GPS navigation processing using the quaternion-based divided difference filter

Divided difference filter (DDF) with quaternion-based dynamic process modeling is applied to global positioning system (GPS) navigation. Using techniques similar to those of the unscented Kalman filter (UKF), the DDF uses divided difference approximations of derivatives based on Stirling’s interpolation formula which results in a similar mean but different posterior covariance compared to the extended Kalman filter (EKF) solutions. The second-order divided difference is obtained from the mean and covariance in second-order polynomial approximation. The quaternion-based dynamic model is adopted for avoiding the singularity problems encountered in the Euler angle method and enhancing the computational efficiency. The proposed method is applied to GPS navigation to increase the navigation estimation accuracy at high-dynamic regions while preserving (without sacrificing) the precision at low-dynamic regions. For the illustrated example, the second-order DDF can deliver about 41–82% accuracy improvement as compared to the EKF. Some properties and performance are assessed and compared to those of the EKF and UKF approaches.     

一种新型非线性滤波理论及其应用

研究一种新型的非线性滤波理论,即Unscented卡尔曼滤波（UKF）,同时为了获得更高的计算效率和确保协方差阵的非负定性,研究了平方根UKF。将UKF和平方根UKF应用到星载GPS卫星定轨中,实际算例表明UKF和平方根UKF的性能要优于常用的推广卡尔曼滤波的性能。     

基于UKF的GPS非线性动态滤波算法

介绍了一种Unscented卡尔曼滤波算法，它通过确定性采样获得一组采样点，可获得更多的观测假设，对系统状态统计特性的估计更加准确，同时该算法无需对系统方程进行线性化，避免了传统的EKF算法由于线性化引入的误差。本文将UKF算法用于GPS非线性动态滤波技术中，建立了仿真模型并定义了仿真条件，与EKF算法的仿真结果相比，在系统状态统计特性未知的情况下，UKF算法对系统状态的估计更准确，定位精度更高。     

GPS/GALLIEO导航系统的抗差EKF模型研究

首先给出扩展卡尔曼滤波(Extended Kalman Filter,EKF)的原理,通过分析粗差在EKF模型中传递特性,给出新的抗差EKF模型。模型根据多余观测分量及预测残差统计,构造抗差等价增益矩阵,通过迭带给出GNSS抗差导航解。为提高模型在动态导航应用中的效率,文章结合统计模型,仅对存在粗差的观测历元进行抗差估计,进一步提高模型实时运行效率。并模拟GPS/Galileo多卫星导航星座及接收机平台的动态轨迹。采用加速度导航方程验证本文模型,并对不同模型运行的时间进行比较。结果表明在粗差存在的情况下,本文模型仍能正确导航,并且改进后的模型能明显提高实时导航的效率。     

BP神经网络在GPS导航中的应用

Kalman滤波常用于GPS动态数据的处理,由于系统存在的不确定性和非先验性,导致滤波产生较大的估计误差,甚至发散。介绍了BP神经网络算法及其非线性逼近能力,并基于BP神经网络的非线性逼近性能设计了BP神经网络进行GPS导航的新算法。实测数据计算结果表明该算法能够真实地反映载体运动轨迹,其导航解具有良好的精度和可靠性。     

Adaptive estimation of multiple fading factors in Kalman filter for navigation applications

Kalman filter is the most frequently used algorithm in navigation applications. A conventional Kalman filter (CKF) assumes that the statistics of the system noise are given. As long as the noise characteristics are correctly known, the filter will produce optimal estimates for system states. However, the system noise characteristics are not always exactly known, leading to degradation in filter performance. Under some extreme conditions, incorrectly specified system noise characteristics may even cause instability and divergence. Many researchers have proposed to introduce a fading factor into the Kalman filtering to keep the filter stable. Accordingly various adaptive Kalman filters are developed to estimate the fading factor. However, the estimation of multiple fading factors is a very complicated, and yet still open problem. A new approach to adaptive estimation of multiple fading factors in the Kalman filter for navigation applications is presented in this paper. The proposed approach is based on the assumption that, under optimal estimation conditions, the residuals of the Kalman filter are Gaussian white noises with a zero mean. The fading factors are computed and then applied to the predicted covariance matrix, along with the statistical evaluation of the filter residuals using a Chi-square test. The approach is tested using both GPS standalone and integrated GPS/INS navigation systems. The results show that the proposed approach can significantly improve the filter performance and has the ability to restrain the filtering divergence even when system noise attributes are inaccurate.     

移动机器人SLAM位姿估计的改进四元数无迹卡尔曼滤波EI北大核心CSCD

在全自主运动控制的移动机器人系统中,自身位姿的估计和校正对于移动机器人的运动至关重要。卡尔曼滤波是解决移动机器人同步定位与地图构建(SLAM)常用方法。相较于卡尔曼滤波,无迹卡尔曼滤波(UKF)无须对复杂的非线性函数进行雅可比矩阵运算。本文基于无迹卡尔曼滤波,根据先验协方差的平方根选择sigma点,计算协方差以及加权均值。用四元数表示姿态,将四元数矢量转换为旋转空间进行矩阵运算,在此基础上设计了一种位姿估计算法——基于四元数平方根的无迹卡尔曼滤波(QSR-UKF)算法。试验将EKF、QSR-UKF、SR-UKFEKF 3种算法的位姿估计结果进行仿真分析,并通过相关定量指标进行了描述,验证了本文算法的有效性。     

GPS导航解算中几种非线性Kalman滤波的理论分析与比较

GPS导航解算中常采用离散线性Kalman滤波模型.由于线性化忽略高次项,加之线性化受初始值精度的影响,导致线性化模型精度很难满足高动态用户需求.为此,分别讨论了扩展Kalman滤波和Bancroft算法以及利用观测信息迭代精化观测方程三种算法,并结合算例进行了比较与分析.     

EKF/UKF在基于地磁场的卫星自主定轨中的应用比较

研究了基于地磁场的自主导航,建立了以卫星轨道动力学方程为基础的系统状态方程,并详细推导了以地磁场矢量为观测量时的观测方程。由于传统的卡尔曼滤波不能解决系统的非线性问题,因此把扩展卡尔曼滤波EKF和无迹卡尔曼滤波UKF引入到系统中;并用Matlab对基于地磁场的自主导航系统进行了仿真。仿真结果表明,UKF有更好的收敛性和稳定性。     

UKF滤波器性能分析及其在轨道计算中的仿真试验

讨论了UT（unscented transform）变换的性质，给出了一种新的扩展型卡尔曼滤波器UKF（unscented Kalman filter），它不仅具有较高的精度，而且不必计算偏导数阵。仿真分析的结果表明，UKF有良好的状态估计性能，使用简便，适合于非线性系统状态估计。     

基于GPS软件接收机的SINS／GPS紧组合系统仿真

为了系统验证SINS／GPS紧组合系统的性能,基于GPS软件接收机,进行了仿真系统构建。仿真系统由轨迹发生器、GPS中频信号模拟器、IMU信号模拟器、GPS软件接收机、SINS导航解算模块、组合滤波算法和导航性能分析模块等部分构成,其中详细设计了GPS软件接收机中的捕获和跟踪算法、SINS解算以及基于伪距和伪距率的组合滤波算法。仿真结果表明：紧组合导航系统收敛性较好,能够一定程度上抑制惯导系统误差的积累,有较好的导航性能。设计的该系统满足紧组合导航系统性能验证的需要,也为后续的超紧组合研究奠定了良好的基础。     

Application of unscented Kalman filter in satellite orbit simulation

A new estimate method is proposed, which takes advantage of the unscented transform method, thus the true mean and covariance are approximated more accurately. The new method can be applied to nonlinear systems without the linearization process necessary for the EKF, and it does not demand a Gaussian distribution of noise and what's more, its ease of implementation and more accurate estimation features enables it to demonstrate its good performance in the experiment of satellite orbit simulation. Numerical experiments show that the application of the unscented Kalman filter is more effective than the EKF.     

State transformation extended Kalman filter for GPS/SINS tightly coupled integration

Extended Kalman filter (EKF) is a widely used estimator for integrated navigation systems, and it works well in general situations. However, in adverse conditions such as partially observable environments and highly dynamic maneuvers, the performance of the traditional EKF-based strap-down inertial navigation system (SINS)/GPS integrated navigation system is easily to be affected by the dynamic changes of the specific force, thus leading to the problem of error covariance inconsistency. Though the inconsistency problem can be overcome to some extent if the system matrix, the states and the error covariance matrix are propagated as fast as possible in the SINS calculation rate, the problem cannot be fully solved. State transformation extended Kalman filter (ST-EKF) mechanization, with a new converted velocity error model for the SINS, is proposed, which can also be used to solve the inconsistency problem. In the ST-EKF, the specific force vector in the system error model is replaced by the nearly constant gravity vector for local navigation. Since the propagation and the updating of the ST-EKF can be executed simultaneously in the updating interval, the computation cost is greatly reduced compared with the traditional EKF. Experiments for the GPS/SINS tightly coupled navigation, including linear vibration Monte Carlo test and an unmanned aerial vehicle flight test, are implemented to evaluate the performance of the proposed ST-EKF. The results show that the proposed ST-EKF has superior performance to the traditional EKF, especially in partially observable situations.     

UKF在GPS/INS组合导航系统中的应用

扩展卡尔曼滤波(EKF)是GPS/INS组合导航系统工程实现中常用的一种数据融合方式。但EKF线性化误差在一定程度上影响了GPS/INS组合导航系统精度的提高。Unscented卡尔曼滤波器(UKF)是一种非线性滤波器,它能有效地减小线性化误差对GPS/INS组合导航系统精度的影响。基于四元数法建立了GPS/INS组合导航系统的非线性误差方程模型;最后通过数字仿真验证了UKF组合导航系统应用中的性能。     

IMU辅助X射线脉冲星的深空探测器精确定姿方法及仿真

为满足深空探测器的精确定姿需求,提出了一种惯性测量单元(IMU)辅助的X射线脉冲星定姿方法。该方法用IMU的速率陀螺来估计航天器短时姿态,观测两颗或多颗脉冲星的X射线辐射信号,将拟合得到的观测矢量作为滤波器信息输入,利用这两种测姿手段在时间和空间上的互补特性,提供一种全天候、抗干扰性强的定姿方法。仿真结果表明,相比于EKF,基于UKF的俯仰、横滚和偏航三姿态角的测量精度可提高21.9%、21.1%和31.7%;与仅使用脉冲星或IMU的定姿方法相比,组合定姿方法的俯仰角估计精度分别提高了32.5%和77.6%。     

顾及时间相关噪声的单频GPS精密单点定位

扩展Kalman滤波(EKF)常常被用于单频GPS精密单点定位。Kalman滤波的前提假设之一是观测噪声为白噪声,即时间不相关,这在实践中往往不能满足。因为单频GPS观测值中包含有很难被完全消除的电离层、对流层等大气折射误差,以及多路径影响误差。这些误差在时间上是相关的,严重地影响了滤波解的精度和收敛时间。这里提出一种顾及时间相关噪声的Kalman滤波,在移动窗口内,利用核估计预测时间相关噪声的系统部分,进而实时修正当前历元的观测值和观测向量的协方差矩阵。该方法还有一个明显的优点就是,在滤波过程中不需要对时间相关误差做任何假设。最后通过一个实测算例验证了该算法的适用性。     

GPS/INS组合导航系统抗差滤波器设计

常规Ｋａｌｍａｎ滤波器已经广泛用于ＧＰＳ／ＩＮＳ组合导航系统,其中假设系统动态模型和噪声统计特性是精确已知的。事实上,这种假设是不符合实际情况的。在组合导航系统中,惯性测量器件的质量不稳定,ＧＰＳ测量误差受外界环境的影响,因而对组合导航系统进行抗差设计是十分必要的。本文利用对策论设计了能使不确定噪声下性能最好的极小极大抗差滤波器,并将其应用到ＧＰＳ／ＩＮＳ组合导航系统中。考虑一个ＩＯ状态的ＧＰＳ／     

非线性系统中卡尔曼滤波的一种新线性化方法

针对测量领域非线性系统卡尔曼滤波的线性化，在分析两种传统线性化方式的基础上．提出了一种新的基于最优估计值的线性化方式。     

多传感器组合导航系统的多尺度分布式滤波算法

将模型的动态系统分析与具有统计特性的多尺度信号变换方法相结合,首先将状态方程采用数据块变换的方式以得到新的状态块方程,并将量测方程表达为数据块的形式;然后将量测向量进行多层小波变换以得到新的量测向量,并结合状态块方程进行卡尔曼滤波;最后根据卡尔曼滤波结果建立多尺度分布式融合估计算法。仿真结果表明,相对于原始尺度的集中式卡尔曼滤波器及原始尺度的多尺度融合算法,本算法可明显地提高系统的滤波精度。