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This manuscript reviews recent progress in optical frequency references and optical communication systems and discusses their utilizations in global satellite navigation systems and satellite geodesy. Lasers stabilized with optical cavities or spectroscopy of molecular iodine are analyzed, and a hybrid architecture is proposed to combine both forms of stabilization with the aim of achieving a target frequency stability of 10-15 [s/s] over a wide range of sampling intervals. The synchronization between two optical frequency references in real-time is realized by means of time and frequency transfer on optical carriers. The technologies enabling coherent optical links are reviewed, and the development of an optical communication system for synchronization, ranging and data communication in space is described. An infrastructure exploiting the capabilities of both optical technologies for the realization of a modernized constellation of navigation satellites emitting highly synchronized signals is reviewed. Such infrastructure, named Kepler system, improves satellite navigation in terms intra-system synchronization, orbit determination accuracy, as well as system monitoring and integrity. The potential impact on geodetic key parameters is addressed.

Accuracy of dynamic precise point positioning (PPP) degrades significantly under users’ challenging environments because of the limited or unavailable GPS observations. To overcome such weakness, a tight-integration system of micro-electromechanical systems (MEMS) inertial measurement unit (IMU), odometer, and GPS ionospheric delay constrained PPP is investigated to provide users positions and attitudes with higher accuracy, reliability, and continuity under the weak GPS observability environments. In this approach, the data from different sensors are integrated in two joint extend Kalman filters (EKF). One is for PPP/INS tight-integration and the other one is for odometer aiding the solutions from INS or PPP/INS tight-integration modes. Here, the advantages of slow time-varying ionospheric delay, high-accuracy in short time of inertial navigation system (INS), and hardly-disturbed odometer are utilized effectively to enhance PPP solutions. The corresponding mathematical models are provided and are evaluated by a set of one-hour real land-borne test data collected from a MEMS IMU, an odometer, and a dual-frequency GPS receiver in suburbs of Wuhan city, China, and also a set of simulated weak satellites availability data which is to imitate the GPS availability under unban canyons. Results indicate that the fusion system can improve navigation accuracy of GPS or GPS/INS significantly. That are, more than fifty percentages position enhancements in north-east-down components, and about forty percentages attitude enhancements in roll-pitch-yaw direction under the weak GPS availability.

Motivated by the IGS real-time Pilot Project, GFZ has been developing its own real-time precise positioning service for various applications. An operational system at GFZ is now broadcasting real-time orbits, clocks, global ionospheric model, uncalibrated phase delays and regional atmospheric corrections for standard PPP, PPP with ambiguity fixing, single-frequency PPP and regional augmented PPP. To avoid developing various algorithms for different applications, we proposed a uniform algorithm and implemented it into our real-time software. In the new processing scheme, we employed un-differenced raw observations with atmospheric delays as parameters, which are properly constrained by real-time derived global ionospheric model or regional atmospheric corrections and by the empirical characteristics of the atmospheric delay variation in time and space. The positioning performance in terms of convergence time and ambiguity fixing depends mainly on the quality of the received atmospheric information and the spatial and temporal constraints. The un-differenced raw observation model can not only integrate PPP and NRTK into a seamless positioning service, but also syncretize these two techniques into a unique model and algorithm. Furthermore, it is suitable for both dual-frequency and sing-frequency receivers. Based on the real-time data streams from IGS, EUREF and SAPOS reference networks, we can provide services of global precise point positioning (PPP) with 5–10 cm accuracy, PPP with ambiguity-fixing of 2–5 cm accuracy, PPP using single-frequency receiver with accuracy of better than 50 cm and PPP with regional augmentation for instantaneous ambiguity resolution of 1–3 cm accuracy. We adapted the system for current COMPASS to provide PPP service. COMPASS observations from a regional network of nine stations are used for precise orbit determination and clock estimation in simulated real-time mode, the orbit and clock products are applied for real-time precise point positioning. The simulated real-time PPP service confirms that real-time positioning services of accuracy at dm-level and even cm-level is achievable with COMPASS only.

In this paper, we obtain explicit formulas for the Hilbert series and Hilbert depth of squarefree Veronese ideals in a standard graded polynomial ring., 7 pages, a gap in the previous version is fixed

In order to obtain crustal deformations of higher spatial resolution, existing GPS networks must be densified. This densification can be carried out using single-frequency receivers at moderate costs. However, ionospheric delay handling is required in the data processing. We adapt the Satellite-specific Epoch-differenced Ionospheric Delay model (SEID) for GPS networks with mixed single- and dual-frequency receivers. The SEID model is modified to utilize the observations from the three nearest dual-frequency reference stations in order to avoid contaminations from more remote stations. As data of only three stations are used, an efficient missing data constructing approach with polynomial fitting is implemented to minimize data losses. Data from large scale reference networks extended with single-frequency receivers can now be processed, based on the adapted SEID model. A new data processing scheme is developed in order to make use of existing GPS data processing software packages without any modifications. This processing scheme is evaluated using a sub-network of the German SAPOS network. The results verify that the new scheme provides an efficient way to densify existing GPS networks with single-frequency receivers.

We implement an automatic orbit quality control procedure in order to reduce the effect of satellite orbit error for near real-time estimating of zenith total delay (ZTD). We estimate the three Keplerian parameters of the GPS orbits that represent the main error sources (semi-major axis, inclination, and argument of perigee). We start with an a priori constraint corresponding to the typical orbit accuracy for each parameter and adjust it iteratively according to its estimated value and variance. This data analysis procedure shows an improvement of 20% in ZTD rms compared to a strategy based only on the quality index provided with the IGS predicted orbits. A real-time test with IGS ultra-rapid orbits also shows significant improvement compared to fixing IGS ultra-rapid orbits. This strategy allows for a totally automated estimation of orbital parameters directly from the real-time GPS data, without altering the accuracy of the ZTD estimates.

In the context of the MAGIC project (Meteorological Applications of GPS Integrated Column Water Vapor Measurements in the Western Mediterranean), zenith tropospheric delays (ZTD) are computed from Global Positioning System (GPS) signals at permanent sites in the western Mediterranean area continuously since November 1998. These time series are compared to the equivalent values estimated by integrating the atmospheric column derived from radiosonde profiles and the HIRLAM numerical weather prediction model in order to determine the error statistics of the data. From a year and a half of data, we show that the difference between radiosonde and GPS ZTD has a standard deviation of 12 mm and a bias of less than 5 mm for most stations. The biases between the GPS ZTD and HIRLAM estimates are smaller, but the standard deviation is greater, usually on the order of 17 mm. The standard deviation of the residuals from both comparisons depends greatly on the humidity which produces an annual signal because of the much higher humidity variability in the summer months.