联方案,对该方案进行了理论分析和数值仿真。结果表明,合理安装９ 个加速度计并适当选取捷联矩阵,则捷联方案无需高精度测量惯性测量单元相对载体旋转角速度也能大大提高载体角速度的精度。为满足相同的导航精度要求,本方案可降低对加速度计精度的要求约１０００ 倍。     

无陀螺惯性测量组合设计及角速度误差补偿方法研究

提出了九加速度计无陀螺惯性测量组合(NGIMU)配置方案,并建立了其实验系统.由于加速度计输出误差的存在,必然引起角速度计算误差随时间累积.针对该项误差,采用一种提高角速度解算精度的新方法,该方法利用角速度乘积项可有效对误差进行补偿.另外在分析加速度计安装位置存在误差的基础上,提出了对加速度计输出具有补偿效应的解算方法,间接提高了角速度的解算精度.最后对上述两种补偿方法进行了角速度仿真和角度测试实验.实验结果证明了方案的可行性和有效性.     

关于刚体转动的角速度和角加速度的讨论

在理论力学教学中，平面运动刚体的转动与基点无关的证明过于简单，本利用矢量代数的知识，证明平面运动刚体的角度与角加速度与基点的选择无关。     

Angular velocity determination of spinning solar sails using only a sun sensor

The direction of the sun is the easiest and most reliable observation vector for a solar sail running in deep space exploration. This paper presents a new method using only raw measurements of the sun direction vector to estimate angular velocity for a spinning solar sail. In cases with a con-stant spin angular velocity, the estimation equation is formed based on the kinematic model for the apparent motion of the sun direction vector;the least-squares solution is then easily calculated. A performance criterion is defined and used to analyze estimation accuracy. In cases with a variable spin angular velocity, the estimation equation is developed based on the kinematic model for the apparent motion of the sun direction vector and the attitude dynamics equation. Simulation results show that the proposed method can quickly yield high-precision angular velocity estimates that are insensitive to certain measurement noises and modeling errors.     

Nonlinear Estimation Via Kalman Filtering

The extended Kalman-Bucy filtering algorithm is applied to the problem of estimating the system parameters of a single-channel missile attitude control system. In particular, noisy observations of body angular rate, normal acceleration, and control surface deflec tion are used in the algorithm to obtain estimates of body angular rate, angle of attack, control surface deflection, air density, and missile velocity. Computational results obtained for this problem are presented. These results are evaluated to determine the applicapility of this estimator as a part of an adaptive control scheme. In addition, a general approach to the formulation of practical nonlinear estimation problems is suggested.     

Coordinated target localization base on pseudo measurement for clustered space robot

This paper presents a coordinated target localization method for clustered space robot.According to the different measuring capabilities of cluster members,the master-slave coordinated relative navigation strategy for target localization with respect to slavery space robots is proposed;then the basic mathematical models,including coordinated relative measurement model and cluster centralized dynamics,are established respectively.By employing the linear Kalman flter theorem,the centralized estimator based on truth measurements is developed and analyzed frstly,and with an intention to inhabit the initial uncertainties related to target localization,the globally stabilized estimator is designed through introduction of pseudo measurements.Furthermore,the observability and controllability of stochastic system are also analyzed to qualitatively evaluate the convergence performance of pseudo measurement estimator.Finally,on-orbit target approaching scenario is simulated by using semi-physical simulation system,which is used to verify the convergence performance of proposed estimator.During the simulation,both the known and unknown maneuvering acceleration cases are considered to demonstrate the robustness of coordinated localization strategy.     

Tracking for maneuvering target trajectories via the 3D circular filter

A circular prediction algorithm is proposed, which integrates the measured data into the filter and constrains the prediction to lie on a smooth curve modeled by an arc of a circle. The circular prediction is entirely defined in relation to three measurements in three-dimensional space. It is therefore not necessary to calculate the center and the radius of the circle. To obtain the statistics of the circular prediction, the unscented transformation has been utilized. The proposed hybrid filter combines the circular prediction and a constant velocity prediction by utilizing the covariance intersection (CI). This combined prediction can be updated with the subsequent measurement using a linear estimator. The proposed technique is compared with standard filters and the interacting multiple model (IMM) approach on a benchmark trajectory which includes coordinated turns and straight line maneuvers.     

On-line Vehicle Motion Estimation from Visual Terrain Information Part II: Ground Velocity and Position Estimation

An algorithm, combining velocity/height estimates, obtained from an airborne body fixed image shift estimator with auxiliary on-board measurements and sparsely stored terrain profile information constitutes an entirely passive autonomous navigation system suitable for moderate-g flight missions. Two versions are addressed. The "naive estimator," in which altitude estimates are multiplied by velocity/height estimaters, yields ground velocity. Position, obtained by integration, diverges with time. The "extended Kalman filter" (EKF) version, in which velocity and position are defined as state space components, locks on the stored terrain profile and does not diverge with time. It degenerates into the "naive estimator" if the terrain is completely flat. Numerical examples indicate excellent performance potential of the EKF estimator.     

A modified forward and backward reaching inverse kinematics based incremental control for space manipulators

Forward and backward reaching inverse kinematics(FABRIK) is an efficient two-stage iterative solver for inverse kinematics of spherical-joint manipulator without the calculation of Jacobian matrix. Based on FABRIK, this paper presents an incremental control scheme for a free-floating space manipulator consists of revolute joints and rigid links with the consideration of joint constraints and dynamic coupling effect. Due to the characteristics of FABRIK, it can induce large angular movements on s...     

On state estimation for an orbiting single tether system

The effects of instrumentation accuracy and configuration on estimation error are studied for the small expandable-tether deployment system (SEDS) using a continuous-discrete extended Kalman filter (CDEKF) state estimator. A twelfth order model that incorporates the rigid body modes of the tether as well as the satellite attitude dynamics is developed. Simulation results using the model and the estimator indicate that the originally planned instrumentation package could not estimate the state vector adequately. Recommendations are made and results presented that reduce the estimation error by adding instruments and increasing selected measurement accuracies     

航天器有限时间输出反馈姿态控制

研究在角速度不可测时航天器的有限时间姿态控制问题。基于有限时间控制技术,提出了由修正Rodrigues参数进行姿态描述的航天器输出反馈姿态控制算法。首先设计了单个航天器的输出反馈姿态控制器,在没有角速度反馈时也能够保证航天器姿态在有限时间内调节到期望姿态。之后,设计了无需绝对角速度和相对角速度信息的多航天器分布式输出反馈姿态控制器。使用Lyapunov理论和图论,对闭环系统全局有限时间稳定性进行了严格的证明。最后对提出的控制算法进行了数值仿真,其结果验证了所设计的航天器输出反馈控制算法的可行性和有效性。     

标量图像测速原理及数值检验

标量图像测速是一种新型的能够测量微小结构的湍流实验测量系统,其理论依据是Schmidt（Sc）数〉1的标量湍流里,标量场脉动的时间尺度和空间耗散尺度要小于对应的速度场脉动的时间尺度和空间耗散尺度,标量脉动比速度脉动具有更强的间歇性,标量场所含信息大于速度场所含信息,从高＆数标量场提取速度场是可能的。笔者详细介绍了标量图像测速原理,并在积分最小化法思想指导下根据标量输运守恒方程及限定条件,建立了积分最小化标量图像测速的数学表示。通过变分法,获得了积分空间每个点的三个速度分量的欧拉特征方程,对欧拉特征方程离散化即可在积分空间建立一线性稀疏方程组。采用变分迭代法对此线性稀疏方程组进行求解即可获得三维速度场,据此采用积分最小化法建立了标量图像测速图像处理系统。还介绍了四维标量场（三维空间加一维时间）的图像采集原理,并采用DNS数据对标量图像测速处理系统进行了数值检验,检验结果表明标量图像测速技术所求解的速度场和DNS精确解之间在结构上是十分相似的,标量图像测速可以正确地提取速度场。     

航空发动机状态变量模型的QPSO寻优混合求解法

针对航空发动机控制和故障诊断中的状态变量模型求解存在的系数矩阵精度不高的问题,结合阶跃响应法和拟合法的基础上,提出了一种基于量子粒子群寻优（QPSO）求取发动机状态变量模型的混合求解法。QPSO优化算法求解A,C矩阵使得状态变量模型和非线性模型在动态过程具有较好的吻合,阶跃响应法求取B,D矩阵保证了模型稳态响应一致。利用混合求解法建立了某型涡轴发动机在某一稳态工作点下的小偏离状态变量模型。仿真结果表明,这种方法不仅增强了状态变量模型的求解精度,相对于单纯的拟合法缩短了求解时间,精确的状态变量模型为进一步的故障诊断和控制系统设计提供了条件。     

Discrete-time min-max tracking

The problem of optimal state estimation of linear discrete-time systems with measured outputs that are corrupted by additive white noise is addressed. Such estimation is often encountered in problems of target tracking where the target dynamics is driven by finite energy signals, whereas the measurement noise is approximated by white noise. The relevant cost function for such tracking problems is the expected value of the standard H/sub /spl infin// performance index, with respect to the measurement noise statistics. The estimator, serving as a tracking filter, tries to minimize the mean-square estimation error, and the exogenous disturbance, which may represent the target maneuvers, tries to maximize this error while being penalized for its energy. The solution, which is obtained by completing the cost function to squares, is shown to satisfy also the matrix version of the maximum principle. The solution is derived in terms of two coupled Riccati difference equations from which the filter gains are derived. In the case where an infinite penalty is imposed on the energy of the exogenous disturbance, the celebrated discrete-time Kalman filter is recovered. A local iterations scheme which is based on linear matrix inequalities is proposed to solve these equations. An illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the target position.     

大圆航行轨迹发生器的设计

轨迹发生器广泛应用于惯性导航与组合导航仿真研究之中,它不仅提供实时角速率和比力值,而且还用来直观检验惯性导航或组合导航算法的正确性、优劣性和误差大小.本文基于惯性导航的基本方程,设计了用于捷联惯导的大圆航行轨迹发生器.针对误差公式推导复杂的特点,用导航仿真的方法对其输出的角速率和比力进行了精度估计,验证了设计的正确性.     

Adaptive sliding mode control for limit protection of aircraft engines

In practice, some sensors of aircraft engines naturally fail to obtain an acceptable measurement for control propose, which will severely degrade the system performance and even deactivate the limit protection function. This paper proposes an adaptive strategy for the limit protection task under unreliable measurement. With the help of a nominal system, an online estimator with gradient adaption law and low-pass filter is devised to evaluate output uncertainty. Based on the estimation result, a sliding mode controller is designed by defining a sliding surface and deriving a control law. Using Lyapunov theorem, the stability of the online estimator and the closed-loop system is detailedly proven. Simulations based on a reliable turbofan model are presented, which verify the stability and effectiveness of the proposed method. Simulation results show that the online estimator can operate against the measurement noise, and the sliding controller can keep relevant outputs within their limits despite slow-response sensors.     

Dynamic simulation of aerial towed decoy system based on tension recurrence algorithm

Dynamic model of aerial towed decoy system is established and simulations are performed to research the dynamic characteristics of the system. Firstly, Kinetic equations based on spinor are built, where the cable is discretized into a number of rigid segments while the decoy is modeled as a rigid body hinged on the cable. Then tension recurrence algorithm is developed to improve computational efficiency, which makes it possible to predict the dynamic response of aerial towed decoy system rapidly and accurately. Subsequently, the efficiency and validity of this algorithm are verified by comparison with Kane's function and further validated by wind tunnel tests.Simulation results indicate that the distance between the towing point and the decoy's center of gravity is suggested to be 5%–20% of the length of decoy body to ensure the stability of system.In up-risen maneuver process, the value of angular velocity is recommended to be less than0.10 rad/s to protect the cable from the aircraft exhaust jet. During the turning movement of aircraft, the cable's extent of stretching outwards is proportional to the aircraft's angular velocity.Meanwhile, the decoy, aircraft and missile form a triangle, which promotes the decoy's performance.