双层无迹卡尔曼滤波

针对无迹卡尔曼滤波（Unscented Kalman fllter,UKF）在强非线性系统中估计效果差的问题,提出了双层无迹卡尔曼滤波（Double layer unscented Kalman filter,DLUKF）算法,该算法用带权值的采样点表征先验分布,而后用内层UKF算法对每个采样点进行更新,最后引入外层UKF算法的更新机制得到估计值和估计协方差.仿真结果表明,相比于传统算法,所提的DLUKF算法可以在较低计算负载下获得较高滤波估计精度.     

基于自适应多提议分布粒子滤波的蒙特卡洛定位算法

针对基于Cubature粒子滤波的蒙特卡罗定位（CMCL）算法存在的计算量大、实时处理能力较差的问题,提出一种基于自适应多提议分布粒子滤波的蒙特卡罗定位（AMPD-MCL）算法。该算法利用Cubature卡尔曼滤波和扩展卡尔曼滤波改进提议分布,融入当前观测信息,减弱粒子退化现象;重采样部分采用Kullback-Leibler距离（KLD）采样,根据粒子在状态空间的分布状况,在线调整下一次滤波迭代所需粒子数,从而减小计算量。仿真实验验证了自适应多提议分布粒子滤波（AMPD-PF）的有效性;同时在机器人操作系统（ROS）上进行实验,结果表明改进算法的平均定位精度达到19.891cm,定位所需粒子数稳定在60,定位时间为45.543s,较CMCL算法在定位精度上提高了71.03%,时间缩短了63.10%。实验结果表明,AMPD-MCL算法减小了定位误差,能实时在线调整粒子数,有效减少了算法计算量,提高了实时处理能力。     

确定采样型强跟踪滤波飞机舵面故障诊断与隔离

为了克服扩展多模型自适应估计中扩展卡尔曼滤波的理论局限性,多重渐消因子强跟踪改进引起的滤波发散现象以及多维高斯故障概率计算量大等问题,本文将一类基于确定解析采样近似方法的非线性次优高斯滤波与多模型自适应估计相结合,提出了改进的多重渐消因子强跟踪非线性滤波快速故障诊断方法.确定采样型滤波克服了扩展卡尔曼滤波的理论局限性;推导了等效多重渐消因子计算方法,避免了非线性系统雅克比矩阵的计算,提高了故障突变时的跟踪性能;提出了基于平方根分解的改进的一步预测协方差更新方程,保证了滤波稳定性;提出了基于欧几里得范数简化的故障概率计算方法,降低了计算量.通过对比仿真验证了3种不同非线性滤波算法及其强跟踪改进算法的有效性,故障诊断方法跟踪性强、速度快、精度高,具有较好的鲁棒性和稳定性.     

转换坐标卡尔曼滤波算法分析

在非线性系统的目标跟踪中,常用的滤波算法是扩展卡尔曼滤波算法（EKFA）,但这种滤波算法常常会发散,近年来,Bar-Shalom等人在二维平面上提出了转换坐标卡尔曼滤波算法（CMKFA）,并通过仿真实验证明了在非线性系统的目标跟踪中此算法优于扩展卡尔曼滤波算法（EKFA）,文中对转换坐标卡尔曼滤波算法进行了深入的研究,通过理论推导证明了当状态方程和测量方程满足一定条件时,转换坐标卡尔曼滤波算法是去偏转换测量值的线性无偏最小方差估计算法。     

基于正交变换的改进CKF算法

为了解决容积卡尔曼滤波(CKF)算法在处理高维问题时出现的非局部采样问题,提出基于采样点正交变换的改进CKF算法(TCKF).从数值积分近似角度导出无迹卡尔曼滤波(UKF)和CKF两种近似滤波算法,并指出CKF只是UKF的一个特例;基于多元Taylor级数展开分析,揭示CKF在克服UKF数值不稳定性问题的同时,引入非局部采样问题;对Cubature点集进行正交变换得到TCKF算法,并从理论上证明,在高维、强非线性等非局部采样问题突出的滤波模型中,TCKF具有比CKF更高的估计精度.仿真实例验证了所提出算法的有效性.     

基于神经计算的GPS／SINS组合导航滤波器设计

将线性二次型最优化方法与Ｈｏｐｆｉｅｌｄ神经网络相结合，研究了一种基于神经计算的滤波算法。而且，将算法应用于全球定位系统（ＧＰＳ）与捷联惯导系统（ＳＩＮＳ）的组合导航，通过计算机仿真，与卡尔曼滤波算法结果进行了比较，说明了该滤波算法的有效性和实用性。     

基于高斯分布的多层无迹卡尔曼滤波算法

在传统无迹卡尔曼滤波(UKF) 中对其估计精度和计算效率起关键作用的是采样算法, 即构造具有权重的样本点. 研究表明, 带权样本点匹配随机变量的阶矩越高滤波的精度越高, 如多项式无迹卡尔曼滤波(PUKF), 但通常此类算法的复杂度过高甚至难以求解. 为此, 基于高斯分布结合高阶矩匹配与无迹卡尔曼滤波线性扩张方 法(LUKF), 提出一种兼顾效率和精度的高斯滤波离线算法. 实验结果表明, 所提出算法拥有比UKF 更高的估计精度和比PUKF 更好的计算效率.

     

基于改进确定性采样滤波的疲劳裂纹扩展RUL预测

针对确定性采样滤波在进行状态估计预测时随维数增加时出现计算量增加且精度不高的问题,提出一种确定性采样滤波的算法并将其应用到疲劳裂纹扩展RUL预测当中去;首先,阐述了确定性采样滤波的基本原理;其次,从多维数值积分的角度分析确定性采样滤波所需计算的数学期望,根据完全对称积分公式计算积分节点值、节点个数和权重;最后,将改进后的确定性采样滤波器应用到构件疲劳裂纹损伤扩展中去,并与无迹卡尔曼滤波算法、容积卡尔曼滤波算法进行比较,提升了裂纹扩展RUL预测的精度,实例仿真分析验证了该方法的可行性和有效性。     

井下捷联惯导系统导航数据处理滤波分析

针对现有煤矿井下定位技术误差较大、准确性不足的问题,引入了捷联惯导系统对煤矿井下人员和设备进行精确定位导航。为进一步提高捷联惯导系统的定位精度,提出了采用扩展卡尔曼滤波和采样卡尔曼滤波对系统数据进行滤波的算法,分析了扩展卡尔曼滤波和采样卡尔曼滤波的滤波原理,并对算法公式以及滤波效果进行了仿真分析。仿真结果表明,在假设井下噪声为高斯白噪声的前提下,采样卡尔曼滤波抖动性较小,曲线更为平滑,即滤波后的数据更加接近于真实数据,能够更准确地反映出坐标信息,且误差基本控制在允许的范围之内,具有较好的滤波效果。     

卡尔曼滤波器及其工程应用

卡尔曼于1960年提出了离散系统线性滤波的递推求解方法即卡尔曼滤波算法。该滤波算法是基于线性最小平方法的、进行有效递推计算的一组数学方程式,算法功能强大,支持对过去、现在和将来状态的估算。本文旨在对离散系统的卡尔曼滤波作应用方面的介绍：包括对基本离散卡尔曼滤波器的描述与讨论;对扩展型卡尔曼滤波的讨论;应用实例进行分析和仿真;讨论卡尔曼滤波在汽车定位与导航工程上的应用。     

A study of the Kalman filter as a state estimator of deterministic and stochastic systems

It is shown that the optimality of the Kalman filter prevents its application to estimate the state of deterministic; systems but that if the gain is slightly modified a deterministic filter is possible. Such a filter is subsequently used to explain some of the difficulties encountered in Kalman filter computations, from which it transpires that much Kalman filtering is essentially an application of a deterministic filter to stochastic problems. To reduce the order of the algorithm the concept of observer robustness is incorporated into the subsequent development of the deterministic filter. Exactly equivalent discrete- and continuous-time algorithms are derived and used for a new treatment of the problem of obtaining estimates of the state variables of a stochastic system when the measurements are free of noise.     

A Seventh‐Degree Cubature Kalman Filter

The fifth‐degree cubature Kalman filter (CKF) has been proved to be a kind of algorithm that has higher precision than the third‐degree CKF and unscented Kalman filter (UKF). In order to further improve the performance of CKF, the seventh‐degree CKF is proposed in this paper by expanding the spherical‐radial rule, and a new kind of deterministic sampling method is derived based on the seventh‐degree cubature rule. Through the comparison in target tracking simulation, the seventh‐degree CKF methods are shown to be able to enhance filtering precision compared to the fifth‐degree CKF, the third‐degree CKF and the UKF filter.     

一种提高无迹卡尔曼滤波精确度的方法

无迹卡尔曼滤波是通过确定性采样,以无迹变换为基础,用卡尔曼线性滤波框架而建立起来的,对非线性系统有很好的滤波效果,但当噪声的影响较大时,精确度将会减低。为解决上述问题,提出了一种提高无迹卡尔曼滤波(UKF)精确度的方法,它将观测噪声和系统噪声引入到采样点中,对噪声进行对称采样处理,同时改进了算法过程,增加了无迹卡尔曼滤波的抗干扰性,与常规无迹卡尔曼滤波(UKF)相比,不仅保持了系统的稳定性,而且提高了精确度,最后通过仿真进行了验证。     

一类非线性滤波器—— UKF 综述

回顾了UKF算法的发展，从一般意义讨论了UT变换算法和采样策略的选择依据，并给出了UKF算法描述．从条件函数和代价函数入手，在给出多种采样策略的基础上对UKF采样策略进行了分析和比较．最后对UKF算法未来可能的研究方向进行了探讨．     

Kalman滤波抗野值方法研究

在Kalman滤波应用过程中 ,观测值中的野值是影响滤波效果的重要因素。当观测中含有野值时 ,破坏了Kalman滤波新息的原有特性 ,从而造成估计不准 ,滤波精度下降。本文提出了修正Kalman滤波新息的方法 ,使修正后的Kalman滤波新息能够保持修正前的新息特性。仿真结果表明 ,本文提出的方法可有效地抑制观测中的野值对系统滤波的不利影响     

机器人视觉Kalman 和FIR 滤波稳像算法设计与比较

稳像是提高基于视觉的移动机器人作业精度的关键。论文建立了完整的稳 像算法流程,包含图像运动学模型、KLT 特征提取、SAD 特征匹配和滤波算法;设计了运 动参数的Kalman 和FIR 滤波算法;并利用MATLAB 实现了运动参数的Kalman 和FIR 滤波 器;仿真验证和对比分析了Kalman 和FIR 滤波器对运动参数的去抖效果。结果表明,机器 人视觉稳像中,Kalman 滤波效果优于FIR 滤波。用VC++和OpenCV 编程实现了基于Kalman 滤波的机器人视觉稳像软件,在双机器人移动平台上开展了实验,稳像计算时间小于视频采 样时间,系统满足机器人对接作业实时性和精度要求。     

一种MEMS加速度计误差分析与校准方法

MEMS传感器测量中一般存在确定性偏差和随机噪声两类误差,为提高其测量精度和稳定性,以MEMS加速度计为例,在建立其测量误差模型的基础上,提出一个综合的校准方案,同时对这两类误差进行补偿。其中使用Allan方差对随机噪声项进行量化分析,并综合采用了最小二乘法计算确定性校准系数,扩展卡尔曼滤波降低随机噪声等方法。通过实验验证,表明该方案可以有效校准加速度计测量的确定性偏差并降低随机噪声干扰,最终经过误差补偿后的测量数据在精度和稳定性方面都有明显提升。     

Computing arrival cost parameters in moving horizon estimation using sampling based filters

Moving horizon estimation (MHE) is a numerical optimization based approach to state estimation, where the joint probability density function (pdf) of a finite state trajectory is sought, which is conditioned on a moving horizon of measurements. The joint conditional pdf depends on the a priori state pdf at the start of the horizon, which is a prediction pdf based on historical data outside the horizon. When the joint pdf is maximized, the arrival cost is a penalty term based on the a priori pdf in the MHE objective function. Traditionally, the a priori pdf is assumed as a multivariate Gaussian pdf and the extended Kalman filter (EKF) and smoother are used to recursively update the mean and covariance. However, transformation of moments through nonlinearity is poorly approximated by linearization, which can result in poor initialization of MHE. Sampling based nonlinear filters completely avoid Taylor series approximations of nonlinearities and attempt to approximate the non-Gaussian state pdf using samples and associated weights or probability mass points. The performance gains of sampling based filters over EKF motivate their use to formulate the arrival cost in MHE. The a priori mean and covariance are more effectively propagated through nonlinearities and the resulting arrival cost term can help to keep the horizon small. It is also possible to find closed-form approximations to the non-Gaussian a priori pdf from the sampling based filters. Thus, more realistic nonparametric arrival cost terms can be included by avoiding the Gaussian assumption. In this paper the use of the deterministic sampling based unscented Kalman filter, the class of random sampling based particle filter and the aggregate Markov chain based cell filter are discussed for initializing MHE. Two simulation examples are included to demonstrate the benefits of these methods over the traditional EKF approach.     

Continuous‐discrete filters for bearings‐only underwater target tracking problems

In this work, we develop a continuous‐discrete shifted Rayleigh filter (CD‐SRF) and a continuous‐discrete sparse‐grid Gauss‐Hermite filter (CD‐SGHF) for a real‐life passive underwater bearings‐only target tracking problem. The stochastic difference equation describing the process model is derived from its continuous equivalent using Ito‐Taylor expansion of order 1.5. The performance of the proposed filters is compared in terms of root mean square error (RMSE), track divergence and computational time. For a fair comparison, popular filters like the unscented Kalman filter (UKF), cubature Kalman filter (CKF) and Gauss–Hermite filter (GHF) are implemented. The effect of initial uncertainty, measurement noise covariance and sampling time on filtering accuracy is also studied. Finally, RMSEs of all the filters are evaluated in comparison with the Cramer–Rao lower bound (CRLB). From simulation results, it was observed that CD filters performed with higher accuracy than their discrete equivalents, with CD‐SRF proving to be the most accurate among all the filters.