扩展卡尔曼滤波和不敏卡尔曼滤波在实时雷达回波反演大气波导中的应用

为了改善雷达回波反演大气波导(RFC)方面存在的单时次、单方位角反演的问题,提出利用扩展卡尔曼滤波和不敏卡尔曼滤波的反演算法对大气波导结构的多方位角实时跟踪反演. 在卡尔曼滤波方法中分别给出大气波导结构的参数化方程、观测方程、滤波算法的状态转移方程,最后导出滤波反演算法的迭代求解流程. 在大气波导结构不随时间变化和随时间变化的两种条件下,对扩展卡尔曼滤波和不敏卡尔曼滤波算法进行数值实验. 实验结果表明,不敏卡尔曼滤波更适用于RFC这高度非线性反演问题,它可能今后为大气波导结构多方位角实时跟踪反演的业务化运行提供理论基础与技术保证. 关键词： 大气波导 雷达回波 扩展卡尔曼滤波 不敏卡尔曼滤波     

一种车载组合导航系统的联邦滤波新算法

针对车载GPS/DR组合导航系统的特点,提出了一种新的联邦滤波算法.子滤波器由两个滤波器构成:一个是卡尔曼滤波器,另一个是Unscented卡尔曼滤波器(UKF),它们分别处理GPS子系统和DR子系统的信息.UKF是一种较新的非线性滤波方法,相对传统的非线性滤波器EKF具有更高的滤波精度和更高的计算效率.联邦滤波器的信息分配因子采用一种基于观测误差的最小均方误差形式,最佳地融合了传感器的输出信息.这种结构降低了联邦滤波器的计算难度和计算量,提高了组合导航系统的可靠性和容错性.仿真结果表明,提出算法的定位精度很高,与UKF算法的效果相当.     

UKF方法在陆地车辆组合导航中的应用

Unscented卡尔曼滤波(UKF)是一种新的非线性滤波算法,将其引入到GPS/DR系统的滤波中,并针对系统模型的特点对原UKF算法进行了简化,建立了新的滤波方法。仿真结果表明,同EKF相比,UKF的滤波精度和稳定性都显著提高了,还可避免计算烦琐的Jacobi矩阵,真正实现了低成本、高精度的导航定位要求。     

基于自适应UKF算法的MEMS陀螺空中在线标定技术

为保证微型卫星定位应用中系统精度与稳定性,需要对姿态传感器进行实时在线标定.在无外界姿态参考时,提出一种用三轴磁强计测量值来实时估计MEMs陀螺的零漂误差的方法,采用UKF滤波算法,将陀螺漂移作为滤波状态向量,通过建立三轴磁强计测量微分方程,作为系统量测方程实现陀螺漂移的最优估计.针对磁强计测量信息易受干扰导致滤波量测模型不准确的问题,将自适应因子引入到UKF中,通过在线监控和调整测量误差,减少陀螺标定的估计误差,增强系统性能.实验结果表明,经过标定,MEMS陀螺精度提高约30%,并且在磁强计有外界干扰时,陀螺的标定结果收敛.将标定后的MEMS陀螺进行姿态解算,其动态误差小于2°.     

基于对偶四元数的双星编队相对位姿测量

为了描述编队卫星中主从星的相对位置和姿态信息,提出了基于对偶四元数的编队卫星相对位姿测量算法。以双星编队飞行的位姿运动为主线,运用对偶四元数工具,充分发挥其能以最简洁的形式表示一般性刚体运动的优点,对卫星轨道和姿态进行分析并建立了对偶四元数位姿模型。同时设计类GPS测量技术来测量编队卫星的相对位置和姿态,该技术载波相位波长和伪码码元比GPS的更短,可获得更高精度的相对测量信号。由于状态方程和观测方程的非线性特征,使用UKF滤波来消除随机噪声对量测过程的干扰。实验结果表明,所设计的算法能够有效估计系统误差,卫星的位置误差和四元数误差收敛于零,验证了该算法的有效性。     

Electromagnetic form factors of nucleons in a relativistic square-root potential model of independent quarks

The nucleon electromagnetic form factorsG _E ^P (q²),G _M ^P (q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV _q(r)=1/2(1+γ ⁰)(ar ^1/2+ν ₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG _E ^P (q²) and G _A (q²) come out as [〈r ²〉 _E ^P ]^1/2=0.86 fm and 〈r _A ² 〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG _πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg _πNN(q²)=12.81 as compared tog _πNN(q²)_exp⋍13.     

Dial-Up Internet Access: A Two-Provider Cost Model

We present a cost model for splitting Internet dial-up traffic (which varies by time-of-day) between two large modem banks. One of the modem banks charges by the hour, the other charges for the peak number-in-system during the day. To study if the possible savings are enough to make the effort worthwhile, we formulate a clairvoyant (“perfect information”) Integer Program that is equivalent to a network flow problem. This leads us to use a ceiling policy. In the stochastic control case, we use a Modified Offered Load (MOL) approximation to explore the properties of the system, and develop a square-root-type rule to set the ceiling in the homogeneous case. We also use simulation to determine an optimal ceiling when we cannot route individual calls precisely. We propose approximations that may be computed for any call duration distribution, and compare their answers to exact differential-equation procedures for Exponential call durations. AMS subject classification: 60K25, 90B18, 68M20, 90B22, 60K30     

Bonds and Options in Exponentially Affine Bond Models

Abstract

In this article we apply the Flesaker–Hughston approach to invert the yield curve and to price various options by letting the randomness in the economy be driven by a process closely related to the short rate, called the abstract short rate. This process is a pure deterministic translation of the short rate itself, and we use the deterministic shift to calibrate the models to the initial yield curve. We show that we can solve for the shift needed in closed form by transforming the problem to a new probability measure. Furthermore, when the abstract short rate follows a Cox–Ingersoll–Ross (CIR) process we compute bond option and swaption prices in closed form. We also propose a short-rate specification under the risk-neutral measure that allows the yield curve to be inverted and is consistent with the CIR dynamics for the abstract short rate, thus giving rise to closed form bond option and swaption prices.     

基于改进无迹卡尔曼滤波器算法的滞回模型参数识别研究

地震产生的周期荷载作用下,钢混桥墩结构表现出滞回行为。为描述滞回行为,研究者提出各类滞回模型,其中BWBN(Bouc-Wen-Baber-Noori)模型可以描述结构滞回行为的强度退化、刚度退化和捏拢效应等典型特征。此外,无迹卡尔曼滤波器UKF(unscented Kalman filter)算法是识别BWBN模型参数的高效方法,但当参数初始值与真实值的偏差过大及缺乏对系统的整体估计时,UKF算法识别过程受到局限。本文改进生成样本点规则,提出改进UKF算法。数值模拟结果表明,在无噪声条件下,改进UKF算法识别得到的参数估计值与准确值的误差平均为1.51%,最大误差为4%;在2%均方根RMS(root mean square)高斯白噪声条件下,误差平均为5.43%,最大误差为18%;在5%RMS高斯白噪声条件下,误差平均为8.9%,最大误差为26%和22%。改进UKF算法识别非线性滞回系统状态估计和BWBN模型参数更加准确和稳定。     

简化超球体SRUKF的GPS/MIMU组合姿态估计

针对加速度计、磁强计易受机动加速度和周围环境影响的问题,提出了一种单基线GPS/MIMU组合姿态估计方法。该方法利用单基线GPS天线代替磁强计提供航向信息,并利用GPS的速度信息对加速度计输出的机动加速度分量进行补偿,构成单基线GPS/MIMU组合姿态确定单元。同时考虑实时性要求,在SRUKF的基础上,引入加性非扩展形式和超球体单形采样,提出了简化超球体平方根UKF算法,通过减少状态维数和采样点的数量,降低算法计算量。建立加性噪声下的单基线GPS/MIMU姿态模型,并采用简化超球体平方根UKF算法进行姿态估计。实验结果表明,单基线GPS的速度信息可以有效提高加速度计对水平倾角的确定精度,姿态估计算法收敛后的最大误差小于0.8°,估计精度与UKF相当,且执行时间仅是UKF的42%。