Improved robust Kalman filter for state model errors in GNSS-PPP/MEMS-IMU double state integrated navigation

The integration of Global Navigation Satellite System (GNSS) with Inertial Navigation Systems (INS) has been actively researched and widely applied as it can provide reliable positioning information continuously. In recent years, Micro Electro Mechanical Systems (MEMS) technology achieves rapid development and Micro Electro Mechanical Systems and Inertial Measurement Unit (MEMS-IMU) has aroused wide concern due to its excellent properties in some cases. However, the observations from MEMS-IMU are easy to be influenced by motion state and location environment because of its manufacturing process. It is not easy to judge whether gross errors are in the state model or the observation model by the widely adopted robust filter based on innovation. In this contribution, we present an improved robust filter with a double state model on the basis of the chi-square distribution of the square of the Mahalanobis distance. The vehicle motion model acts as the external constraint information and can be adopted to construct robust statistic with the results from INS mechanization. And then a robust factor was determined to adjust the observation noise covariance matrix. To evaluate the performance of this method, the simulation test and the field test based on locomotive platform of Nottingham Geospatial Institute (NGI) were carried out. According to the results, in the simulation test, the position improvements are 33%, 30% in the north and east directions; in the real test, the loosely and tightly coupled was adopted and the position accuracy can be improved by about 50–60% in the horizontal direction and the improvement of the pitch and the roll accuracy was lower than the azimuth accuracy due to poor observability and experimental scene which is of the characteristics of small elevation change. Therefore, the proposed robust filter could diminish the effect of the gross error from MEMS-IMU and enhance the integrated system.     

A new stochastic model considering satellite clock interpolation errors in precise point positioning

Precise clock products are typically interpolated based on the sampling interval of the observational data when they are used for in precise point positioning. However, due to the occurrence of white noise in atomic clocks, a residual component of such noise will inevitable reside within the observations when clock errors are interpolated, and such noise will affect the resolution of the positioning results. In this paper, which is based on a twenty-one-week analysis of the atomic clock noise characteristics of numerous satellites, a new stochastic observation model that considers satellite clock interpolation errors is proposed. First, the systematic error of each satellite in the IGR clock product was extracted using a wavelet de-noising method to obtain the empirical characteristics of atomic clock noise within each clock product. Then, based on those empirical characteristics, a stochastic observation model was structured that considered the satellite clock interpolation errors. Subsequently, the IGR and IGS clock products at different time intervals were used for experimental validation. A verification using 179 stations worldwide from the IGS showed that, compared with the conventional model, the convergence times using the stochastic model proposed in this study were respectively shortened by 4.8% and 4.0% when the IGR and IGS 300-s-interval clock products were used and by 19.1% and 19.4% when the 900-s-interval clock products were used. Furthermore, the disturbances during the initial phase of the calculation were also effectively improved.     

粗差拟准检定法在星载GPS低轨卫星定轨中的应用

利用自适应卡尔曼滤波进行星载GPS低轨卫星定轨时,必须解决量测方程中经常存在的粗差问题．在分析以往方法的优缺点后,用拟准检定法来探测和修正量测方程中存在的粗差．该法的优点是辨识粗差准确率高,能同时定位多个粗差．另外,为了克服星载GPS低轨卫星定轨的滤波器可能出现的数值不稳定性及发散现象,还采用了UD分解算法及Sage自适应滤波器．最后用一个CHAMP卫星的模拟算例验证本方法的可行性和有效性．     

Kalman filtering for GPS/magnetometer integrated navigation system

This paper investigated the data processing method for a GPS/IMU/magnetometer integrated system with Kalman filtering (KF). As a result of GPS/IMU/magnetometer land vehicle system, dead-reckoning of magnetometer and accelerometer integrated subsystem bridged very well the GPS signal outage due to the trees on the two sides of the road. Both differential GPS data processing method and the carrier-phase method with magnetometers’ outputs for predicting the car position, velocity, and acceleration (PVA) are presented. The results from DGPS with Kinematical Positioning (KINPOS) software shown that the averages of the north, east, and down direction standard deviation (short for “std”) are 0.014, 0.010, and 0.018 m, respectively. The std of velocities and accelerations derived by the position and velocity differentiation are 10, 7, 13 mm/s, 7, 5, 9 mm/s², respectively. This method for getting velocities and accelerations requires higher accurate position coordinates. But the position accuracy has frequently been degraded in this case when the car drove under the trees or other similar kinematical environments. That caused the larger velocity and acceleration errors. While the results from the carrier-phase method are std of the velocities = 2.1 mm/s, 1.3 mm/s, 3.7 mm/s in north, east, down, and std of the accelerations = 1.5 mm/s², 0.9 mm/s², 2.3 mm/s² for the static test period; as compared with KINPOS software results, std of the velocity difference between the carrier-phase method and the DGPS method = 7 mm/s, 6.9 mm/s, 9.7 mm/s in north, east, down direction, and std of acceleration difference = 5.0 mm/s², 4.5 mm/s², 7.5 mm/s² in north, east, down direction for the kinematical test period. Obviously, errors come from both the carrier-phase method and DGPS velocity and acceleration results derived directly by the position differentiation. In addition, better accuracy of positions than that before KF has been got by means of velocities and accelerations derived by the carrier-phase method after KF.     

Using only observation station data for PPP ambiguity resolution by UPD estimation

This article proposes a new method for uncalibrated phase delay (UPD) estimation to improve the accuracy of precise point positioning (PPP), which uses only observation station data. This means that the station used to generate the UPDs is the same station to which they are applied. First, dual-frequency observation equations based on a raw PPP model are developed. Then, the UPDs are calculated from integer linear combinations of float ambiguities. Third, with the UPD corrections, the least-squares ambiguity decorrelation adjustment (LAMBDA) method is utilized to obtain the integer ambiguities. Since only observation station data are used for UPD estimation, the partial ambiguity resolution (PAR) method is adopted to increase the possibility of finding a subset of integer ambiguities. The UPD estimation and ambiguity resolution are performed in each epoch. To obtain the correct integer ambiguity, the ratio test and success rate (bootstrapping) are used to evaluate the estimated integer ambiguity. Finally, by treating the integer ambiguities as constants, fixed solutions can be obtained. Quality control is also applied throughout the entire data processing procedure to obtain high quality float and fixed solutions. Data from 22 stations of the International Global Navigation Satellite System (GNSS) Service (IGS) in East Asia on day of year (DOY) 206, 2017, are used to verify the feasibility of this method. The experimental results show that compared with the float solution, the proposed method can significantly improve the accuracy in the east, north and up directions by 24%, 21% and 18% for static PPP and 36%, 18% and 34% for dynamic PPP, respectively. However, the accuracy of the proposed method is still lower than that of the fixed solutions obtained by the PRIDE-PPPAR software, in which the fractional cycle bias is computed based on reference network data. These findings sufficiently show that the proposed method can offer better solution accuracy than the float solution. However, the quality of the UPDs estimated only from observation station data is not as good as that of the estimates obtained based on reference network data.     

基于扩展卡尔曼滤波的舰机相对位姿估测

通过将基于扩展卡尔曼滤波的长序列图像分析方法与单目视觉技术相结合,把无人机自主着舰视觉导引中舰机间相对位姿的估测,转化为机载摄像机对着舰靶标平面3D位姿的实时估测问题.首先根据透视投影理论,建立了以摄像机的透镜中心为原点且Z轴与光轴重合的摄像机坐标系和世界坐标系,然后利用机载摄像机连续拍摄的靶标图像序列,选择描述相对运动的3个欧拉角、平移向量及它们的速度作为状态变量;由靶标角点的提取和帧间匹配,建立了反映着舰靶标上特征点的图像坐标和状态变量之间关系的观测方程,带入扩展卡尔曼滤波器,估测出舰机的相对运动参数.计算机数据仿真和基于DSP平台的半实物仿真试验验证了算法的有效性和鲁棒性.      

Kalman滤波估算电离层延迟的一种优化方法

频间偏差（Inter Frequency Bias，IFB）通常会给电离层延迟的解算带来误差.目前从电离层延迟中消除频间偏差的方法是基于GPS双频观测数据建立垂直电离层模型，利用卡尔曼滤波实时估算电离层模型系数和频间偏差.然而滤波过程中的测量噪声协方差矩阵没有考虑系统观测量之间的相关性，这会导致滤波模型不准确，进而影响最后求解的电离层延迟的准确性.本文选取了美国19个参考站的GPS双频观测数据，利用卡尔曼滤波实时估算电离层模型系数以及频间偏差.在滤波过程中，通过将先验频间偏差的估计方差引入测量噪声方差，实现对测量噪声协方差矩阵的优化.计算结果表明，优化后得到的卫星频间偏差与欧洲定轨中心（Center for Orbit Determination in Europe，CODE）得到的频间偏差更接近.将优化后的电离层延迟代入伪距解算，得到的位置误差的标准差在东向和天顶向分别下降了12.5%和15.4%，天顶向误差平均值下降了17.6%，定位精度得到提高.      

导航解算中的有色噪声及其协方差矩阵自适应拟合

使用Kalman滤波进行动态导航定位解算需要涉及函数模型和随机模型, 而在实际应用中, 精确的函数模型和随机模型很难直接给出, 因此, 动态Kalman滤波的精度和可靠性将会受到函数模型误差和随机模型误差的影响. 在假设观测噪声和动力学模型噪声主要是具有一阶自相关特性的有色噪声的基础上, 提出了一种基于移动窗口的有色噪声函数模型和随机模型的自适应拟合法. 给出了计算有色噪声估值和噪声协方差矩阵的表达式, 并利用实测数据验证了模型及算法的可行性和实用性. 计算结果表明, 该算法能有效抵制有色噪声对导航滤波结果的影响.      

Ambiguity resolution in precise point positioning with hourly data for global single receiver

Integer ambiguity resolution (IAR) can improve precise point positioning (PPP) performance significantly. IAR for PPP became a highlight topic in global positioning system (GPS) community in recent years. More and more researchers focus on this issue. Progress has been made in the latest years. In this paper, we aim at investigating and demonstrating the performance of a global zero-differenced (ZD) PPP IAR service for GPS users by providing routine ZD uncalibrated fractional offsets (UFOs) for wide-lane and narrow-lane. Data sets from all IGS stations collected on DOY 1, 100, 200 and 300 of 2010 are used to validate and demonstrate this global service. Static experiment results show that an accuracy better than 1 cm in horizontal and 1–2 cm in vertical could be achieved in ambiguity-fixed PPP solution with only hourly data. Compared with PPP float solution, an average improvement reaches 58.2% in east, 28.3% in north and 23.8% in vertical for all tested stations. Results of kinematic experiments show that the RMS of kinematic PPP solutions can be improved from 21.6, 16.6 and 37.7 mm to 12.2, 13.3 and 34.3 mm for the fixed solutions in the east, north and vertical components, respectively. Both static and kinematic experiments show that wide-lane and narrow-lane UFO products of all satellites can be generated and provided in a routine way accompanying satellite orbit and clock products for the PPP user anywhere around the world, to obtain accurate and reliable ambiguity-fixed PPP solutions.     

Evaluation of rapid phase clock/bias products for PPP ambiguity resolution and its application to the M7.1 2019 Ridgecrest,California earthquake

Precise point positioning with ambiguity resolution (PPP-AR) is a useful tool for high-precision geodetic and geophysical applications, while phase bias products are the prerequisite to implement PPP-AR. Wuhan University has been providing the final (the best operationally post-processing solution based) phase clock/bias products with a latency of two weeks since March of 2019, while a dedicated open-source software package PRIDE PPP-AR is released to leverage these products for high-precision positioning. In order to satisfy some both time and precision critical applications, such as rapid earthquake response, Wuhan University also released rapid (with comparable quality but with much shorter delivery latency) phase clock/bias products with a latency of less than 24 h and updated PRIDE PPP-AR in July 2019. We first introduce the phase clock/bias generation and validation schemes and the maintenance of routine products provision. Then, with 14 days (July 2 to July 15 in 2019) of GPS data collected from 146 globally distributed IGS (International GNSS Service) stations, we evaluated the positioning performance of the rapid products with respect to their final counterparts. It is found that positioning precision of PPP-AR using rapid products is comparable to that using final products, especially in kinematic positioning mode. When rapid products are used, the RMS of PPP-AR in static mode with respect to IGS weekly solutions can reach 1.7 mm, 1.8 mm and 5.5 mm in the east, north and up components, respectively. Furthermore, the RMS of epoch-wise positions with respect to daily solutions for the east, north and up components are 0.51 cm, 0.57 cm and 1.51 cm for PPP-AR with rapid products in kinematic mode. It demonstrates that the rapid phase clock/bias products can sufficiently meet the precision requirement of most geodetic and geophysical applications yet with much shorter time delay. Finally, we study the July 6th M7.1 2019 Ridgecrest, California earthquake using the rapid phase clock/bias products and demonstrate their comparable performance against the final products.     

面向装备RUL预测的平行仿真技术

装备平行仿真是系统建模与仿真领域的新兴仿真技术,已经成为研究热点。在装备维修保障领域中,分析了装备剩余寿命（RUL）预测存在的突出问题,即模型参数固定、不具备自适应演化能力,成为阻碍实现装备剩余寿命自适应预测的首要因素。结合装备平行仿真理论,在建模分析的基础上提出了面向装备剩余寿命预测的平行仿真框架,该框架以Wiener状态空间模型为基础仿真模型,在动态注入的装备退化观测数据驱动下,利用期望最大化（EM）算法在线更新模型参数,并利用卡尔曼滤波（KF）算法实现仿真输出数据与观测数据的同化（DA）,从而实现仿真模型动态演化,使得仿真输出不断逼近装备真实退化状态,为准确预测剩余寿命提供高逼真度仿真模型和数据输出。以某轴承性能退化数据为数据驱动源,对该框架进行了验证,仿真结果表明平行仿真方法能准确仿真装备性能退化过程,在提高预测精度的基础上实现了装备剩余寿命的自适应预测,有力证明了平行仿真方法的可行性和有效性。      

有关鲁棒状态估计的研究评述

研究了有关带模型误差系统的鲁棒状态估计问题。详细讨论了模型误差对滤波器性能的影响,并简单介绍了几种鲁棒状态估计方案。最后指出了将来可能的研究方向。     

四元数UKF超紧密组合导航滤波方法

针对GPS/SINS(Global Positioning System/Strapdown Inertial Navigation Sys-tem)超紧密组合导航系统线性化滤波在高动态、弱GPS信号等环境下性能下降严重的问题,提出了一种以四元数UKF(Unscented Kalman Filter)为基础的GPS/SINS超紧密组合导航系统非线性滤波方法.通过分析GPS与SINS在超紧密组合导航系统中的关系,提出了一种利用SINS信息来估计、修正GPS载波信号的方法,在此基础上建立了组合导航滤波的状态方程和量测方程;以四元数乘性误差模型为基础,提出了一种可应用于UKF滤波的求解四元数加权均值的方法;提出了基于四元数UKF的GPS/SINS超紧密组合导航滤波方法.仿真实验表明:在高动态环境下,四元数UKF滤波方法增强了GPS/SINS超紧密组合导航系统的定位精度和抗干扰能力.     

一种用于高动态GPS频率估计的滤波算法

针对常用高动态GPS(Global Positioning System)频率估计算法扩展卡尔曼滤波(EKF,Extended Kalman Filter)的缺陷,提出了一种新的称为简化无迹高斯粒子滤波(SUGPF,Simplified Unscented Gaussian Particle Filter)的算法.SUGPF将卡尔曼滤波(KF,Kalman Filter)、无迹卡尔曼滤波(UKF,Unscented Kalman Filter)与高斯粒子滤波(GPF, Gaussian Particle Filter)三者相结合.在时间更新阶段,用KF的方法更新预测分布;在测量更新阶段,用UKF的方法得到重要采样函数,并用GPF的方法更新后验分布.仿真结果表明:与EKF和UKF相比,SUGPF性能更优越,功能更全面,在高斯与非高斯观测噪声环境下均能取得与GPF类似的良好性能,并且其计算复杂度低于GPF.     

地基单站GNSS的电离层VTEC高精度解算方法

利用IGS提供的双频GNSS观测数据，分析了Kalman方法解算电离层垂直总电子含量（Vertical Total Electron Content，VTEC）存在的问题，提出了Kriging-Kalman改进解算方法，并对两种方法解算的电离层VTEC进行分析和比较.结果表明:在低纬地区，当观测卫星数量发生改变时，Kalman方法解算的VTEC存在跳变异常，Kriging-Kalman方法解算的VTEC变化较为平稳，不存在跳变现象.对比分析耀斑期间两种方法解算VTEC的变化，发现Kalman方法解算的VTEC变化明显小于耀斑引起VTEC的增量；Kriging-Kalman方法解算结果与实际变化相一致.表明Kriging-Kalman方法计算精度更高，能够更精确计算耀斑等剧烈异常空间天气活动期间的VTEC及其变化，有利于电离层VTEC日常精确监测、研究和工程应用.      

Dual-frequency carrier smoothed code filtering with dynamical ionospheric delay modeling

In GNSS applications, carrier-smoothed-code is a widely used technique to combine code pseudo-range and carrier phase measurements. A dynamical ionospheric delay modeling method is proposed based on Kalman filter and least-squares theory. The level of the process noise is adaptively tuned along with the real-time KF state estimation, based on the online variance component estimation method. Meanwhile, the correlations of the time differenced carrier phase measurements are considered. This approach avoids overly optimistically evaluating the estimate and improves the transient accuracy of the estimates. A real GPS dataset is employed to check the performance of the proposed method under different conditions. The results show that the new algorithm can model the ionospheric delay variation well with different sampling intervals or even in ionospheric abnormal environment. The positioning accuracy can be confirmed, about 21%, 35% and 16% better are obtained in the N, E, and U direction than raw dataset.     

基于Kalman滤波器的卫星钟实时异常监测算法

基于卫星钟钟差的Kalman滤波器模型,提出了一种卫星钟实时异常监测算法,对算法原理进行了讨论,并利用IGS精密钟差数据,对算法进行了性能验证。结果表明：该算法对卫星钟的异常情况（包括单点相位跳变与连续相位跳变）可以进行有效监测,同时还可以完成异常数据的剔除与替换,并且具有较小的替换误差。该算法具有显著的实时性,可以应用于星载原子钟的实时异常监测中。     

一种适用于星间测距网的抗差方案设计

主要讨论了利用星间测距进行星座自主导航的导航算法设计,考虑系统的自主性,算法必须具有检测错误节点和抵抗粗差的能力。为此,文章通过分析星间测距网的特殊性,提出一种以抗差最小二乘为基础,适用于星间测距网的抗差方案。根据失效节点和观测粗差对残差影响的差异,提出分步处理的方法。通过算例比较几种常见抗差方案,验证了文中设计的抗差方案的有效性。     

车载GPS/DR组合导航系统的研究

介绍了车载GPS(Global Positioning System)/DR(Dead Reckoning)组合导航系统的设计,在对GPS/DR组合导航系统中主要误差来源分析的基础上,建立了表示这些误差的数学模型.根据组合系统的数据融合原理,提出一种基于对观测量进行误差补偿的迭代扩展组合卡尔曼滤波算法.对车载GPS/DR组合导航系统提供的实际数据的处理结果表明,该算法在提高GPS定位精度的情况下,能很好地修正DR系统的积累误差,大大提高了组合系统的完整性、可靠性.      

Enhanced multipath mitigation method based on multi-resolution CNR model and adaptive statistical test strategy for real-time kinematic PPP

This study proposes an enhanced multipath mitigation method based on multi-resolution carrier-to-noise-ratio (CNR) model and adaptive statistical test strategy for real-time kinematic precise point positioning (PPP) applications. The multi-resolution CNR model is established with GPS observation data collected from DOY 152 to 181 of 2019 by 230 globally distributed IGS stations, which used to analyze the relevant factors affecting CNR. Statistical results indicate that the CNR is not only related to the satellite elevation, but also closely related to the receiver types and specific satellite. The maximum difference between different receivers can reach 20 dB for the same satellite at the same elevation. In addition, the performance of the CNR is also obviously different between each satellite, and the maximum difference between different satellites is about 10 dB for the same receiver at the same elevation. Hence, in terms of the method which is based on CNR information for multipath detection and mitigation, the independence of receiver types, satellite and frequency must be considered. With the above analysis, this study developed a multi-resolution CNR model based on different receiver types, different satellites and different elevation firstly. Then, combined with the adaptive statistical test strategy which is based on the difference of CNR between inter-frequency and the difference of CNR between adjacent epochs, the multipath can be detected effectively. For the epoch which affected by multipath, the down-weighted strategy based on CNR is adopted to mitigate the influence of multipath on positioning. Real-time kinematic PPP data are collected to assess the proposed method, and the results demonstrate that the proposed method can detect the multipath effectively, and the detection rate can reach 90.28%. Moreover, after adopting the mitigation strategy, the RMS bias of the east, north and up components are improved about 19.95%, 17.89% and 23.07% compared to the original results, respectively. It is worth noting that this proposed method is also suitable for other GNSS, such as GLONASS and BDS, but the corresponding CNR model must be established simultaneously.