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.     

Using Allan variance to improve stochastic modeling for accurate GNSS/INS integrated navigation

MEMS-based integrated system of a global navigation satellite system (GNSS) and an inertial navigation system (INS) has been widely used in various navigation applications. However, such integration encounters some major limitations. On the one hand, the noisy MEMS-based INS undermines the accuracy with time during the frequently occurring GNSS outages caused by signal blockage or attenuation in certain situations such as urban canyon, tunnels, and high trees. On the other hand, the model mismatch between actual GNSS error and the assumed one would also degrade the obtained accuracy even with continuous GNSS aiding. To improve the overall performance for GNSS/MEMS-INS, better error models can be obtained using Allan variance (AV) analysis technique for modeling inertial sensor errors instead of the commonly recommended auto-regressive processes, and on the other hand, the measurement update in Kalman filter is improved using innovation filtering and AV calculation. The performance of each method and the combined algorithm is evaluated by a field test with either differential GNSS (DGNSS) or single-point positioning (SPP) as external aid. In addition to the considerable navigation enhancement brought by each method, the experimental results show the combined algorithm accomplishes overall accuracy improvements by about 18% (position), 8% (velocity), and 38% (attitude) for integration with DGNSS, and by about 15% (position), 75% (velocity), and 77% (attitude) for that with SPP, compared with corresponding traditional counterparts.     

低轨卫星导航增强星座地基观测仿真系统设计

现阶段整星座低轨卫星观测数据的缺失制约了LEO卫星导航增强研究,针对该问题,本文设计了LEO导航增强星座地基观测仿真系统,构建生成了LEO星座伪距和载波相位观测值的仿真模型;介绍了仿真系统设计流程和架构、仿真地基LEO观测数据;使用RTKLIB进行了标准单点定位（SPP）和精密单点定位（PPP）解算,验证了仿真系统搭建的正确性,以及伪距和载波观测值仿真的正确性。结果表明,相较于只考虑几何距离的地基观测数据,该系统考虑各误差模型后观测数据置信度高,可用于支撑LEO导航增强星座定位研究。     

An enhanced MEMS-INS/GNSS integrated system with fault detection and exclusion capability for land vehicle navigation in urban areas

We describe an enhanced quality control algorithm for the MEMS-INS/GNSS integrated navigation system. It aims to maintain the system’s reliability and availability during global navigation satellite system (GNSS) partial and complete data loss and disturbance, and hence to improve the system’s performance in urban environments with signal obstructions, tunnels, bridges, and signal reflections. To reduce the inertial navigation system (INS) error during GNSS outages, the stochastic model of the integration Kalman filter (KF) is informed by Allan variance analysis and the application of a non-holonomic constraint. A KF with a fault detection and exclusion capability is applied in the loosely and tightly coupled integration modes to reduce the adverse influence of abnormal GNSS data. In order to evaluate the performance of the proposed navigation system, road tests have been conducted in an urban area and the system’s reliability and integrity is discussed. The results demonstrate the effectiveness of different algorithms for reducing the growth of INS error.     

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...     

一种车辆GPS/DR/DMAP组合导航系统

车辆导航系统常采用GPS/DR组合导航方式,在实际使用中若采用联邦滤波器,由于设计结构复杂,各种参数选取对滤波器的性能影响较大,选取不当反而引起导航精度的降低。本文设计了一种GPS/DR滤波器,这种滤波器当GPS接收机在失锁时仍能够为用户导航,并且该滤波器结构简单,设计简易。本文采用了DMAP,纠正了车辆相对于道路的偏差。实测导航实验验证了该滤波器能够满足导航精度要求,适用于城市中车辆导航应用。     

Adaptive GPS/INS integration for relative navigation

Relative navigation based on GPS receivers and inertial measurement units is required in many applications including formation flying, collision avoidance, cooperative positioning, and accident monitoring. Since sensors are mounted on different vehicles which are moving independently, sensor errors are more variable in relative navigation than in single-vehicle navigation due to different vehicle dynamics and signal environments. In order to improve the robustness against sensor error variability in relative navigation, we present an efficient adaptive GPS/INS integration method. In the proposed method, the covariances of GPS and inertial measurements are estimated separately by the innovations of two fundamentally different filters. One is the position-domain carrier-smoothed-code filter and the other is the velocity-aided Kalman filter. By the proposed two-filter adaptive estimation method, the covariance estimation of the two sensors can be isolated effectively since each filter estimates its own measurement noise. Simulation and experimental results demonstrate that the proposed method improves relative navigation accuracy by appropriate noise covariance estimation.     

Quasi-stationary sea surface topography estimation by the multiple input/output method

 Multiple input/multiple output system theory (MIMOST) is briefly presented, and the application of the method to the quasi-stationary sea surface topography (QSST) estimation and the filtering of the input observations are discussed. The repeat character of satellite altimetry missions provides more than one sample of the measured sea surface height (SSH) field, and an approximation of the input signal and error power spectral densities can be determined using this successive information. A case study in the Labrador Sea is considered using SSHs from ERS1 phases C and G, ERS1-GM, ERS2 phase A and TOPEX/POSEIDON altimetric missions in combination with shipborne gravity anomalies. The time period of the observations in this study is from 1993 to 1998. Some comparisons between the techniques used for the power spectral density approximation are carried out and some remarks on the properties of the estimated QSST are presented. Received: 19 October 1999 / Accepted: 23 October 2000     

导航卫星原子钟频率稳定度估计的小波方差方法

国内外学者对小波方差理论在原子钟性能分析方面的应用做了一些研究,但相关文献对小波方差的定义及其表征稳定度的特性描述却并不完全一致,这给应用研究造成不便。为此,首先根据时域方差定义的原理,相应地提出了小波方差、重叠小波方差和小波总方差的概念,然后经综合归纳,针对性地选择给出了应用于原子钟频率稳定度估计的"尺度域"小波方差的定义计算公式及等效自由度的计算方法。最后,通过一个算例与时域方差进行比较分析,总结明确了两者的关系及小波方差的特点,从而说明小波系列方差可以有效地进行原子钟频率稳定度的估计。     

GPS/MEMS INS integrated system for navigation in urban areas

This paper evaluates the performance of a tightly coupled GPS/INS integrated system based on low cost MEMS IMUs in dense urban areas, and investigates two different methods to improve its performance. The first method used is to derive observations from two different constraint equations reflecting the behavior of a typical land vehicle. The first constraint equation is derived assuming that the vehicle does not slip and always remains in contact with the ground. If these assumptions are true the velocity of the vehicle in the plane perpendicular to the forward direction should be zero. The second constraint equation is derived from the fact that the height does not change much in a short time interval in a land vehicular environment. Thus, when a GPS outage occurs (partial/complete), the integrated system combines the INS and constraints-derived virtual measurements to keep the position and velocity errors bounded. This method is suitable for use in real-time applications. The second method is specifically suitable for a post-mission application and involves the use of Rauch-Tung-Striebel (RTS) smoother. The designed system performance is evaluated using two data sets collected in dense urban areas. The obtained results demonstrate the effectiveness of different algorithms considered, in controlling the INS error growth, and indicates the potential of MEMS IMUs for use in land vehicle navigation applications.     

3-D voxel-based solid modeling of a broad-leaved tree for accurate volume estimation using portable scanning lidar

We developed a method to produce a 3-D voxel-based solid model of a tree based on portable scanning lidar data for accurate estimation of the volume of the woody material. First, we obtained lidar measurements with a high laser pulse density from several measurement positions around the target, a Japanese zelkova tree. Next, we converted lidar-derived point-cloud data for the target into voxels. The voxel size was 0.5 cm × 0.5 cm × 0.5 cm. Then, we used differences in the spatial distribution of voxels to separate the stem and large branches (diameter > 1 cm) from small branches (diameter ⩽ 1 cm). We classified the voxels into sets corresponding to the stem and to each large branch and then interpolated voxels to fill out their surfaces and their interiors. We then merged the stem and large branches with the small branches. The resultant solid model of the entire tree was composed of consecutive voxels that filled the outer surface and the interior of the stem and large branches, and a cloud of voxels equivalent to small branches that were discretely scattered in mainly the upper part of the target. Using this model, we estimated the woody material volume by counting the number of voxels in each part and multiplying the number of voxels by the unit voxel volume (0.13 cm³). The percentage error of the volume of the stem and part of a large branch was 0.5%. The estimation error of a certain part of the small branches was 34.0%.     

导航工程专业最优估计课程教学改革与思考

为满足武汉大学测绘学院导航工程专业后续课程和导航技术发展需要,最优估计课程实施了理论与实践融合的教学改革.本论文首先介绍导航工程专业对最优估计课程的要求,接着分析了本课程的教学理念,然后探讨了课程内容优化、教材改进、教学方法和手段改革等一系列举措,最后对存在的问题进行思考并提出了改进方案.     

北斗/惯导的快速混合高斯UKF算法

为进一步改善北斗/惯导中无迹卡尔曼滤波的精度,针对导航系统中噪声随机模型本质上的非高斯分布特性,结合有限高斯概率分布可近似任意概率密度函数的理论,以混合高斯UKF滤波为框架,提出了一种快速混合高斯UKF算法。该算法使用奇异值分解替代无迹变换产生采样点中的协方差平方根计算,和迭代中构造有限分量混合高斯模型二次近似后验二阶矩减少子滤波器数量的思路,改善了传统算法子滤波器数量随迭代次数成指数变化而增加计算成本的状况,一定程度上提高了计算的实时性。通过对北斗/惯导紧耦合系统的数据仿真实验,结果分析表明:相对于传统算法,本文提出的新算法在保证滤波精度的同时,计算量较低、实时性较好,适合于处理非高斯非线性北斗/惯导组合导航定位的滤波计算问题。     

Using high resolution QuickBird imagery for crop identification and area estimation

Imagery from recently launched high spatial resolution satellite sensors offers new opportunities for crop assessment and monitoring. A 2.8-m multispectral QuickBird image covering an intensively cropped area in south Texas was evaluated for crop identification and area estimation. Three reduced-resolution images with pixel sizes of 11.2 m, 19.6 m, and 30.8 m were also generated from the original image to simulate coarser resolution imagery from other satellite systems. Supervised classification techniques were used to classify the original image and the three aggregated images into five crop classes (grain sorghum, cotton, citrus, sugarcane, and melons) and five non-crop cover types (mixed herbaceous species, mixed brush, water bodies, wet areas, and dry soil/roads). The five non-crop classes in the 10-category classification maps were then merged as one class. The classification maps were filtered to remove the small inclusions of other classes within the dominant class. For accuracy assessment of the classification maps, crop fields were ground verified and field boundaries were digitized from the original image to determine reference field areas for the five crops. Overall accuracy for the unfiltered 2.8-m, 11.2-m, 19.6-m, and 30.8-m classification maps were 71.4, 76.9, 77.1, and 78.0%, respectively, while overall accuracy for the respective filtered classification maps were 83.6, 82.3, 79.8, and 78.5%. Although increase in pixel size improved overall accuracy for the unfiltered classification maps, the filtered 2.8-m classification map provided the best overall accuracy. Percentage area estimates based on the filtered 2.8-m classification map (34.3, 16.4, 2.3, 2.2, 8.0, and 36.8% for grain sorghum, cotton, citrus, sugarcane, melons, and non-crop, respectively) agreed well with estimates from the digitized polygon map (35.0, 17.9, 2.4, 2.1, 8.0, and 34.6% for the respective categories). These results indicate that QuickBird imagery can be a useful data source for identifying crop types and estimating crop areas.     

A wavelet-extreme learning machine for low-cost INS/GPS navigation system in high-speed applications

The combined navigation system consisting of both global positioning system (GPS) and inertial navigation system (INS) results in reliable, accurate, and continuous navigation capability when compared to either a GPS or an INS stand-alone system. To improve the overall performance of low-cost micro-electro-mechanical systems (MEMS)-based INS/GPS by considering a high level of stochastic noise on low-cost MEMS-based inertial sensors, a highly complex problems with noisy real data, a high-speed vehicle, and GPS signal outage during our experiments, we suggest two approaches at different steps: (1) improving the signal-to-noise ratio of the inertial sensor measurements and attenuating high-frequency noise using the discrete wavelet transform technique before data fusion while preserving important information like the vehicle motion information and (2) enhancing the positioning accuracy and speed by an extreme learning machine (ELM) which has the characteristics of quick learning speed and impressive generalization performance. We present a single-hidden layer feedforward neural network which is employed to optimize the estimation accuracy and speed by minimizing the error, especially in the high-speed vehicle and real-time implementation applications. To validate the performance of our proposed method, the results are compared with an adaptive neuro-fuzzy inference system (ANFIS) and an extended Kalman filter (EKF) method. The achieved accuracies are discussed. The results suggest a promising and superior prospect for ELM in the field of positioning for low-cost MEMS-based inertial sensors in the absence of GPS signal, as it outperforms ANFIS and EKF by approximately 50 and 70%, respectively.     

Using CORINE land cover and the point survey LUCAS for area estimation

CORINE land cover 2000 (CLC2000) is a European land cover map produced by photo-interpretation of Landsat ETM+ images. Its direct use for area estimation can be strongly biased and does not generally report single crops. CLC areas need to be calibrated to give acceptable statistical results.LUCAS (land use/cover area frame survey) is a point survey carried out in 2001 and 2003 in the European Union (EU15) on a systematic sample of clusters of points. LUCAS is especially useful for area estimation in geographic units that do not coincide with administrative regions, such as set of coastal areas defined with a 10 km buffer. Some variance estimation issues with systematic sampling of clusters are analysed.The contingency table obtained overlaying CLC and LUCAS gives the fine scale composition of CLC classes. Using CLC for post-stratification of LUCAS is equivalent to the direct calibration estimator when the sampling units are points. Stratification is easier to adapt to a scheme in which the sampling units are the clusters of points used in LUCAS 2001/2003.     

基于SINS／GPS的无人机组合导航系统建模与仿真

根据无人机的飞行特点以及SINS(捷联惯导)和GPS(全球定位系统)的优缺点,利用轨迹发生器设计无人机的飞行轨迹,建立基于SINS/GPS的无人机组合导航系统,依据卡尔曼滤波的相关原理对系统进行数学建模和计算仿真,验证无人机SINS/GPS组合导航系统的可靠性。