No abstract

On August 22, 2014, the satellites GSAT-0201 and GSAT-0202 of the European GNSS Galileo were unintentionally launched into eccentric orbits. Unexpectedly, this has become a fortunate scientific opportunity since the onboard hydrogen masers allow for a sensitive test of the redshift predicted by the theory of general relativity. In the present Letter we describe an analysis of approximately three years of data from these satellites including three different clocks. For one of these we determine the test parameter quantifying a potential violation of the combined effects of the gravitational redshift and the relativistic Doppler shift. The uncertainty of our result is reduced by more than a factor 4 as compared to the values of Gravity Probe A obtained in 1976.

We report on a new test of the gravitational redshift and thus of local position invariance, an integral part of the Einstein equivalence principle, which is the foundation of general relativity and all metric theories of gravitation. We use data spanning 1008 days from two satellites of Galileo, Europe's global satellite navigation system (GNSS), which were launched in 2014, but accidentally delivered on elliptic rather than circular orbits. The resulting modulation of the gravitational redshift of the onboard atomic clocks allows the redshift determination with high accuracy. Additionally specific laser ranging campaigns to the two satellites have enabled a good estimation of systematic effects related to orbit uncertainties. Together with a careful conservative modelling and control of other systematic effects we measure the fractional deviation of the gravitational redshift from the prediction by general relativity to be (0.19 ± 2.48) × 10 −5 at 1 sigma, improving the best previous test by a factor 5.6. To our knowledge, this represents the first reported improvement on one of the longest standing results in experimental gravitation, the Gravity Probe A hydrogen maser rocket experiment back in 1976.

SUMMARYStandardization activities on Digital Video Broadcasting-Satellite services to Handheld Devices (DVB-SH) have driven the need for a consolidated Land Mobile Satellite (LMS) narrowband channel model. In the DVB-SH system, the satellite broadcasts a signal carrying multimedia services aimed directly to a variety of mobile (handheld or vehicular) and fixed terminals.A three-state LMS channel model that describes the narrowband propagation channel in three possible shadowing states-line-of-sight conditions, moderate shadowing and deep shadowing-had been selected as a baseline for physical layer simulation of the DVB-SH waveform. This type of model, capable of generating complex time series, was originally selected, because it is the simplest model that allows the simulation of first-and second-order effects of the LMS channel in a realistic manner. The main limitations of such model are, first of all, that a classification in three states does not necessarily correspond with reality and, secondly, that the statistical parameters for each state were fixed for a given scenario and elevation angle. Those limitations may impact the selection of Physical Layer parameters of the DVB-SH standard.A new channel model is proposed based on the original three-state model including two major modifications: a reduction in the number of states and the introduction of a versatile selection of statistical parameters describing each state. Furthermore, the state machine is governed either by Markov or by semiMarkov chains. The new-state classification does not necessarily correspond to intuitive physical definitions of the states as before (line-of-sight, shadowing) but instead to channel variations that share similar statistical characteristics. The two-states are termed for convenience, Good and Bad states, representing a range of LOS-to-moderate shadowing and moderate-to-deep shadowing, respectively. For the model parameters selection, datasets at L-and S-band have been analysed using an iterative algorithm that includes automatic data classification and parameter extraction. The proposed model is considered more suitable for the analysis of DVB-SH test cases.This study starts with an overview of the main DVB-SH system parameters and assumptions. The original three-state model is briefly introduced; the new model is presented in detail, including simulator implementation. Finally, both models and experimental data sets are compared on a statistical basis. The performance of both models are discussed to show how effective the model is for the representation of shadowed conditions and therefore, its suitability for the analysis and optimal configuration of the physical and link layer parameters (namely physical layer interleaver size, link layer protection time, overall redundancy, etc.).

Higher-order ionospheric effects (I2+) are one of the main limiting factors in very precise Global Navigation Satellite Systems (GNSS) processing, for applications where millimeter accuracy is demanded. This paper summarizes a comprehensive study of the I2+ effects in range and in GNSS precise products such as receiver position and clock, tropospheric delay, geocenter offset, and GNSS satellite position and clock. All the relevant higher-order contributions are considered: second and third orders, geometric bending, and slant total electron content (dSTEC) bending (i.e., the difference between the STEC for straight and bent paths). Using a realistic simulation with representative solar maximum conditions on GPS signals, both the effects and mitigation errors are analyzed. The usage of the combination of multifrequency L band observations has to be rejected due to its increased noise level. The results of the study show that the main two effects in range are the second-order ionospheric and dSTEC terms, with peak values up to 2 cm. Their combined impacts on the precise GNSS satellite products affects the satellite Z coordinates (up to +1 cm) and satellite clocks (more than ±20 ps). Other precise products are affected at the millimeter level. After correction the impact on all the precise GNSS products is reduced below 5 mm. We finally show that the I2+ impact on a Precise Point Positioning (PPP) user is lower than the current uncertainties of the PPP solutions, after applying consistently the precise products (satellite orbits and clocks) obtained under I2+ correction.