Chuang Shi

Precise orbit determination of Beidou Satellites with precise positioning

Chinese Beidou satellite navigation system constellation currently consists of eight Beidou satellites and can provide preliminary service of navigation and positioning in the Asia-Pacific Region. Based on the self-developed software Position And Navigation Data Analysis(PANDA) and Beidou Experimental Tracking Stations (BETS), which are built by Wuhan University, the study of Beidou precise orbit determination, static precise point positioning (PPP), and high precision relative positioning, and differential positioning are carried out comprehensively. Results show that the radial precision of the Beidou satellite orbit determination is better than 10 centimeters. The RMS of static PPP can reach several centimeters to even millimeters for baseline relative positioning. The precision of kinematic pseudo-range differential positioning and RTK mode positioning are 2–4 m and 5–10 cm respectively, which are close to the level of GPS precise positioning. Research in this paper verifies that, with support of ground reference station network, Beidou satellite navigation system can provide precise positioning from several decimeters to meters in the wide area and several centimeters in the regional area. These promising results would be helpful for the implementation and applications of Beidou satellite navigation system.

Total least squares adjustment in partial errors-in-variables models: algorithm and statistical analysis

The weighted total least squares (TLS) method has been developed to deal with observation equations, which are functions of both unknown parameters of interest and other measured data contaminated with random errors. Such an observation model is well known as an errors-in-variables (EIV) model and almost always solved as a nonlinear equality-constrained adjustment problem. We reformulate it as a nonlinear adjustment model without constraints and further extend it to a partial EIV model, in which not all the elements of the design matrix are random. As a result, the total number of unknowns in the normal equations has been significantly reduced. We derive a set of formulae for algorithmic implementation to numerically estimate the unknown model parameters. Since little statistical results about the TLS estimator in the case of finite samples are available, we investigate the statistical consequences of nonlinearity on the nonlinear TLS estimate, including the first order approximation of accuracy, nonlinear confidence region and bias of the nonlinear TLS estimate, and use the bias-corrected residuals to estimate the variance of unit weight.

Recent Development of PANDA Software in GNSS Data Processing

Under the financial support of several Chinese national scientific projects, PANDA (Positioning And Navigation Data Analyst) software developed originally by Wuhan University has achieved the advanced level in the world. PANDA is currently recognized as a main research tool in several famous institutes in the GNSS community. In this paper, the recent development of PANDA software is introduced, including the COSMIC orbit determination in low Earth orbits, the real-time GPS satellite orbit and clock determination and precise point positioning with ambiguity resolution. It is concluded that PANDA is of great improvement in the past five years, and more advancement will be made in its pragmatic aspect especially in engineering applications.

Precise orbit determination of BeiDou constellation based on BETS and MGEX network.

Chinese BeiDou Navigation Satellite System is officially operational as a regional constellation with five Geostationary Earth Orbit (GEO) satellites, five Inclined Geosynchronous Satellite Orbit (IGSO) satellites and four Medium Earth Orbit (MEO) satellites. Observations from the BeiDou Experimental Tracking Stations (BETS) and the IGS Multi-GNSS Experiment (MGEX) network from 1 January to 31 March 2013 are processed for orbit determination of the BeiDou constellation. Various arc lengths and solar radiation pressure parameters are investigated. The reduced set of ECOM five-parameter model produces better performance than the full set of ECOM nine-parameter model for BeiDou IGSO and MEO. The orbit overlap for the middle days of 3-day arc solutions is better than 20 cm and 14 cm for IGSO and MEO in RMS, respectively. Satellite laser ranging residuals are better than 10 cm for both IGSO and MEO. For BeiDou GEO, the orbit overlap of several meters and satellite laser ranging residuals of several decimetres can be achieved.

Evaluation of ASTER GDEM using GPS benchmarks and SRTM in China

The Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model (GDEM) has generated one of the most complete high-resolution digital topographic data sets of the world to date. The ASTER GDEM covers land surfaces between 83° N and 83° S at a spatial resolution of 1 arc-second (approximately 30 m at the equator). As an improvement over Shuttle Radar Topography Mission (SRTM) coverage, the ASTER GDEM will be a very useful product for many applications, such as relief analysis, hydrological studies, and radar interferometry. In this article, its absolute vertical accuracy in China was assessed at five study sites using ground control points (GCPs) from high-accuracy GPS benchmarks and also using a DEM-to-DEM comparison with the Consultative Group on International Agriculture Research Consortium for Spatial Information (CGIAR-CSI) SRTM DEM Version 4.1. It is demonstrated that the vertical accuracy of ASTER GDEM is 26 m (root mean square error (RMSE)) against GPS-GCPs, while for the SRTM DEM it is 23 m. Furthermore, height differences in the GDEM-SRTM comparison appear to be overestimated in the areas with a south or southwest aspect in the five study areas. To a certain extent, the error can be attributed to variations in heights due to land-cover effects and undefined inland waterbodies. But the ASTER GDEM needs further error-mitigating improvements to meet the expected accuracy specification. However, as for its unprecedented detail, it is believed that the ASTER GDEM offers a major alternative in accessibility to high-quality elevation data.

An in situ hand calibration method using a pseudo-observation scheme for low-end inertial measurement units

MEMS chips have become ideal candidates for various applications since they are small sized, light weight, have low power consumption and are extremely low cost and reliable. However, the performance of MEMS sensors, especially their biases and scale factors, is highly dependent on environmental conditions such as temperature. Thus a quick and convenient calibration is needed to be conducted by users in field without any external equipment or any expert knowledge of calibration. A novel and efficient in situ hand calibration method is presented to meet these demands in this paper. The algorithm of the proposed calibration method makes use of the navigation algorithm of the loosely-coupled GPS/INS integrated systems, but replaces the GPS observations with a kind of pseudo-observations, which can be stated as follows: if an inertial measurement unit (IMU) was rotating approximately around its measurement center, the range of its position and its linear velocity both would be within a limited scope. Using a Kalman filtering algorithm, the biases and scale factors of both accelerometer triad and gyroscope triad can be calibrated together within a short period (about 30 s), requiring only motions by hands. Real test results show that the proposed method is suitable for most consumer grade MEMS IMUs due to its zero cost, easy operation and sufficient accuracy.

Real-time detection and repair of cycle slips in triple-frequency GNSS measurements

Cycle slip detection and repair are prerequisites to the use of the global navigation satellite system (GNSS) carrier phases for precise positioning. Modern GNSS techniques introduce triple- or multi-frequency signals that are beneficial for cycle slip detection and repair. We present a new real-time cycle slip detection and repair method based on the independent linear combinations of undifferenced triple-frequency GNSS observations. The proposed method forms three types of linear combinations based on the original observations. These combinations are called extra-wide lane (EWL), wide lane (WL), and narrow lane (NL). Cycle slips on the combinations are determined sequentially in three cascaded steps. The first step employs the geometry-free and ionosphere-free Hatch–Melbourne–Wübbena combination to determine and repair the EWL cycle slips. The second step subtracts the cycle-slip-repaired EWL combination from the WL combination to eliminate the geometry part of the WL combination. This subtraction results in a new function that contains the WL ambiguity and residual ionospheric delay. This function is differenced at two consecutive epochs to determine the WL cycle slips. The residual ionospheric delay difference is ignored because of its small magnitude relative to WL wavelength. The third step determines the NL cycle slips in the same manner as in the second step. The difference is that the cycle-slip-repaired EWL combination is replaced with the more accurate cycle-slip-repaired WL combination. Moreover, the residual ionospheric delay difference is compensated by the ionospheric delay rate derived from the original carrier phase observations. When the EWL, WL, and NL cycle slips are determined, cycle slips on the original carrier phase observations can be uniquely identified. The proposed approach has been tested on 30-s triple-frequency BeiDou navigation satellite system data under different levels of ionospheric variations, and on 30-s triple-frequency global positioning system and quasi-zenith satellite system data. Results indicate that the approach can effectively detect and correct cycle slips even for one cycle under low sampling rate or active ionospheric conditions on each frequency in real time.

Estimating the yaw-attitude of BDS IGSO and MEO satellites

Precise knowledge and consistent modeling of the yaw-attitude of GNSS satellites are essential for high-precision data processing and applications. As the exact attitude control mechanism for the satellites of the BeiDou Satellite Navigation System (BDS) is not yet released, the reverse kinematic precise point positioning (PPP) method was applied in our study. However, we confirm that the recent precise orbit determination (POD) processing for GPS satellites could not provide suitable products for estimating BDS attitude using the reverse PPP because of the special attitude control switching between the nominal and the orbit-normal mode. In our study, we propose a modified processing schema for studying the attitude behavior of the BDS satellites. In this approach, the observations of the satellites during and after attitude switch are excluded in the POD processing, so that the estimates, which are needed in the reverse PPP, are not contaminated by the inaccurate initial attitude mode. The modified process is validated by experimental data sets and the attitude yaw-angles of the BDS IGSO and MEO satellites are estimated with an accuracy of better than

Precise orbit determination of BeiDou constellation: method comparison

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