基于Unscented Kalman滤波的飞行器天文/地磁自主导航算法研究(英文)

针对地磁场模型精度低而引起的导航精度不高及基于轨道动力学方程的天文导航算法的局限性问题,提出了一种利用天文/地磁信息为观测量的飞行器自主导航方法,并建立了动力学方程,同时推导了观测方程。算法采用星光矢量与地磁矢量的夹角为观测量,采用UKF滤波器估计飞行器的速度和位置,并进行了仿真研究。仿真结果表明,该算法的精度要远高于单纯的地磁导航,滤波的收敛性和稳定性较好,导航误差不随时间累积,有工程应用价值。     

基于MEMS传感器的姿态测量系统设计

为解决单目三维扫描装置摄像机标定完成后姿态不能改变的问题,针对单目三维扫描装置使用过程中的运动方式与特点,设计了一款基于 MEMS 传感器的姿态测量系统。采用四元数对姿态进行解算,通过三轴姿态确定(TRAID)算法构建量测模型,以无迹卡尔曼滤波(UKF)算法进行数据融合,能有效抑制姿态解算过程中陀螺仪的漂移问题。实验结果表明,利用该系统进行姿态测量时静态误差低于±0.2°,动态误差低于±1°,系统实时性好、适用于动态三维扫描系统。     

Estimation and empirical evaluation of the time-dependent Extended-CIR term structure model

Email: ym{at}onetel.net.uk Empirical study of 25 years US Treasury bills data shows thateven when the spot interest rate remains fixed, its volatilityvaries significantly over time. Constant-coefficient modelscannot capture these changes as they give rise to time-homogeneousdistributions. Maximum likelihood fitting of a one-factor time-dependentExtended-CIR model of the term structure, whose closed-formsolution was previously obtained by the author, shows that itcan capture these changes, as well as achieve significantlyhigher likelihood value. It is shown that exploitation of theclosed-form solutions substantially improves the accuracy andefficiency of Monte Carlo simulations over high-order discretizationalgorithms. It is also shown that the feasibility of exact one-to-onecalibration of the model to any continuous yield curve allowsvaluation of bond options significantly more accurately andefficiently.     

低成本MINS/GPS组合导航中卡尔曼滤波算法的综合应用研究

在基于DSP的低成本MINS/GPS组合导航系统中,针对DSP的实型变量位数不足的缺点,在卡尔曼滤波器的设计中同时运用了状态与偏差解耦算法和平方根算法,并推导出状态与偏差解耦-平方根算法的具体公式,既能减少计算量,又能增强滤波的数值稳定性。     

四轴飞行器视觉组合导航系统设计与实现

为实现四轴飞行器的自主飞行,设计了该视觉导航系统;采用基于ARM处理器的飞行控制器和导航控制器的双CPU结构,提高了系统的运行速度;飞行控制部分采用四元数解算姿态,运用经典的PID控制设计了X、Y、Z三个轴的PID控制器进行整个系统的飞行控制;导航部分采用不敏卡尔曼滤波(UKF)融合惯导位置和视觉位置,从而给出载体最优位置,提高导航精度;实验结果表明,基于图像和惯性导航的视觉组合导航方式可使导航精度保持在0.5 m内,同时整个系统具有较好的快速性和稳定性。     

非线性约束优化的光滑化平方根罚函数

介绍一种非线性约束优化的不可微平方根罚函数,为这种非光滑罚函数提出了一个新的光滑化函数和对应的罚优化问题,获得了原问题与光滑化罚优化问题目标之间的误差估计. 基于这种罚函数,提出了一个算法和收敛性证明,数值例子表明算法对解决非线性约束优化具有有效性.     

改进的CS-UKF加速度方差自适应跟踪算法

针对基于当前统计模型的状态噪声协方差阵中的加速度方差调整方法对一般机动目标、非机动目标跟踪精度差的问题,研究其改进方法;在建立机动目标当前统计模型离散状态方程和雷达导引头离散观测方程的基础上;利用雷达导引头测量信息和位置预测值之间的扰动对加速度方差进行调整,提出了改进的加速度方差自适应调整无迹卡尔曼滤波跟踪算法;数字仿真验证了该算法对非机动目标、一般机动目标以及高机动目标均具有良好的跟踪效果。     

基于平方根无迹卡尔曼滤波平滑算法的水下纯方位目标跟踪（英文）

为了避免被动跟踪中非线性带来的计算复杂化及跟踪精度的下降,提出将平方根无迹卡尔曼滤波平滑算法(SR-UKFS)应用到水下纯方位目标跟踪。SR-UKFS利用Rauch-Tung-Striebel(RTS)平滑算法将平方根无迹卡尔曼滤波(SR-UKF)作为前向滤波算法得到的目标状态估计向后平滑,得到前一时刻目标状态估计,再利用该状态估计值进行再次滤波得到当前时刻目标状态估计。该算法得到的前一时刻的目标状态估计更加精确,从而进一步提高了目标跟踪的精度。最后,通过对SR-UKFS算法和SR-UKF算法的跟踪性能进行了对比分析和验证,仿真结果表明在相同条件下,SR-UKFS算法能减少59%的位置误差和54%的速度误差,SR-UKFS算法应用于水下纯方位目标跟踪系统是有效的,为水下纯方位目标跟踪系统的工程实现提供了非常有价值的参考。     

Simplification of the Gram Matrix Eigenvalue Problem for Quadrature Amplitude Modulation Signals

In quantum information science, it is very important to solve the eigenvalue problem of the Gram matrix for quantum signals. This allows various quantities to be calculated, such as the error probability, mutual information, channel capacity, and the upper and lower bounds of the reliability function. Solving the eigenvalue problem also provides a matrix representation of quantum signals, which is useful for simulating quantum systems. In the case of symmetric signals, analytic solutions to the eigenvalue problem of the Gram matrix have been obtained, and efficient computations are possible. However, for asymmetric signals, there is no analytic solution and universal numerical algorithms that must be used, rendering the computations inefficient. Recently, we have shown that, for asymmetric signals such as amplitude-shift keying coherent-state signals, the Gram matrix eigenvalue problem can be simplified by exploiting its partial symmetry. In this paper, we clarify a method for simplifying the eigenvalue problem of the Gram matrix for quadrature amplitude modulation (QAM) signals, which are extremely important for applications in quantum communication and quantum ciphers. The results presented in this paper are applicable to ordinary QAM signals as well as modified QAM signals, which enhance the security of quantum cryptography.     

Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon

We study the asymptotic statistical behavior of the 2-dimensional periodic Lorentz gas with an infinite horizon. We consider a particle moving freely in the plane with elastic reflections from a periodic set of fixed convex scatterers. We assume that the initial position of the particle in the phase space is random with uniform distribution with respect to the Liouville measure of the periodic problem. We are interested in the asymptotic statistical behavior of the particle displacement in the plane as the timet goes to infinity. We assume that the particle horizon is infinite, which means that the length of free motion of the particle is unbounded. Then we show that under some natural assumptions on the free motion vector autocorrelation function, the limit distribution of the particle displacement in the plane is Gaussian, but the normalization factor is (t logt)^1/2 and nott ^1/2 as in the classical case. We find the covariance matrix of the limit distribution.