Enhancing Satellite Clock Bias Prediction Accuracy in the Case of Jumps with an Improved Grey Model

Ye Yu,Rui Hu,Tao Duan,Mo Huang,Changyuan Wang,Mahmoud Mesbah

doi:10.1155/2020/8186568

Abstract

High accuracy and reliable predictions of the bias of in-orbit atomic clocks are crucial to the application of satellites, while their clocks cannot transfer time information with the earth stations. It brings forward a new short-term, mid-long-term, and long-term prediction approach with the grey predicting model (GM(1, 1)) improved by the least absolute deviations (GM(1, 1)-LAD) when there are abnormal cases (larger fluctuations, jumps, and/or singular points) in SCBs. Firstly, it introduces the basic GM(1, 1) models. As the parameters of the conventional GM(1, 1) model determined by the least squares method (LSM) is not the best in these cases, leading to magnify the fitting errors at the abnormal points, the least absolute deviations (LAD) is used to optimize the conventional GM(1, 1) model. Since the objective function is a nondifferentiable characteristic, some function transformation is inducted. Then, the linear programming and the simplex method are used to solve it. Moreover, to validate the prediction performances of the improved model, six prediction experiments are performed. Compared with those of the conventional GM(1, 1) model and autoregressive moving average (ARMA) model, results indicate that (1) the improved model is more adaptable to SCBs predictions of the abnormal cases; (2) the root mean square (RMS) improvement for the improved model are 5.7%∼81.7% and 6.6%∼88.3%, respectively; (3) the maximum improvement of the pseudorange errors (PE) and mean absolute errors (MAE) for the improved model could reach up to 88.30%, 89.70%, and 87.20%, 85.30%, respectively. These results suggest that our improved method can enhance the prediction accuracy and PE for these abnormal cases in SCBs significantly and effectively and deliver a valuable insight for satellite navigation.

Highlights

Atomic clocks are part of the Global Navigation Satellite System (GNSS) and have been placed on the board of satellites [1, 2]. ese atomic clocks are generally the core of sophisticated scientific and technological systems, and their behaviour perform a direct and significant impact on the entire performances of the GNSS [3, 4]
The percentage improvement of pseudorange errors (PE) and mean absolute errors (MAE) is calculated for the improved model compared with those of the conventional GM(1, 1) model and the autoregressive moving average (ARMA) model, which are shown in Tables 1 and 2
In the conventional GM(1, 1) model prediction process, the parameter estimation is performed using least squares method (LSM), which cannot guarantee that the parameters are optimal in predicting satellite clock bias (SCB) with larger fluctuations, jumps, and/or singular points

Summary

Introduction

Atomic clocks are part of the Global Navigation Satellite System (GNSS) and have been placed on the board of satellites [1, 2]. ese atomic clocks are generally the core of sophisticated scientific and technological systems, and their behaviour perform a direct and significant impact on the entire performances of the GNSS [3, 4]. Due to its own performances and the influence of the complex environment in the space, the clock bias needs to be compared and calibrated with the ground station’s atomic clock to maintain more accurate time information. E short-term clock bias predicted in advance is necessary to participate in navigation and positioning when communications are interrupted for short periods of time. In the case of satellite malfunction for a long period of time, the mid-long-term and long-term clock bias predicted beforehand can be used to maintain the basic performances of the whole system. Erefore, prediction accuracy’s improving of satellite clock bias (SCB) is of vital importance for the autonomous navigation capability of satellites and the precision of real-time positioning [9, 10] In the case of satellite malfunction for a long period of time, the mid-long-term and long-term clock bias predicted beforehand can be used to maintain the basic performances of the whole system. erefore, prediction accuracy’s improving of satellite clock bias (SCB) is of vital importance for the autonomous navigation capability of satellites and the precision of real-time positioning [9, 10]

Methods

Results

Conclusion