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

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.

Improved GM (1,1) Model by Optimizing Initial Condition to Predict Satellite Clock Bias

“…ere are many kinds of prediction models, including linear model, quadratic polynomial (QP) [4,5], grey system model (GM) [6], auto-regressive integrated moving average model (ARIMA) [7], Kalman lter model [8], support vector machine model (SVM) [9], machine learning [10][11][12][13], model designed based on the basic principle of the neural network [14], and combined model [15]. Grey model acts as a signi cant role in clock bias prediction because of its simple expression and excellent prediction e ect with less modelling data [16,17]. Univariate rst-order di erential model GM (1,1) is an important part of the grey model, which is widely used in SCB prediction.…”

Prediction of Coalbed Methane Production in China Based on an Optimized Grey System Model

“…In the past 30 years, scholars have made a series of achievements on the grey forecasting models, and their development can be briefly summed up from three dimensions. First, the model structure has gone through a model suitable for modeling an approximately homogeneous exponential sequence, a model suitable for modeling approximately nonhomogeneous exponential sequence, − and adaptive models with intelligent adjustable structure. , Second, the modeling object has expanded from the single real-number sequence to various modeling sequences such as interval grey number sequence, discrete grey number sequence and grey isomerism data sequence. − Third, in terms of parameter optimization, some models have been upgraded in the optimization of the initial value, , the background value , and the order. , These studies enriched and improved the system of grey forecasting model, promoted the wide application of grey forecasting model, − and laid a theoretical foundation for successfully solving various practical problems.…”