量测噪声自动加权Kalman滤波

从Kalman滤波技术的稳定性出发,分析了Kalman滤波算法的实质及容量发散的原因。提出在Kalman滤波中引入了系统量测噪声协方差阵（R）的计算,并对其加权,从而影响滤波增益,抑制发散。推算舰位／GPS组合导航的应用仿真表明：量测噪声自动加权Kalman滤波算法对系统模型误差和量测噪声协方差误差具有良好的自适应性。     

基于模糊卡尔曼滤波量测噪声自适应校正的方法研究

针对噪声的统计特性与实际不符时滤波器发散的现象，提出了一种适用于导航、制导以及其它控制系统的模糊自适应卡尔曼滤波器。基于模糊规则自适应改变测量噪声方差R，实现滤波器参数的在线改进，以缩小实际的滤波误差，提高滤波精度。     

衰减记忆平方根UPF算法及其在组合导航中的应用

针对用UPF算法进行导航滤波计算可能出现协方差矩阵不对称或负定的问题,在研究衰减记忆滤波和平方根滤波的基础上,以Unscented粒子滤波为框架,提出一种新的衰减记忆平方根UPF算法。该算法利用衰减因子减小历史信息对滤波的影响,增强当前量测信息在滤波计算中的作用。然后,以协方差矩阵的平方根阵代替协方差矩阵进行滤波解算,保证了协方差矩阵的对称性和非负定性,提高了滤波算法数值稳定性和解算精度。将提出的算法应用到SINS/SAR组合导航系统中进行仿真验证,并与UPF算法进行比较,结果表明,提出算法的滤波性能明显优于UPF算法,能提高组合导航系统的滤波精度。     

具有乘性噪声和随机量测时滞的目标跟踪算法

针对在机动目标跟踪过程中产生的乘性量测噪声与随机量测时滞问题,提出了一种改进的高斯滤波(GF)算法,并给出了该算法的一种具体实现形式——随机时滞和乘性噪声容积卡尔曼滤波器(CKF-RDMN)。首先,利用一组满足伯努利分布的随机序列描述随机出现的量测时滞现象。其次,利用乘性噪声满足高斯条件分布的特性,改进量测更新过程。最后依据三阶球径容积法则,对高斯积分进行求解。由于该算法是对经典GF算法的改进,因此,也可作为通用的滤波框架解决上述问题。通过与推广无迹卡尔曼滤波和推广扩展卡尔曼滤波对比,仿真结果表明,CKF-RDMN在解决乘性量测噪声与随机量测时滞问题时,具有更高的估计精度。     

基于指数渐消遗忘因子的组合导航自适应滤波算法

量测信息异常导致的噪声统计特性变化容易引起组合导航滤波精度下降甚至发散.针对Sage-Husa自适应滤波算法估计系统量测噪声参数性能对遗忘因子依赖性强的问题,提出了基于指数渐消遗忘因子的自适应滤波算法.在对故障检测函数判断量测噪声统计特性研究的基础上,构建了基于指数函数的动态遗忘因子模型,提升量测信息异常情况下的导航精...     

一种新的自适应UKF算法及其在组合导航中的应用

为了提高组合导航系统的滤波精度,提出一种带噪声统计估计器的自适应UKF滤波算法。该算法根据协方差匹配原理,利用UKF滤波算法的残差序列与新息序列,在线估计、调整系统过程噪声和量测噪声的统计特性,提高UKF的自适应能力,克服了标准UKF在系统噪声统计未知或不准确情况下滤波精度下降甚至发散的问题。将提出的算法应用于SINS/BDS组合导航系统进行仿真验证,并与标准UKF和抗差UKF进行比较,结果表明,提出的自适应UKF得到的水平位置误差和天向误差分别在[?6.2 m,?6.4 m]与[?9.8 m,?8.6 m]以内,滤波性能明显优于标准UKF与抗差UKF,提高了组合导航系统的解算精度。     

基于渐消记忆滤波的1点RANSAC单目视觉姿态估计算法

针对1点RANSAC(Random Sample Consensus)单目视觉EKF(Extended Kalman Filter)算法中的滤波发散问题,分析了滤波发散的产生原因,提出了一种基于渐消记忆滤波的1点RANSAC单目视觉姿态估计算法。该算法通过在EKF滤波方程中引入加权因子,逐渐加大当前数据的权重,相应地减少旧数据的权重,有效地扼制了算法中的滤波发散问题。最后通过两组验证性实验验证说明了算法的有效性。实验结果表明:该算法能够有效地解决1点RANSAC单目视觉EKF算法中的滤波发散问题,具有更高的精度。第一组双轴联动实验,航向角的平均误差减小2.4158?,俯仰角平均误差减小0.1782?;第二组偏航轴大角度转动实验,摄像机航向角的估计误差一直保持在1.5?以内。     

导航系统白噪声误差特性的在线统计估计

本文提出了一种无需参考系统，对3个以上导航系统同时进行白噪声误差特性在线统计估计的方法，并进行了仿真实验和实航数据分析。     

一种基于Gauss von Mises分布模型的非线性量测更新方法

基于状态空间模型的许多传统滤波算法都基于Rn空间中的高斯分布模型,但当状态向量中包含角变量或方向变量时,难以达到理想的效果。针对J.T.Horwood等提出的nS?R流形上的Gauss Von Mises(GVM)多变量概率密度分布,扩展了狄拉克混合逼近方法,给出了联合分布的GVM逼近方法,推导了后验分布的GVM参数计算公式,设计了量测更新状态估计算法。将J.T.Horwood等的时间更新算法与所提出的量测更新算法相结合,可实现基于GVM分布的递推贝叶斯滤波器(GVMF)。仿真结果表明,当状态向量符合GVM概率分布模型时,GVMF对角变量的估计明显优于传统的扩展卡尔曼滤波器。     

一类广义连续-离散系统量测丢失情况下鲁棒滤波算法

有噪声的非线性广义连续-离散系统的状态估计问题是目前一个较新的研究领域。量测丢失可能会导致系统动态模型的状态估计值与动态方程真实值产生较大偏差。为解决该问题,针对一类量测丢失情况下的范数有界非线性广义连续-离散系统,提出一种基于鲁棒扩展卡尔曼滤波(REKF)算法的状态估计方法。首先,给出参数并使用欧拉离散化方法将理想化的广义连续-离散系统转化为非奇异离散系统,但这样的处理方式导致转换得到的非奇异离散系统动态模型中存在新增不确定项。针对该问题,提出最优上界以保证卡尔曼滤波误差协方差矩阵收敛。其次,针对转化得到的非奇异离散系统,提出基于该优化上界的扩展卡尔曼滤波方法,用于在量测丢失时对系统的动态模型量进行观测。最后,仿真算例验证了该方法的有效性。     

Sequential non-linear least-square estimation for damage identification of structures

An early detection of structural damage is an important goal of any structural health monitoring system. In particular, the ability to detect damages on-line, based on vibration data measured from sensors, will ensure the reliability and safety of the structures. In this connection, innovative data analysis techniques for the on-line damage detection of structures have received considerable attentions recently, although the problem is quite challenging. In this paper, we proposed a new data analysis method, referred to as the sequential non-linear least-square (SNLSE) approach, for the on-line identification of structural parameters. This new approach has significant advantages over the extended Kalman filter (EKF) approach in terms of the stability and convergence of the solution as well as the computational efforts involved. Further, an adaptive tracking technique recently proposed has been implemented in the proposed SNLSE to identify the time-varying system parameters of the structure. The accuracy and effectiveness of the proposed approach have been demonstrated using the Phase I ASCE structural health monitoring benchmark building, a non-linear elastic structure and non-linear hysteretic structures. Simulation results indicate that the proposed approach is capable of tracking on-line the changes of structural parameters leading to the identification of structural damages.     

Nodeless variable finite element method for heat transfer analysis by means of flux-based formulation and mesh adaptation

Based on flux-based formulation, a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes. The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior. The technique generates small elements in the regions of steep solution gradients to provide accurate solution, and meanwhile it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory. The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions. These problems are: (a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating, and (b) a transient heat conduction analysis in a long plate subjected to a moving heat source. The English text was polished by Yunming Chen.     

An efficient method for computing local quantities of interest in elasticity based on finite element error estimation

We present an efficient finite element method for computing the engineering quantities of interest that are linear functionals of displacement in elasticity based on a posteriori error estimate. The accuracy of quantities is greatly improved by adding the approximate cross inner product of errors in the primal and dual problems, which is calculated with an inexpensive gradient recovery type error estimate, to the quantities obtained from the finite element solution. With less CPU time, the accuracy of the improved quantities obtained with the proposed method on the coarse finite element mesh is similar to that of the quantities obtained from the finite element solutions on the finer mesh. Three quantities related to the local displacement, local stress and stress intensity factor are computed with the proposed method to verify its efficiency.     

一种小型无人倾转旋翼机全包线飞行的参数估计方法(英文)

小型无人倾转旋翼机的核心是飞行控制系统与捷联惯性导航系统(SINS)。针对小型无人倾转旋翼机的不同飞行模式设计了一套线性、计算效率高的捷联导航算法,为控制系统提供真实可靠的反馈参数。在直升机悬停与小速度飞行模式,利用加速度计与磁强计的输出计算测量姿态角并根据角度与角速率的关系设计低阶线性姿态估计算法,递推解算出MEMS陀螺的漂移特性,并实时补偿测量的角速率。在倾转与飞机飞行模式飞行器具有持续加速与高速的飞行特性,利用磁强计解算当前航向并引入GPS的速度与位置参数,设计了基于误差的线性Kalman滤波器,提高持续加速飞行状态的姿态估计精度。数值仿真表明在全包线飞行过程中设计的捷联导航算法具有良好的测量精度,并利用小型无人倾转旋翼机的飞行试验,验证了算法的估计性能与可靠性。     

抗差自适应滤波的导向钻具动态姿态测量方法

针对钻井工程中,导向钻井工具在近钻头振动条件下,由于底部钻具振动对导向工具姿态测量造成严重干扰,使得姿态参数失真,导致姿态测量不准确的问题。为了消除或削弱振动对空间姿态测量的不利影响,快速解算出准确的钻具姿态参数,提出一种抗差自适应滤波的动态姿态测量方法,利用等价权函数和自适应因子合理的分配信息,有效地滤除钻具振动对动态姿态测量的影响。仿真实验和实钻井数据试验证明,采用该算法能滤除近钻头振动干扰信号,井斜角控制在5.5°左右,工具面角测量误差小于6°,有效地提高了导向钻井工具姿态参数的动态测量精度,解决动态测量时姿态参数测不准的问题。     

Sequential non-linear least-square estimation for damage identification of structures with unknown inputs and unknown outputs

The detection of structural damages real-time on-line, based on vibration data measured from sensors, is an important but challenging research topic, and it has received considerable attentions recently. Due to practical limitations, it is highly desirable to install as few sensors as possible in the structural health monitoring system, leading to incomplete measurements of structural responses and excitations. The traditional time-domain analysis techniques, such as the least-square estimation (LSE) method and the extended Kalman filter (EKF) approach, require that all the external excitations (inputs) be available, which may not be the case for most structural health monitoring systems. Recently, the adaptive sequential non-linear least-square estimate (SNLSE) method has been proposed for the on-line identification of structural damages. In this paper, we extend the SNLSE method to cover the general case with unknown (unmeasured) excitations (inputs) and unknown (unmeasured) acceleration responses (outputs) in order to reduce the number of sensors required in the structural health monitoring system, referred to as the SNLSE-UI-UO. Analytic recursive solutions for the new approach are derived and presented. The accuracy and effectiveness of the proposed approach have been demonstrated using the Phase I ASCE structural health monitoring benchmark building, a 5-degree-of-freedom non-linear hysteretic building model, and a 3-story steel frame finite-element model. Simulation results indicate that the proposed approach is capable of tracking the changes of structural parameters leading to the identification of damages.     

Improvement of parameter estimation for non-linear hysteretic systems with slip by a fast Bayesian bootstrap filter

Modeling and identification of non-linear hysteretic systems are widely encountered in the structural dynamics field, especially for the hysteresis with slip. A model, called SL model, which can describe the pinching of most practical hysteresis loops perfectly was proposed by Baber and Noori (J. Eng. Mech. 111 (1985) 1010). A method of estimating the parameters of SL model on the basis of input-output data based on bootstrap filter was proposed by the writers. Bootstrap filter is a filtering method based on Bayesian state estimation and Monte Carlo method, which has the great advantage of being able to handle any functional non-linearity and system and/or measurement noise of any distribution. The standard bootstrap filter, however, is not time efficient, i.e., it is very time consuming and is not suitable for real-time applications. In this paper, previous work by the writers is extended to do the parameter estimation of SL model by a fast Bayesian bootstrap filtering technique. Simulation results are presented to demonstrate the performance of the algorithm.     

水下滑翔器位姿估计的改进高斯混合粒子滤波器设计与验证（英文）

近年用于水下滑翔器的低成本导航系统成为研究热点,导航器件的成本与精度之间的折中问题仍然是目前的难题。针对因使用低成本的导航元件而造成低精度位姿估计的问题,提出用于位姿估计的改进高斯混合粒子滤波(IGMPF)方法。用高斯混合模型来估计非高斯噪声,改进的粒子滤波进一步提高位姿估计精度。为了验证其效果,该方法应用于自主设计的水下滑翔器导航系统中并做了车载实验,实验结果表明所提IGMPF方法在实际应用中比传统的EKF和UKF表现更优,姿态角和位移误差比EKF和UKF减小了至少30%。     

Adaptive finite elements for the steady free fall of a body in a Newtonian fluid

The numerical simulation of the free fall of a solid body in a viscous fluid is a challenging task since it requires computational domains which usually need to be several order of magnitude larger than the solid body in order to avoid the influence of artificial boundaries. Toward an optimal mesh design in that context, we propose a method based on the weighted a posteriori error estimation of the finite element approximation of the fluid/body motion. A key ingredient for the proposed approach is the reformulation of the conservation and kinetic equations in the solid frame as well as the implicit treatment of the hydrodynamic forces and torque acting on the solid body in the weak formulation. Information given by the solution of an adequate dual problem allows one to control the discretization error of given functionals. The analysis encompasses the control of the free fall velocity, the orientation of the body, the hydrodynamic force and torque on the body. Numerical experiments for the two dimensional sedimentation problem validate the method. To cite this article: V. Heuveline, C. R. Mecanique 333 (2005).