Determination of GPS orbits to submeter accuracy

Orbits for satellites of the Global Positioning System (GPS) were determined with submeter accuracy. Tests used to assess orbital accuracy include orbit comparisons from independent data sets, orbit prediction, ground baseline determination, and formal errors. One satellite tracked 8 hours each day shows rms error below 1 m even when predicted more than 3 days outside of a 1-week data arc. Differential tracking of the GPS satellites in high Earth orbit provides a powerful relative positioning capability, even when a relatively small continental U.S. fiducial tracking network is used with less than one-third of the full GPS constellation. To demonstrate this capability, baselines of up to 2000 km in North America were also determined with the GPS orbits. The 2000 km baselines show rms daily repeatability of 0.3 to 2 parts in 10 to the 8th power and agree with very long base interferometry (VLBI) solutions at the level of 1.5 parts in 10 to the 8th power. This GPS demonstration provides an opportunity to test different techniques for high-accuracy orbit determination for high Earth orbiters. The best GPS orbit strategies included data arcs of at least 1 week, process noise models for tropospheric fluctuations, estimation of GPS solar pressure coefficients, and combine processing of GPS carrier phase and pseudorange data. For data arc of 2 weeks, constrained process noise models for GPS dynamic parameters significantly improved the situation

PPP-RTK and inter-system biases: the ISB look-up table as a means to support multi-system PPP-RTK

PPP-RTK has the potential of benefiting enormously from the integration of multiple GNSS/RNSS systems. However, since unaccounted inter-system biases (ISBs) have a direct impact on the integer ambiguity resolution performance, the PPP-RTK network and user models need to be flexible enough to accommodate the occurrence of system-specific receiver biases. In this contribution we present such undifferenced, multi-system PPP-RTK full-rank models for both network and users. By an application of (Formula presented.)-system theory, the multi-system estimable parameters are presented, thereby identifying how each of the three PPP-RTK components are affected by the presence of the system-specific biases. As a result different scenarios are described of how these biases can be taken into account. To have users benefit the most, we propose the construction of an ISB look-up table. It allows users to search the table for a network receiver of their own type and select the corresponding ISBs, thus effectively realizing their own ISB-corrected user model. By applying such corrections, the user model is strengthened and the number of integer-estimable user ambiguities is maximized

An analytical study of PPP-RTK corrections: precision, correlation and user-impact

PPP-RTK extends the PPP concept by providing single-receiver users, next to orbits and clocks, also information about the satellite phase and code biases, thus enabling single-receiver ambiguity resolution. It is the goal of the present contribution to provide an analytical study of the quality of the PPP-RTK corrections as well as of their impact on the user ambiguity resolution performance. We consider the geometry-free and the geometry-based network derived corrections, as well as the impact of network ambiguity resolution on these corrections. Next to the insight that is provided by the analytical solutions, the closed form expressions of the variance matrices also demonstrate how the corrections depend on network parameters such as number of epochs, number of stations, number of satellites, and number of frequencies. As a result we are able to describe in a qualitative sense how the user ambiguity resolution performance is driven by the data from the different network scenarios

Review and principles of PPP-RTK methods

PPP-RTK is integer ambiguity resolution-enabled precise point positioning. In this contribution, we present the principles of PPP-RTK, together with a review of different mechanizations that have been proposed in the literature. By application of S-system theory, the estimable parameters of the different methods are identified and compared. Their interpretation is essential for gaining a proper insight into PPP-RTK in general, and into the role of the PPP-RTK corrections in particular. We show that PPP-RTK is a relative technique for which the ‘single-receiver user’ integer ambiguities are in fact double-differenced ambiguities. We determine the transformational links between the different methods and their PPP-RTK corrections, thereby showing how different PPP-RTK methods can be mixed between network and users. We also present and discuss four different estimators of the PPP-RTK corrections. It is shown how they apply to the different PPP-RTK models, as well as why some of the proposed estimation methods cannot be accepted as PPP-RTK proper. We determine analytical expressions for the variance matrices of the ambiguity-fixed and ambiguity-float PPP-RTK corrections. This gives important insight into their precision, as well as allows us to discuss which parts of the PPP-RTK correction variance matrix are essential for the user and which are not

Review of code and phase biases in multi-GNSS positioning

A review of the research conducted until present on the subject of Global Navigation Satellite System (GNSS) hardware-induced phase and code biases is here provided. Biases in GNSS positioning occur because of imperfections and/or physical limitations in the GNSS hardware. The biases are a result of small delays between events that ideally should be simultaneous in the transmission of the signal from a satellite or in the reception of the signal in a GNSS receiver. Consequently, these biases will also be present in the GNSS code and phase measurements and may there affect the accuracy of positions and other quantities derived from the observations. For instance, biases affect the ability to resolve the integer ambiguities in Precise Point Positioning (PPP), and in relative carrier phase positioning when measurements from multiple GNSSs are used. In addition, code biases affect ionospheric modeling when the Total Electron Content is estimated from GNSS measurements. The paper illustrates how satellite phase biases inhibit the resolution of the phase ambiguity to an integer in PPP, while receiver phase biases affect multi-GNSS positioning. It is also discussed how biases in the receiver channels affect relative GLONASS positioning with baselines of mixed receiver types. In addition, the importance of code biases between signals modulated onto different carriers as is required for modeling the ionosphere from GNSS measurements is discussed. The origin of biases is discussed along with their effect on GNSS positioning, and descriptions of how biases can be estimated or in other ways handled in the positioning process are provided.QC 20170922</p

Clues from joint inversion of tsunami and geodetic data of the 2011 Tohoku-oki earthquake

The 2011 Tohoku-oki (Mw 9.1) earthquake is so far the best-observed megathrust rupture, which allowed the collection of unprecedented offshore data. The joint inversion of tsunami waveforms (DART buoys, bottom pressure sensors, coastal wave gauges, and GPS-buoys) and static geodetic data (onshore GPS, seafloor displacements obtained by a GPS/acoustic combination technique), allows us to retrieve the slip distribution on a non-planar fault. We show that the inclusion of near-source data is necessary to image the details of slip pattern (maximum slip ~48 m, up to ~35 m close to the Japan trench), which generated the large and shallow seafloor coseismic deformations and the devastating inundation of the Japanese coast. We investigate the relation between the spatial distribution of previously inferred interseismic coupling and coseismic slip and we highlight the importance of seafloor geodetic measurements to constrain the interseismic coupling, which is one of the key-elements for long-term earthquake and tsunami hazard assessment

Precise GRACE baseline determination using GPS

Precision relative navigation is an essential aspect of spacecraft formation flying missions, both from an operational and a scientific point of view. When using GPS as a relative distance sensor, dual-frequency receivers are required for high accuracy at large inter-satellite separations . This allows for a correction of the relative ionospheric path delay and enables double difference integer ambiguity resolution. Although kinematic relative positioning techniques demonstrate promising results for hardware-in-the-loop simulations, they were found to lack an adequate robustness in real-world applications. To overcome this limitation, an extended Kalman Filter modeling the relative spacecraft dynamics has been developed. The filter processes single difference GPS pseudorange and carrier phase observations to estimate the relative position and velocity along with empirical accelerations and carrier phase ambiguities. In parallel, double difference carrier phase ambiguities are resolved on both frequencies using the least square ambiguity decorrelation adjustment (LAMBDA) method in order to fully exploit the inherent measurement accuracy. The combination of reduced dynamic filtering with the LAMBDA method results in smooth relative position estimates as well as fast and reliable ambiguity resolution. The proposed method has been validated with data from the gravity recovery and climate experiment (GRACE) mission. For an 11-day data arc, the resulting solution matches the GRACE K-Band Ranging System measurements with an accuracy of 1 mm, whereby 83% of the double difference ambiguities are resolved