状态约束卡尔曼滤波的导航定位精度分析

针对满足一些状态约束的线性系统,通常的卡尔曼滤波未能有效利用状态约束信息,从而限制了导航定位解算性能的问题,该文将线性系统的状态约束条件融入卡尔曼滤波中,充分利用状态约束信息,对比分析了准确测量法、估计投影法、系统投影法和滑动时域估计法4种状态约束下的卡尔曼滤波方法,以提高卡尔曼滤波的导航状态估计精度。以陆地车辆导航定位的状态估计为对象,对比分析了非约束卡尔曼滤波和带有状态约束的卡尔曼滤波的状态估计精度,结果表明,状态约束卡尔曼滤波可以明显提高导航定位精度。     

Application of Adaptive Kalman Filtering Algorithm in IMU/GPS Integrated Navigation System

The IMU(inertial measurement unit) error equations in the earth fixed coordinates are introduced firstly. A fading Kalman filtering is simply introduced and its shortcomings are analyzed, then an adaptive filtering is applied in IMU/GPS integrated navigation system, in which the adaptive factor is replaced by the fading factor. A practical example is given. The results prove that the adaptive filter combined with the fading factor is valid and reliable when applied in IMU/GPS integrated navigation system.     

海洋测深数据的抗差Kalman滤波

从线式测深模式要求出发,构建了海洋水深测量过程中的测船位置滤波模型和深度数据的滤波模型,并在此基础上,给出了测线上位置数据和深度数据Kalman滤波的一般解和抗差解,并结合海洋水深测量特点,构建了满足水深数据剔除异常值的截断权函数和滤波方案,实例分析表明,抗差滤波方法能够有效地控制测船位置粗差,在选择截断权函数情况下,抗差滤波方法能够有效地剔除水深跳点和假水深。     

组合导航抗差自适应卡尔曼滤波

针对组合导航系统的定位精度与稳定性要求不断提高的现状,该文引入一种观测噪声协方差与抗差自适应相结合的Kalman滤波算法。利用新息向量和移动窗口协方差分析法,动态自适应修正观测噪声协方差阵;通过分析基于状态不符值、方差分量的统计量构造的自适应因子所存在的问题,提出一种由预测残差向量构造的自适应因子。仿真结果表明,该方法能够有效抑制观测异常对组合导航定位精度的影响。     

非完整约束的OD/SINS自适应组合导航方法

在地面车载组合导航GNSS/OD/SINS中,全球导航卫星系统（GNSS）信号容易受到环境的干扰甚至发生中断,将非完整性约束（NHC）应用于里程计（OD）/捷联惯性导航系统（SINS）组合,可以有效抑制GNSS信号中断期间组合导航系统的误差发散。通常NHC的噪声设定基于固定的经验值,然而在实际运动过程中,车辆运行轨迹复杂多变,其运动状态不能完全满足NHC前提假设,经验给定的噪声无法准确反映车辆实际运动情况。为此,本文分析了NHC噪声与车辆运动状态的关系,构建了一种基于车辆运动状态的NHC噪声自适应方法。通过所选场景的实测数据验证表明：采用噪声自适应的NHC/OD/SINS组合导航结果相比于固定噪声的NHC/OD/SINS组合,在GNSS信号中断110 s、车辆连续转弯的情况下,最大水平位置误差减小了68.4%;在GNSS信号中断74 s、车辆直线行驶的情况下,最大水平位置误差减小了87.3%;能较好地抑制GNSS中断期间组合导航系统的误差发散。     

Robust multiple update-rate Kalman filter for new generation navigation signals carrier tracking

GPS Solutions - The study of ionospheric scintillation has played a critical role in ionospheric research and also in satellite positioning. This is due to the growing influence of GNSS in...     

Robust Kalman filtering based on Mahalanobis distance as outlier judging criterion

A robust Kalman filter scheme is proposed to resist the influence of the outliers in the observations. Two kinds of observation error are studied, i.e., the outliers in the actual observations and the heavy-tailed distribution of the observation noise. Either of the two kinds of errors can seriously degrade the performance of the standard Kalman filter. In the proposed method, a judging index is defined as the square of the Mahalanobis distance from the observation to its prediction. By assuming that the observation is Gaussian distributed with the mean and covariance being the observation prediction and its associate covariance, the judging index should be Chi-square distributed with the dimension of the observation vector as the degree of freedom. Hypothesis test is performed to the actual observation by treating the above Gaussian distribution as the null hypothesis and the judging index as the test statistic. If the null hypothesis should be rejected, it is concluded that outliers exist in the observations. In the presence of outliers scaling factors can be introduced to rescale the covariance of the observation noise or of the innovation vector, both resulting in a decreased filter gain. And the scaling factors can be solved using the Newton’s iterative method or in an analytical manner. The harmful influence of either of the two kinds of errors can be effectively resisted in the proposed method, so robustness can be achieved. Moreover, as the number of iterations needed in the iterative method may be rather large, the analytically calculated scaling factor should be preferred.     

自适应卡尔曼滤波在GPS/DR组合导航中的应用

针对在观测条件较差的情况下卡尔曼滤波的鲁棒性较差,本文设计了一种自适应卡尔曼滤波模型。通过实际车载GPS/DR组合导航试验,结果表明该模型在观测质量较差的情况下能够抑制较大的偏差,相对于标准卡尔曼滤波模型,其平面定位精度提高了近一倍,达到2～3m。因此,在观测环境较差的情况下建议采用渐消自适应卡尔曼滤波模式进行组合导航。     

抗差卡尔曼滤波及其在动态水准网平差中的应用

介绍了标准卡尔曼滤波方程,总结了稳健M估计的基本方法,并根据等价权原理导出卡尔曼滤波的抗差估计方程,方程的形式与卡尔曼滤波方程相似,给出了卡尔曼滤波稳健估计的计算步骤.最后,以动态水准监测为例进行了模拟计算,证明了该方法的有效性.     

动态系统的抗差Kaliman滤波

离散历元的动态观测量及其相应的动态模型可能存在异常，若数据处理模型不考虑对这些异常的特别处理，则动态模型参数估值及其所提供的动态信息将极不可靠。基于贝叶斯统计和抗差估计原理，我们构造了一种抗差滤波算法。该算法考虑观测分布和参数验前分布均为污染分布。并利用一个实测网验算该算法和模型的可靠性。     

Unscented Kalman filter with nonlinear dynamic process modeling for GPS navigation

This paper preliminarily investigates the application of unscented Kalman filter (UKF) approach with nonlinear dynamic process modeling for Global positioning system (GPS) navigation processing. Many estimation problems, including the GPS navigation, are actually nonlinear. Although it has been common that additional fictitious process noise can be added to the system model, however, the more suitable cure for non convergence caused by unmodeled states is to correct the model. For the nonlinear estimation problem, alternatives for the classical model-based extended Kalman filter (EKF) can be employed. The UKF is a nonlinear distribution approximation method, which uses a finite number of sigma points to propagate the probability of state distribution through the nonlinear dynamics of system. The UKF exhibits superior performance when compared with EKF since the series approximations in the EKF algorithm can lead to poor representations of the nonlinear functions and probability distributions of interest. GPS navigation processing using the proposed approach will be conducted to validate the effectiveness of the proposed strategy. The performance of the UKF with nonlinear dynamic process model will be assessed and compared to those of conventional EKF.     

抗差卡尔曼滤波在GPS动态定位中的应用

基于Kalman滤波的GPS动态定位中，动态观测量及其相应的动态模型可能存在异常，若数据处理不考虑对这些异常的特别处理，则模糊度的估值及其所提供的动态信息将极不可靠，按抗差估计原理，文中构造了状态向量和观测值对模糊度的影响函数，并由此建立了动态GPS定位的抗差Kalman滤波解法，实际计算验证了该方法的实用性和可靠性。     

抗差卡尔曼滤波在GPS动态定位中的应用

基于Kalman滤波的GPS动态定位中,动态观测量及其相应的动态模型可能存在异常,若数据处理不考虑对这些异常的特别处理,则模糊度的估值及其所提供的动态信息将极不可靠.按抗差估计原理,文中构造了状态向量和观测值对模糊度的影响函数,并由此建立了动态GPS定位的抗差Kalman滤波解法.实际计算验证了该方法的实用性和可靠性.     

MDB: A design tool for integrated navigation systems

The design of an integrated navigation system requires that various aspects are taken into consideration. In this paper the aspect of reliability (in the statistical sense) is more closely investigated. A particular measure of reliability, the Minimal Detectable Bias (MDB), is considered. Its use as a design tool for integrated navigation systems is described and is illustrated by an example.     

基于椭球GPS/DR导航模型的鲁棒滤波研究

为了获得更精确的运动物体的数学模型,本文建立了GPS/DR组合导航系统的椭球模型,并将含参模型转化为不确定性参数滤波模型,并利用鲁棒卡尔曼滤波算法和鲁棒H∞滤波算法进行了仿真,从滤波的稳健性和效率两个方面进行了分析,得出在椭球GPS/DR导航模型下,鲁棒H∞滤波算法比鲁棒卡尔曼滤波更符合工程实际应用的滤波方法。     

Robust Kalman filter for rank deficient observation models

A robust Kalman filter is derived for rank deficient observation models. The datum for the Kalman filter is introduced at the zero epoch by the choice of a generalized inverse. The robust filter is obtained by Bayesian statistics and by applying a robust M-estimate. Outliers are not only looked for in the observations but also in the updated parameters. The ability of the robust Kalman filter to detect outliers is demonstrated by an example. Received: 8 November 1996 / Accepted: 11 February 1998     

基于CRInSAR和kalman滤波的监测地表三维形变的研究

CRInSAR技术克服了传统DInSAR的一些不足,成为近年来的研究热点,但单一的CRInSAR技术只能监测LOS的一维形变。而kalman滤波采用状态空间的概念,可以用来估计平稳或非平稳的多维信号随机过程,已经被广泛地应用于动态数据处理之中。因此本文以CRInSAR模型为基础,将不同时间跨度的干涉数据作为动态数据,构建相应的观测方程和状态方程,并以经典的kalman滤波估计角反射器的三维形变量和三维形变速度。实践证明,该方法是合理可行的。     

Integrated GPS/INS navigation system with dual-rate Kalman Filter

A dual-rate Kalman Filter (DRKF) has been developed to integrate the time-differenced GPS carrier phases and the GPS pseudoranges with INS measurements. The time-differenced GPS carrier phases, which have low noise and millimeter measurement precision, are integrated with INS measurements using a Kalman Filter with high update rates to improve the performance of the integrated system. Since the time-differenced GPS carrier phases are only relative measurements, when integrated with INS, the position error of the integrated system will accumulate over time. Therefore, the GPS pseudoranges are also incorporated into the integrated system using a Kalman Filter with a low update rate to control the accumulation of system errors. Experimental tests have shown that this design, compared to a conventional design using a single Kalman Filter, reduces the coasting error by two-thirds for a medium coasting time of 30?s, and the position, velocity, and attitude errors by at least one-half for a 45-min field navigation experiment.     

有色噪声作用下的抗差卡尔曼滤波

根据用GPS载波相位三差观测量进行动态定位或精密导航的需求,推导了动态噪声、观测噪声为有色噪声的抗差卡尔曼滤波公式。白噪声的抗差卡尔曼滤波是有色噪声的抗差卡尔曼滤波的特例,有色噪声的抗差卡尔曼滤波为白噪声的抗差卡尔曼滤波的推广。     

后向平滑与抗差估计融合的SRCKF滤波

将后向平滑平方根容积卡尔曼滤波用于GPS动态单点定位数据处理,并探讨了粗差对后向平滑滤波的影响。借鉴经典卡尔曼滤波抗差估计思想,给出平方根容积卡尔曼滤波的抗差算法以抵抗量测粗差,而当判断不含粗差时使用后向平滑算法,在有效提高滤波精度的同时避免了抗差滤波对每个历元都需进行迭代运算。实测GPS动态数据验证了算法的有效性。