An Improved Fast Estimation of Satellite Phase Fractional Cycle Biases

Satellite phase fractional cycle biases (FCBs) are crucial to precise point positioning with ambiguity resolution (PPP–AR), and they can improve the accuracy and reliability of a solution. Traditional methods need multiple iterations and need to keep the same reference when estimating satellite phase fractional cycle biases. In this paper, we propose an improved fast estimation of FCB, which does not need any iterations and can select any reference when estimating FCB. We compare the suitability and precision of a traditional and a proposed method by BDS-3 experiments. The results of the FCB experiments show that the calculated time of the proposed method is less than the traditional method and that computation efficiency is increased by 34.71%. These two methods have a similar rate of fixed epochs and ambiguities in the static and dynamic models. However, the time to first fix (TTFF) of the proposed method decreased by 19.69% and 28.83% for the static and dynamic models, respectively. The results show that the proposed method has a better convergence time in PPP–AR.

LS-VCE Applied to Stochastic Modeling of GNSS Observation Noise and Process Noise

Stochastic models play a crucial role in global navigation satellite systems (GNSS) data processing. Many studies contribute to the stochastic modeling of GNSS observation noise, whereas few studies focus on the stochastic modeling of process noise. This paper proposes a method that is able to jointly estimate the variances of observation noise and process noise. The method is flexible since it is based on the least-squares variance component estimation (LS-VCE), enabling users to estimate the variance components that they are specifically interested in. We apply the proposed method to estimate the variances for the dual-frequency GNSS observation noise and for the process noise of the receiver code bias (RCB). We also investigate the impact of the stochastic model upon parameter estimation, ambiguity resolution, and positioning. The results show that the precision of GNSS observations differs in systems and frequencies. Among the dual-frequency GPS, Galileo, and BDS code observations, the precision of the BDS B3 observations is highest (better than 0.2 m). The precision of the BDS phase observations is better than two millimeters, which is also higher than that of the GPS and Galileo observations. For all three systems, the RCB process noise ranges from 0.5 millimeters to 1 millimeter, with a data sampling rate of 30 s. An improper stochastic model of the observation noise results in an unreliable ambiguity dilution of precision (ADOP) and position dilution of precision (PDOP), thus adversely affecting the assessment of the ambiguity resolution and positioning performance. An inappropriate stochastic model of RCB process noise disturbs the estimation of the receiver clock and the ionosphere delays and is thus harmful for timing and ionosphere retrieval applications.

Real-Time Precise Orbit Determination for LEO between Kinematic and Reduced-Dynamic with Ambiguity Resolution

The real-time integer-ambiguity resolution of the carrier-phase observation is one of the most effective approaches to enhance the accuracy of real-time precise point positioning (PPP), kinematic precise orbit determination (KPOD), and reduced-dynamic precise orbit determination (RPOD) for low earth orbit (LEO) satellites. In this study, the integer phase clock (IPC) and wide-lane satellite bias (WSB) products from CNES (Centre National d’Etudes Spatiales) are used to fix ambiguity in real time. Meanwhile, the three models of real-time PPP, KPOD, and RPOD are applied to validate the contribution of ambiguity resolution. Experimental results show that (1) the average positioning accuracy of IGS stations for ambiguity-fixed solutions is improved from about 7.14 to 5.91 cm, with an improvement of around 17% compared to the real-time float PPP solutions, with enhancement in the east-west direction particularly significant, with an improvement of about 29%; (2) the average accuracy of the estimated LEO orbit with ambiguity-fixed solutions in the real-time KPOD and RPOD mode is improved by about 16% and 10%, respectively, with respect to the corresponding mode with the ambiguity-float solutions; (3) the performance of real-time LEO RPOD is better than that of the corresponding KPOD, regardless of fixed- or float-ambiguity solutions. Moreover, the average ambiguity-fixed ratio can reach more than 90% in real-time PPP, KPOD, and RPOD.

Single Epoch Ambiguity Resolution of Small-Scale CORS with Multi-Frequency GNSS

The network real-time kinematic (RTK) technique uses continuously operating reference stations (CORS) within a geographic area to model the distance dependent errors, allowing users in the area to solve ambiguities. A key step in network RTK is to fix ambiguities between multiple reference stations. When a new satellite rises or when maintenance happens, many unknown parameters are involved in the mathematical model, and traditional methods take some time to estimate the integer ambiguities reliably. The purpose of this study is the single-epoch ambiguity resolution on small-scale CORS network with inter-station distance of around 50 km. A new differencing scheme is developed to explore the full potential of multi-frequency Global Navigation Satellite System (GNSS). In this scheme, a differencing operation is formed between satellites with the closest mapping functions. With the new differencing scheme, tropospheric error can be mostly neglected after the correction, as well as the double-differencing operation. Numerical tests based on two baselines of 49 km and 35 km show that the success rate of ambiguity resolution can reach more than 90%. The single-epoch ambiguity resolution for reference stations brings many benefits to the network RTK service, for example, the instantaneous recovery after maintenance or when a new satellite rises.

An Elevation Ambiguity Resolution Method Based on Segmentation and Reorganization of TomoSAR Point Cloud in 3D Mountain Reconstruction

Tomographic Synthetic Aperture Radar (TomoSAR) is a breakthrough of the traditional SAR, which has the three-dimentional (3D) observation ability of layover scenes such as buildings and high mountains. As an advanced system, the airborne array TomoSAR can effectively avoid temporal de-correlation caused by long revisit time, which has great application in high-precision mountain surveying and mapping. The 3D reconstruction using TomoSAR has mainly focused on low targets, while there are few literatures on 3D mountain reconstruction. Due to the layover phenomenon, surveying in high mountain areas remains a difficult task. Consequently, it is meaningful to carry out the research on 3D mountain reconstruction using the airborne array TomoSAR. However, the original TomoSAR mountain point cloud faces the problem of elevation ambiguity. Furthermore, for mountains with complex terrain, the points located in different elevation periods may intersect. This phenomenon increases the difficulty of solving the problem. In this paper, a novel elevation ambiguity resolution method is proposed. First, Density-Based Spatial Clustering of Applications with Noise (DBSCAN) and Gaussian Mixture Model (GMM) are combined for point cloud segmentation. The former ensures coarse segmentation based on density, and the latter allows fine segmentation of the abnormal categories caused by intersection. Subsequently, the segmentation results are reorganized in the elevation direction to reconstruct all possible point clouds. Finally, the real point cloud can be extracted automatically under the constraints of the boundary and elevation continuity. The performance of the proposed method is demonstrated by simulations and experiments. Based on the airborne array TomoSAR experiment in Leshan City, Sichuan Province, China in 2019, the 3D model of the surveyed mountain is presented. Moreover, three kinds of external data are applied to fully verify the validity of this method.