Combining multiple arcs for orbit determination using normal equations

<p>The normal equations are widely used to combine elementary least squares solutions, to solve very large problems which are not possible to handle directly. The principle is to reduce each problem to a minimal set of parameters present in the global problem, without removing the corresponding information, and connect them. For instance, one important application is the combination over years of daily network solutions, as performed for the ITRF (Altamimi et al., 2016) [1].</p><p>The approach can also be used in orbit determination to connect arcs solutions in order to construct the solution of a global arc. This was applied for example for GPS constellation solutions as in the article written by Beutler et al. (1996) [2]. Due to the size of the problems, it is interesting to divide for example a three days solution into three one day solutions. Another advantage is that the one day solutions are usually efficiently processed by the orbit determination software. For rapid or ultra-rapid GNSS products this is also very interesting, as the solutions are needed very often for small shifts of the global arc (for example 24 hours arcs, shifted every 6 hours in the case of ultra-rapid products). A further extension is to construct recursive solutions from these elementary arcs, leading to a filter similar to a Kalman filter.</p><p>We propose a unified methodology, associated with an efficient implementation compatible with our least squares software GINS, allowing us to solve the various problems ranging from arc connection to sequential filtering. The final objective is to construct efficient GNSS ultra-rapid products.</p><p>The application on a simple problem consisting in connecting different SLR arcs is shown, as a test case to develop and implement the methodology. In this case, the global solution can also be directly constructed for validation purposes. This study includes the construction of the solution at the end points of the elementary arcs, and also the recovery of the global solution state vectors at every epoch.</p><p>The next step will be to implement more complex parameterizations (including measurement parameters, which are not present in the SLR test case), and to apply this for GNSS constellation solutions.</p>

Extended Geometry and Probability Model for GNSS+ Constellation Performance Evaluation

We proposed an extended geometry and probability model (EGAPM) to analyze the performance of various kinds of (Global Navigation Satellite System) GNSS+ constellation design scenarios in terms of satellite visibility and dilution of precision (DOP) et al. on global and regional scales. Different from conventional methods, requiring real or simulated satellite ephemerides, this new model only uses some basic parameters of one satellite constellation. Verified by the reference values derived from precise satellite ephemerides, the accuracy of visible satellite visibility estimation using EGAPM gets an accuracy better than 0.11 on average. Applying the EGAPM to evaluate the geometry distribution quality of the hybrid GNSS+ constellation, where highly eccentric orbits (HEO), quasi-zenith orbit (QZO), inclined geosynchronous orbit (IGSO), geostationary earth orbit (GEO), medium earth orbit (MEO), and also low earth orbit (LEO) satellites included, we analyze the overall performance quantities of different constellation configurations. Results show that QZO satellites perform slightly better in the Northern Hemisphere than IGSO satellites. HEO satellites can significantly improve constellation geometry distribution quality in the high latitude regions. With 5 HEO satellites included in the third-generation BeiDou navigation satellite system (BDS-3), the average VDOP (vertical DOP) of the 30° N–90° N region can be decreased by 16.65%, meanwhile satellite visibility can be increased by 38.76%. What is more, the inclusion of the polar LEO constellation can significantly improve GNSS service performance. When including with 288 LEO satellites, the overall DOPs (GDOP (geometric DOP), HDOP (horizontal DOP), PDOP (position DOP), TDOP (time DOP), and VDOP) are decreased by about 40%, and the satellite visibility can be increased by 183.99% relative to the Global Positioning System (GPS) constellation.

Helmert Variance Component Estimation for Multi-GNSS Relative Positioning

The Multi-constellation Global Navigation Satellite System (Multi-GNSS) has become the standard implementation of high accuracy positioning and navigation applications. It is well known that the noise of code and phase measurements depend on GNSS constellation. Then, Helmert variance component estimation (HVCE) is usually used to adjust the contributions of different GNSS constellations by determining their individual variances of unit weight. However, HVCE requires a heavy computation load. In this study, the HVCE posterior weighting was employed to carry out a kinematic relative Multi-GNSS positioning experiment with six short-baselines from day of year (DoY) 171 to 200 in 2019. As a result, the HVCE posterior weighting strategy improved Multi-GNSS positioning accuracy by 20.5%, 15.7% and 13.2% in east-north-up (ENU) components, compared to an elevation-dependent (ED) priori weighting strategy. We observed that the weight proportion of both code and phase observations for each GNSS constellation were consistent during the entire 30 days, which indicates that the weight proportions of both code and phase observations are stable over a long period of time. It was also found that the quality of a phase observation is almost equivalent in each baseline and GNSS constellation, whereas that of a code observation is different. In order to reduce the time consumption of the HVCE method without sacrificing positioning accuracy, the stable variances of unit weights of both phase and code observations obtained over 30 days were averaged and then frozen as a priori information in the positioning experiment. The result demonstrated similar ENU improvements of 20.0%, 14.1% and 11.1% with respect to the ED method but saving 88% of the computation time of the HCVE strategy. Our study concludes with the observations that the frozen variances of unit weight (FVUW) could be applied to the positioning experiment for the next 30 days, that is, from DoY 201 to 230 in 2019, improving the positioning ENU accuracy of the ED method by 18.1%, 13.2% and 10.6%, indicating the effectiveness of the FVUW.

Blind Spoofing GNSS Constellation Detection Using a Multi-Antenna Snapshot Receiver

Spoofing of global navigation satellite system (GNSS) signals threatens positioning systems. A counter-method is to detect the presence of spoofed signals, followed by a warning to the user. In this paper, a multi-antenna snapshot receiver is presented to detect the presence of a spoofing attack. The spatial similarities of the array steering vectors are analyzed, and different metrics are used to establish possible detector functions. These include subset methods, Eigen-decomposition, and clustering algorithms. The results generated within controlled spoofing conditions show that a spoofed constellation of GNSS satellites can be successfully detected. The derived system-level detectors increase performance in comparison to pair-wise methods. A controlled test setup achieved perfect detection; however, in real-world cases, the performance would not be as ideal. Some detection metrics and features for blind spoofing detecting, with an array of antennas, are identified, which opens the field for future advanced multi-detector developments.