A new nonlinear robust filter is proposed in this paper to deal with the outliers of an integrated Global Positioning System/Strapdown Inertial Navigation System (GPS/SINS) navigation system. The influence of different design parameters for an H ∞ cubature Kalman filter is analysed. It is found that when the design parameter is small, the robustness of the filter is stronger. However, the design parameter is easily out of step in the Riccati equation and the filter easily diverges. In this respect, a singular value decomposition algorithm is employed to replace the Cholesky decomposition in the robust cubature Kalman filter. With large conditions for the design parameter, the new filter is more robust. The test results demonstrate that the proposed filter algorithm is more reliable and effective in dealing with the outliers in the data sets produced by the integrated GPS/SINS system. K E Y

Abstract. Water vapor is the basic parameter used to describe atmospheric conditions. It is rarely contained in the atmosphere during the water cycle, but it is the most active element in rapid space-time changes. Measuring and monitoring the distribution and quantity of water vapor is a necessary task. GPS tomography is a powerful means of providing high spatiotemporal resolution of water vapor density. In this paper, a spatial structure model of a humidity field is constructed using voxel nodes, and new parameterizations for acquiring data about water vapor in the troposphere via GPS are proposed based on inverse distance weighted (IDW) interpolation. Unlike the density of water vapor that is constant within a voxel, the density at a certain point is determined by IDW interpolation. This algorithm avoids the use of horizontal constraints to smooth voxels that are not crossed by satellite rays. A prime number decomposition (PND) access order scheme is introduced to minimize correlation between slant wet delay (SWD) observations. Four experimental schemes for GPS tomography are carried out in dry weather from 2 to 8 August 2015 and rainy days from 9 to 15 August 2015. Using 14 days of data from the Hong Kong Satellite Positioning Reference Station Network (SatRef), the results indicate that water vapor density derived from 4-node methods is more robust than that derived from that of 8 nodes or 12 nodes, or that derived from constant refractivity schemes and the new method has better performance under stable weather conditions than unstable weather (e.g., rainy days). The results also indicate that an excessive number of interpolations in each layer reduce accuracy. However, the accuracy of the tomography results is gradually reduced with increases in altitude below 7000 m. Moreover, in the case of altitudes between 7000 m and the upper boundary layer, the accuracy can be improved by a boundary constraint.

The recent advances of low-cost GNSS receivers have broadened their application field not only in positioning and navigation, but also in deformation monitoring of civil engineering structures and geohazards. Even though some consumer-grade low-cost GNSS receivers can achieve cm-level accuracy, their lower performance compared to the dual-frequency high-end GNSS receivers restricts its systematic application of GNSS technology in monitoring projects. In this study, the noise level and performance of the low-cost GNSS receivers are assessed against geodetic receivers in terms of precision and availability when subjected to different measurements conditions, such as antenna grade, satellite constellation, and base station (antenna-receiver), based on zero- and short-baseline measurements. Furthermore, a new method is developed where a dual low-cost GNSS rover-system is formed by deploying two closely spaced low-cost GNSS receivers (30 cm apart), aiming to model their common error (multipath, satellite constellation, etc.) and reduce their noise level. The analysis of the zero- and short-baseline measurements reveals the potential improvement of the precision of the low-cost receiver by using multi-GNSS measurements and the importance of using a GNSS base station with geodetic antenna. However, development of a methodology which is based on adopting the sidereal filtering and the common mode error technique for the two closely spaced low-cost GNSS receivers may lead to precision of mm-level. The proposed methodology may broaden the application of low-cost GNSS receivers in monitoring networks and mainly for slowly developed deformations.