Spacecraft Doppler tracking with possible violations of LLI and LPI:upper bounds from one-way measurements on MEX

We analyze the post-fit residuals of one-way Doppler tracking data from the Mars Express （MEX） spacecraft to test possible violations of local Lorentz invariance （LLI） and local position invariance （LPI）. These one-way Doppler observations were carried out on 2011 August 7 for about 20 minutes at Sheshan Station of Shanghai Astronomical Observatory in China. These downlink signals were sent by MEX for telemetry at X-band. Because we are not able to decode the data in the form of teleme- try and separate them from the carrier frequency, this makes the post-fit residuals of the Doppler data degrade to the level of 0.1 m s^-1. Even so, the residuals can still impose upper bounds on LLI and LPI at 10^-1, which is consistent with the prediction based on our analysis of the detectability. Although the upper bounds given by three-way Doppler tracking of MEX are better than those obtained in the present work, one-way Doppler measurements still provide a unique chance to test possible violations of LLI and LPI far from the ground stations.

Analysis of the wide area differential correction for BeiDou global satellite navigation system

The regional BeiDou Satellite System, or BDS2, broadcasts a differential correction as Equivalent Satellite Clock Correction to correct both orbit and satellite clock errors. For the global BDS, or BDS3, satellite orbit and clock corrections conforming with RTCA standards will be broadcast to authorized users. The hybrid constellation and regional monitoring network pose challenges for the high precision separation of orbit and satellite clock corrections. Three correction models of kinematic,dynamic and Two-way Satellite Time Frequency Transfer(TWSTFT)-based dynamic were studied to estimate the satellite orbit and clock corrections. The correction accuracy of the three models is compared and analyzed based on the BDS observation data. Results show that the accuracies(root mean square, RMS) of dual-frequency real-time positioning for the three models are about 1.76 m, 1.78 m and 2.08 m respectively, which are comparable with the performance of WAAS and EGNOS. With dynamic corrections, the precision of Precise Point Positioning(PPP) experiments may reach about 23 cm after convergence.

f and g series solutions to a post-Newtonian two-body problem with parameters β and γ

Classical Newtonian f and g series for a Keplerian two-body problem are extended for the case of a post-Newtonian two-body problem with parameters β and γ. These two parameters are introduced to parameterize the post-Newtonian approximation of alternative theories of gravity and they are both equal to1 in general relativity. Up to the order of 30, we obtain all of the coefficients of the series in their exact forms without any cutoff for significant figures. The f and g series for the post-Newtonian two-body problem are also compared with a Runge-Kutta order 7 integrator. Although the f and g series have no superiority in terms of accuracy or efficiency at the order of 7, the discrepancy in the performances of these two methods is not quite distinct. However, the f and g series have the advantage of flexibility for going to higher orders.Some examples of relativistic advance of periastron are given and the effect of gravitational radiation on the scheme of f and g series is evaluated.

Relativistic time transfer for a Mars lander:from proper time to Areocentric Coordinate Time

As the first step in relativistic time transfer for a Mars lander from its proper time to the time scale at the ground station, we investigate the transformation between proper time and Areocentric Coordinate Time （TCA） in the framework of IAU Resolutions. TCA is a local time scale for Mars, which is analogous to the Geocentric Coordinate Time （TCG） for Earth. This transformation contains two contributions： inter- hal and external. The internal contribution comes from the gravitational potential and the rotation of Mars. The external contribution is due to the gravitational fields of other bodies （except Mars） in the Solar System. When the （in）stability of an onboard clock is assumed to be at the level of 10-13, we find that the internal contribution is dominated by the gravitational potential of spherical Mars with necessary corrections asso- ciated with the height of the lander on the areoid, the dynamic form factor of Mars, the flattening of the areoid and the spin rate of Mars. For the external contribution, we find the gravitational effects from other bodies in the Solar System can be safely neglected in this case after calculating their maximum values.

Orbit determination and prediction for Beidou GEO satellites at the time of the spring/autumn equinox

Geostationary(GEO) satellites form an indispensable component of the constellation of Beidou navigation system(BDS). The ephemerides, or predicted orbits of these GEO satellites(GEOs), are broadcast to positioning, navigation, and timing users. User equivalent ranging error(UERE) based on broadcast message is better than 1.5 m(root formal errors: RMS) for GEO satellites. However, monitoring of UERE indicates that the orbital prediction precision is significantly degraded when the Sun is close to the Earth's equatorial plane(or near spring or autumn Equinox). Error source analysis shows that the complicated solar radiation pressure on satellite buses and the simple box-wing model maybe the major contributor to the deterioration of orbital precision. With the aid of BDS' two-way frequency and time transfer between the GEOs and Beidou time(BDT, that is maintained at the master control station), we propose a new orbit determination strategy, namely three-step approach of the multi-satellite precise orbit determination(MPOD). Pseudo-range(carrier phase) data are transformed to geometric range(biased geometric range) data without clock offsets; and reasonable empirical acceleration parameters are estimated along with orbital elements to account for the error in solar radiation pressure modeling. Experiments with Beidou data show that using the proposed approach, the GEOs' UERE when near the autumn Equinox of 2012 can be improved to 1.3 m from 2.5 m(RMS), and the probability of user equivalent range error(UERE)<2.0 m can be improved from 50% to above 85%.

Estimation of the inter-frequency clock bias for the satellites of PRN25 and PRN01

We present two efficient approaches,namely the epoch-differenced(ED) and satellite-and epoch-differenced(SDED) approaches,for the estimation of IFCBs of the two Block IIF satellites.For the analysis,data from 18 stations from the IGS network spanning 96 d is processed.Results show that the IFCBs of PRN25 and PRN01 exhibit periodical signal of one orbit revolution with a magnitude up to 18 cm.The periodical variation of the IFCBs is modeled by a sinusoidal function of the included angle between the sun,earth and the satellite.The presented model enables a consistent use of L1/L2 clock products in L1/L5-based positioning.The algorithm is incorporated into the MGPSS software at SHAO(Shanghai Astronomical Observatory,Chinese Academy of Sciences) and is used to monitor the IFCB variation in near real-time.

Precise absolute positioning for a single-frequency user

A new strategy to realize precise absolute positioning for a single-frequency user is presented. In the presented strategy, the receiver clock and ambiguities are removed using the satelliteand epoch-differenced (SDED) algorithm. As a further development of the SDED algorithm, a regional augmentation network is used to generate the SDED atmospheric delays at the user. The weakened mathematic property due to the epoch-differenced operation is improved by adding the generated atmospheric delays and applying the robust estimation. To test the new approach, the 24-h data at 5 Continuous Operation Reference Station (CORS) stations in Shanghai is processed. The results show a more than 96% success rate, defined as the case where three directions achieve the desired positioning accuracy of 10 cm, when the observation is longer than 20 min. The 20-min static results show that the new method can reach an accuracy of 3.42, 4.76 and 9.26 cm in the North, East and Up directions, respectively. An experiment was carried out to assess the kinematic positioning. The results show that the kinematic positioning accuracy is 4.11, 5.31 and 4.05 cm in the north-south, east-west and height directions,respectively.