Heike Bock

Bio: Heike Bock is an academic researcher from University of Bern. The author has contributed to research in topics: Orbit determination & Global Positioning System. The author has an hindex of 23, co-authored 70 publications receiving 3327 citations.

GNSS processing at CODE: status report

Abstract: Since May 2003, the Center for Orbit Determination in Europe (CODE), one of the analysis centers of the International GNSS Service, has generated GPS and GLONASS products in a rigorous combined multi-system processing scheme, which promises the best possible consistency of the orbits of both systems. The resulting products, in particular the satellite orbits and clocks, are easily accessible by the user community. In the first part of this article, we focus on the generation of the combined global products at CODE, where we put emphasis not only on accuracy, but also on completeness. We study the impact of GLONASS on the CODE products, and the benefit of using them. Last, but not least, we introduce AGNES (Automated GNSS Network for Switzerland), a regional tracking network of small extensions (roughly 400 km East–West, 200 km North–South), which consequently tracks all GNSS satellites and analyzes their measurements using the CODE products.

High-rate GPS clock corrections from CODE: support of 1 Hz applications

Abstract: GPS zero-difference applications with a sampling rate up to 1 Hz require corresponding high-rate GPS clock corrections. The determination of the clock corrections in a full network solution is a time-consuming task. The Center for Orbit Determination in Europe (CODE) has developed an efficient algorithm based on epoch-differenced phase observations, which allows to generate high-rate clock corrections within reasonably short time (< 2 h) and with sufficient accuracy (on the same level as the CODE rapid or final clock corrections, respectively). The clock determination procedure at CODE and the new algorithm is described in detail. It is shown that the simplifications to speed up the processing are not causing a significant loss of accuracy for the clock corrections. The high-rate clock corrections have in essence the same quality as clock corrections determined in a full network solution. In order to support 1 Hz applications 1-s clock corrections would be needed. The computation time, even for the efficient algorithm, is not negligible, however. Therefore, we studied whether a reduced sampling is sufficient for the GPS satellite clock corrections to reach the same or only slightly inferior level of accuracy as for the full 1-s clock correction set. We show that high-rate satellite clock corrections with a spacing of 5 s may be linearly interpolated resulting in less than 2% degradation of accuracy.

Phase center modeling for LEO GPS receiver antennas and its impact on precise orbit determination

Abstract: Most satellites in a low-Earth orbit (LEO) with demanding requirements on precise orbit determination (POD) are equipped with on-board receivers to collect the observations from Global Navigation Satellite systems (GNSS), such as the Global Positioning System (GPS). Limiting factors for LEO POD are nowadays mainly encountered with the modeling of the carrier phase observations, where a precise knowledge of the phase center location of the GNSS antennas is a prerequisite for high-precision orbit analyses. Since 5 November 2006 (GPS week 1400), absolute instead of relative values for the phase center location of GNSS receiver and transmitter antennas are adopted in the processing standards of the International GNSS Service (IGS). The absolute phase center modeling is based on robot calibrations for a number of terrestrial receiver antennas, whereas compatible antenna models were subsequently derived for the remaining terrestrial receiver antennas by conversion (from relative corrections), and for the GNSS transmitter antennas by estimation. However, consistent receiver antenna models for space missions such as GRACE and TerraSAR-X, which are equipped with non-geodetic receiver antennas, are only available since a short time from robot calibrations. We use GPS data of the aforementioned LEOs of the year 2007 together with the absolute antenna modeling to assess the presently achieved accuracy from state-of-the-art reduced-dynamic LEO POD strategies for absolute and relative navigation. Near-field multipath and cross-talk with active GPS occultation antennas turn out to be important and significant sources for systematic carrier phase measurement errors that are encountered in the actual spacecraft environments. We assess different methodologies for the in-flight determination of empirical phase pattern corrections for LEO receiver antennas and discuss their impact on POD. By means of independent K-band measurements, we show that zero-difference GRACE orbits can be significantly improved from about 10 to 6 mm K-band standard deviation when taking empirical phase corrections into account, and assess the impact of the corrections on precise baseline estimates and further applications such as gravity field recovery from kinematic LEO positions.

A silent slip event on the deeper Cascadia subduction interface.

Abstract: Continuous Global Positioning System sites in southwestern British Columbia, Canada, and northwestern Washington state, USA, have been moving landward as a result of the locked state of the Cascadia subduction fault offshore In the summer of 1999, a cluster of seven sites briefly reversed their direction of motion No seismicity was associated with this event The sudden displacements are best explained by ∼2 centimeters of aseismic slip over a 50-kilometer-by-300-kilometer area on the subduction interface downdip from the seismogenic zone, a rupture equivalent to an earthquake of moment magnitude 67 This provides evidence that slip of the hotter, plastic part of the subduction interface, and hence stress loading of the megathrust earthquake zone, can occur in discrete pulses

Resolution of GPS carrier-phase ambiguities in Precise Point Positioning (PPP) with daily observations

Abstract: Precise Point Positioning (PPP) has been demonstrated to be a powerful tool in geodetic and geodynamic applications. Although its accuracy is almost comparable with network solutions, the east component of the PPP results is still to be improved by integer ambiguity fixing, which is, up to now, prevented by the presence of the uncalibrated phase delays (UPD) originating in the receivers and satellites. In this paper, it is shown that UPDs are rather stable in time and space, and can be estimated with high accuracy and reliability through a statistical analysis of the ambiguities estimated from a reference network. An approach is implemented to estimate the fractional parts of the single-difference (SD) UPDs between satellites in wide- and narrow-lane from a global reference network. By applying the obtained SD-UPDs as corrections to the SD-ambiguities at a single station, the corrected SD-ambiguities have a naturally integer feature and can therefore be fixed to integer values as usually done for the double-difference ones in the network mode. With data collected at 450 stations of the International GNSS Service (IGS) through days 106 to 119 in 2006, the efficiency of the presented ambiguity-fixing strategy is validated using IGS Final products. On average, more than 80% of the independent ambiguities could be fixed reliably, which leads to an improvement of about 27% in the repeatability and 30% in the agreement with the IGS weekly solutions for the east component of station coordinates, compared with the real-valued solutions.

Subduction zone coupling and tectonic block rotations in the North Island, New Zealand

Abstract: [1] The GPS velocity field in the North Island of New Zealand is dominated by the long-term tectonic rotation of the eastern North Island and elastic strain from stress buildup on the subduction zone thrust fault. We simultaneously invert GPS velocities, earthquake slip vectors, and geological fault slip rates in the North Island for the angular velocities of elastic crustal blocks and the spatially variable degree of coupling on faults separating the blocks. This approach allows us to estimate the distribution of interseismic coupling on the subduction zone interface beneath the North Island and the kinematics of the tectonic block rotations. In agreement with previous studies we find that the subduction zone interface beneath the southern North Island has a high slip rate deficit during the interseismic period, and the slip rate deficit decreases northward along the margin. Much of the North Island is rotating as several, distinct tectonic blocks (clockwise at 0.5-3.8 deg Myr -1 ) about nearby axes relative to the Australian Plate. This rotation accommodates much of the margin-parallel component of motion between the Pacific and Australian plates. On the basis of our estimation of the block kinematics we suggest that rotation of the eastern North Island occurs because of the southward increasing thickness of the subducting Hikurangi Plateau. These results have implications for our understanding of convergent margin plate boundary zones around the world, particularly with regard to our knowledge of mechanisms for rapid tectonic block rotations at convergent margins and the role of block rotations in the slip partitioning process.

Short Note: A global model of pressure and temperature for geodetic applications

Abstract: The empirical model GPT (Global Pressure and Temperature), which is based on spherical harmonics up to degree and order nine, provides pressure and temperature at any site in the vicinity of the Earth’s surface. It can be used for geodetic applications such as the determination of a priori hydrostatic zenith delays, reference pressure values for atmospheric loading, or thermal deformation of Very Long Baseline Interferometry (VLBI) radio telescopes. Input parameters of GPT are the station coordinates and the day of the year, thus also allowing one to model the annual variations of the parameters. As an improvement compared with previous models, it reproduces the large pressure anomaly over Antarctica, which can cause station height errors in the analysis of space-geodetic data of up to 1 cm if not considered properly in troposphere modelling. First tests at selected geodetic observing stations show that the pressure biases considerably decrease when using GPT instead of the very simple approaches applied to various Global Navigation Satellite Systems (GNSS) software packages so far. GPT also provides an appropriate model for the annual variability of global temperature.

Single receiver phase ambiguity resolution with GPS data

Abstract: Global positioning system (GPS) data processing algorithms typically improve positioning solution accuracy by fixing double-differenced phase bias ambiguities to integer values. These “double-difference ambiguity resolution” methods usually invoke linear combinations of GPS carrier phase bias estimates from pairs of transmitters and pairs of receivers, and traditionally require simultaneous measurements from at least two receivers. However, many GPS users point position a single local receiver, based on publicly available solutions for GPS orbits and clocks. These users cannot form double differences. We present an ambiguity resolution algorithm that improves solution accuracy for single receiver point-positioning users. The algorithm processes dual- frequency GPS data from a single receiver together with wide-lane and phase bias estimates from the global network of GPS receivers that were used to generate the orbit and clock solutions for the GPS satellites. We constrain (rather than fix) linear combinations of local phase biases to improve compatibility with global phase bias estimates. For this precise point positioning, no other receiver data are required. When tested, our algorithm significantly improved repeatability of daily estimates of ground receiver positions, most notably in the east component by approximately 30% with respect to the nominal case wherein the carrier biases are estimated as real values. In this “static” test for terrestrial receiver positions, we achieved daily repeatability of 1.9, 2.1 and 6.0 mm in the east, north and vertical (ENV) components, respectively. For kinematic solutions, ENV repeatability is 7.7, 8.4, and 11.7 mm, respectively, representing improvements of 22, 8, and 14% with respect to the nominal. Results from precise orbit determination of the twin GRACE satellites demonstrated that the inter-satellite baseline accuracy improved by a factor of three, from 6 to 2 mm up to a long-term bias. Jason-2/Ocean Surface Topography Mission precise orbit determination tests results implied radial orbit accuracy significantly below the 10 mm level. Stability of time transfer, in low-Earth orbit, improved from 40 to 7 ps. We produced these results by applying this algorithm within the Jet Propulsion Laboratory’s (JPL’s) GIPSY/OASIS software package and using JPL’s orbit and clock products for the GPS constellation. These products now include a record of the wide-lane and phase bias estimates from the underlying global network of GPS stations. This implies that all GIPSY–OASIS positioning users can now benefit from this capability to perform single-receiver ambiguity resolution.