Tianhe Xu

GPS/BDS short-term ISB modelling and prediction

The Chinese BeiDou Navigation Satellite System (BDS) has completed its first milestone by providing coverage of the Asia–Pacific area navigation service since December 27, 2012. With the combination of BDS, the GNSS precise point positioning (PPP) can improve its positioning accuracy, availability and reliability. However, in order to achieve the best positioning solutions, the inter-system bias (ISB) between GPS and BDS must be resolved as precisely as possible. In this study, a 1-week period (GPS week 1810) of GPS/BDS observations for 18 distributed stations from the International GNSS Service Multi-GNSS Experiment are processed. Primarily, the ISB is estimated by an extended Kalman filter as a piece-wise parameter every 30xa0min. Then we generate a smoothed ISB series (ISB_s) with a sliding window median filter to reject the outliers from the original estimated ISB series (ISB_o). After analysing the characteristics of the ISB_s, a short-term station-dependent ISB model based on a 1-week period is proposed in this study. This model consists of a quadratic polynomial in time and two or three periodic functions with diurnal and semi-diurnal periods. Frequency spectrum analysis is used to determine the periods of the periodic functions, and the coefficients of the quadratic function and the periodic functions are estimated by least squares. For model verification, we compare the ISB derived from the model (ISB_m) with ISB_s (assumed the true values). The comparisons indicate an almost normal distribution. It is found that the proposed model is consistent with the true values: the root-mean-square (RMS) values being about 0.7xa0ns, and some stations are even better. This means that the short-term ISB model proposed has a high fitting accuracy. Hence, it can be used for ISB prediction. Comparing the prediction ISB series (ISB_p) with ISB_s in the following week (GPS week 1811), we can draw the conclusion that the accuracy of the prediction declines with an increase in the time period. The 1-day period precision can achieve 0.57–1.21xa0ns, while the accuracy of the 2-day prediction decreases to 0.77–1.72xa0ns. Hence, we recommend a predicting duration of 1xa0day. The proposed model will be beneficial for subsequent GPS/BDS PPP or precise orbit determination (POD) since the ISB derived from this model can be considered as a priori constraint in the PPP/POD solutions. With this a priori constraint, the convergence time can be shortened by 19.6, 16.1 and 2.4xa0% in N, E and U components, respectively. The accuracy of result in the E component is remarkably improved by 11.9xa0%.

GNSS navigation and positioning for the GEOHALO experiment in Italy

AbstractnGEOHALO is a joint experiment of several German institutes for atmospheric research and earth observation where exploring airborne gravimetry over Italy using the High Altitude and LOng Range (HALO) aircraft data is one of the major goals. The kinematic positioning of the aircraft, on which all remote sensing instruments are located, by Global Navigation Satellite System (GNSS) is affected by the characteristics of long-distance, long-time duration, and high-platform dynamics which are a key factor for the success of the GEOHALO project. We outline the strategy and method of GNSS data processing which takes into account multiple GNSS systems (GPS and GLONASS), multiple static reference stations including stations from the International GNSS Service (IGS) and the EUropean REFerence network (EUREF), multiple GNSS-receiving equipments mounted on the kinematic platform, geometric relations between multiple antennas, and assumptions of similar characteristic of atmospheric effects within a small area above the aircraft. From this precondition, various data processing methods for kinematic positioning have been developed, applied and compared. It is shown that the proposed method based on multiple reference stations and multiple kinematic stations with a common atmospheric delay parameter can effectively improve the reliability and accuracy of GNSS kinematic positioning.n

M-estimator for the 3D symmetric Helmert coordinate transformation

The M-estimator for the 3D symmetric Helmert coordinate transformation problem is developed. Small-angle rotation assumption is abandoned. The direction cosine matrix or the quaternion is used to represent the rotation. The

A Maneuvered GEO Satellite Orbit Determination Using Robustly Adaptive Kalman Filter

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Spatiotemporal Evaluation of GNSS-R Based on Future Fully Operational Global Multi-GNSS and Eight-LEO Constellations

3×1 multiplicative error vector is defined to represent the rotation estimation error. An analytical solution can be employed to provide the initial approximate for iteration, if the outliers are not large. The iteration is carried out using the iterative reweighted least-squares scheme. In each iteration after the first one, the measurement equation is linearized using the available parameter estimates, the reweighting matrix is constructed using the residuals obtained in the previous iteration, and then the parameter estimates with their variance-covariance matrix are calculated. The influence functions of a single pseudo-measurement on the least-squares estimator and on the M-estimator are derived to theoretically show the robustness. In the solution process, the parameter is rescaled in order to improve the numerical stability. Monte Carlo experiments are conducted to check the developed method. Different cases to investigate whether the assumed stochastic model is correct are considered. The results with the simulated data slightly deviating from the true model are used to show the developed method’s statistical efficacy at the assumed stochastic model, its robustness against the deviations from the assumed stochastic model, and the validity of the estimated variance-covariance matrix no matter whether the assumed stochastic model is correct or not.

The Impacts of the Ionospheric Observable and Mathematical Model on the Global Ionosphere Model

The 3D similarity coordinate transformation with the Gauss–Helmert error model is investigated. The first-order error analysis of an analytical least-squares solution to this problem is developed in detail. While additive errors are assumed in the translation and scale estimates, a 3xa0×xa01 multiplicative error vector is defined to effectively parameterize the rotation matrix estimation error. The propagation of the errors in the coordinate measurements to the errors in the estimated transformation parameters is derived step-by-step, and the formulae for calculating the variance–covariance matrix of the estimated parameters are presented.

Adaptive Kalman filter based on variance component estimation for the prediction of ionospheric delay in aiding the cycle slip repair of GNSS triple-frequency signals

After a brief discussion on the dynamic and geometric orbit determinations, the observation model, dynamic model and Kalman filter for a geostationary (GEO) satellite orbit determination are introduced. A robustly adaptive Kalman filter based on variance component estimation is proposed for orbit determination of a maneuvered GEO satellite. The main idea is to use robust estimation to resist the influence of measurement outliers and use an adaptive factor to control the effect of dynamic model errors. Simulations with the Chinese ground tracking network for a maneuvered GEO satellite were conducted to verify the performance of the proposed orbit determination technique. The results show that it can efficiently control both the influence of outliers and that of thrust force, and can provide high and reliable orbit accuracy.

Robust combination of IGS analysis center GLONASS clocks

When applying the Global Navigation Satellite System (GNSS) for precise kinematic positioning in airborne and shipborne gravimetry, multiple GNSS receiving equipment is often fixed mounted on the kinematic platform carrying the gravimetry instrumentation. Thus, the distances among these GNSS antennas are known and invariant. This information can be used to improve the accuracy and reliability of the state estimates. For this purpose, the known distances between the antennas are applied as a priori constraints within the state parameters adjustment. These constraints are introduced in such a way that their accuracy is taken into account. To test this approach, GNSS data of a Baltic Sea shipborne gravimetric campaign have been used. The results of our study show that an application of distance constraints improves the accuracy of the GNSS kinematic positioning, for example, by about 4 mm for the radial component.