A BDS-2/BDS-3 Integrated Method for Ultra-Rapid Orbit Determination with the Aid of Precise Satellite Clock Offsets

Abstract

The accuracy of ultra-rapid orbits is a key parameter for the performance of GNSS (Global Navigation Satellite System) real-time or near real-time precise positioning applications. The quality of the current BeiDou demonstration system (BDS) ultra-rapid orbits is lower than that of GPS, especially for the new generational BDS-3 satellites due to the fact that the availability of the number of ground tracking stations is limited, the geographic distribution of these stations is poor, and the data processing strategies adopted are not optimal. In this study, improved data processing strategies for the generation of ultra-rapid orbits of BDS-2/BDS-3 satellites are investigated. This includes both observed and predicted parts of the orbit. First, the predicted clock offsets are taken as constraints in the estimation process to reduce the number of the unknown parameters and improve the accuracy of the parameter estimates of the orbit. To obtain more accurate predicted clock offsets for the BDS’ orbit determination, a denoising method (also called the Tikhonov regularization algorithm), inter-satellite correlation, and the partial least squares method are all incorporated into the clock offsets prediction model. Then, the Akaike information criterion (AIC) is used to determine the arc length in the estimation models by taking the optimal arc length in the estimation of the initial orbit states into consideration. Finally, a number of experiments were conducted to evaluate the performance of the ultra-rapid orbits resulting from the proposed methods. Results showed that: (1) Compared with traditional models, the accuracy improvement of the predicted clock offsets from the proposed methods were 40.5% and 26.1% for BDS-2 and BDS-3, respectively; (2) the observed part of the orbits can be improved 9.2% and 5.0% for BDS-2 and BDS-3, respectively, by using the predicted clock offsets as constraints; (3) the accuracy of the predicted part of the orbits showed a high correlation with the AIC value, and the accuracy of the predicted orbits could be improved up to 82.2%. These results suggest that the approaches proposed in this study can significantly enhance the accuracy of the ultra-rapid orbits of BDS-2/BDS-3 satellites.

Improved Strategies for BeiDou Ultrarapid Satellites’ Clock Bias Prediction Using BDS-2 and BDS-3 Integrated Processing

“…where V k is the clock bias series error. In the widely used strategy of modelling clock bias series [6,24], the two-step method for the solution of model coefficients, trend and periodic terms, is divided into two independent parts, which should be theoretically obtained in one-step estimation. Moreover, due to the differences among on-board atomic clocks, the number and types of model coefficients cannot be expressed as same forms for all satellites.…”

“…In previous research studies, several strategies were mainly focused on the neural network to analyze the part of residuals in the prediction model [5,8]. Moreover, the combination of the partial least squares (PLS) and the BPNN algorithms was proposed and discussed to conduct the ultrarapid clock bias prediction [6,24]. However, due to the lack of accuracy information for satellite on-board clock, it is difficult to model and predict the model residuals with a desired method, such as the abnormal values of residuals occurring in certain epochs [24].…”

“…Additionally, an optimized strategy was selected to conduct the prediction of BDS ultrarapid satellites' clock biases, in which the nonlinear terms were analyzed and modelled by a backpropagation neural network (BPNN) algorithm [8]. At present, more than 40 BDS satellites, including BDS-2 and BDS-3, jointly provide the high-accuracy positioning, navigation, and timing services (PNT) [24]. For BDS-3 satellite on-board clock, the advantages and characteristics of BDS-3 experimental satellite clock bias prediction with the aid of intersatellite linking observations were discussed [25].…”

“…Furthermore, it is indicated that the stability of BDS-3 satellite on-board atomic clock frequency is better than that of BDS-2 with more than an order of magnitude [26]. In our previous research studies, the preliminary results of BDS-2 and BDS-3 satellites' integrated prediction for ultrarapid products were outputted and analyzed by the introduction of the intersatellite correlation [6], and its impact on ultrarapid estimation was also investigated [24]. According to one-month period of experiments, the results indicated that BDS ultrarapid satellitepredicted clock bias products can be optimized with the intersatellite correlation, which increased the accuracy of 18hour prediction by 30.7%-47.3% and 49.9%-59.3% for BDS-2 and BDS-3, respectively.…”

“…Compared with the widely used strategy of modelling clock bias prediction [5,8], two main issues should be discussed and optimized in the estimation of model parameters: (1) the steps of modelling are usually divided into two parts, namely, trend and periodic terms, in which the correlations among unknown parameters are ignored [6]; (2) only the significant periodic terms (two in BDS-2 and three in BDS-3) in modelling were considered [24], which inevitably results in significant fitting residuals. erefore, to obtain a more accurate and reliable clock bias prediction model, the strategy should be further improved and optimized, such as the optimal clock bias model parameters.…”