Satellite Clock Bias Prediction Research Articles

Enhancing satellite clock bias prediction in BDS with LSTM-attention model

Enhancing satellite clock bias prediction in BDS with LSTM-attention model

Improved BDS-2/3 Satellite Ultra-Fast Clock Bias Prediction Based with the SSA-ELM Model

Ultra-fast satellite clock bias (SCB) products play an important role in real-time precise point positioning. Considering the low accuracy of ultra-fast SCB, which is unable to meet the requirements of precise point position, in this paper, we propose a sparrow search algorithm to optimize the extreme learning machine (SSA-ELM) algorithm in order to improve the performance of SCB prediction in the Beidou satellite navigation system (BDS). By using the sparrow search algorithm's strong global search and fast convergence ability, we further improve the prediction accuracy of SCB of the extreme learning machine. This study uses ultra-fast SCB data from the international GNSS monitoring assessment system (iGMAS) to perform experiments. First, the second difference method is used to evaluate the accuracy and stability of the used data, demonstrating that the accuracy between observed data (ISUO) and predicted data (ISUP) of the ultra-fast clock (ISU) products is optimal. Moreover, the accuracy and stability of the new rubidium (Rb-II) clock and hydrogen (PHM) clock onboard BDS-3 are superior to those of BDS-2, and the choice of different reference clocks affects the accuracy of SCB. Then, SSA-ELM, quadratic polynomial (QP), and a grey model (GM) are used for SCB prediction, and the results are compared with ISUP data. The results show that when predicting 3 and 6 h based on 12 h of SCB data, the SSA-ELM model improves the prediction model by ~60.42%, 5.46%, and 57.59% and 72.27%, 44.65%, and 62.96% as compared with the ISUP, QP, and GM models, respectively. When predicting 6 h based on 12 h of SCB data, the SSA-ELM model improves the prediction model by ~53.16% and 52.09% and by 40.66% and 46.38% compared to the QP and GM models, respectively. Finally, multiday data are used for 6 h SCB prediction. The results show that the SSA-ELM model improves the prediction model by more than 25% compared to the ISUP, QP, and GM models. In addition, the prediction accuracy of the BDS-3 satellite is better than that of the BDS-2 satellite.

Mind evolutionary algorithm optimization in the prediction of satellite clock bias using the back propagation neural network

Satellite clock bias is the key factor affecting the accuracy of the single point positioning of a global navigation satellite system. The traditional model back propagation (BP) neural network is prone to local optimum problems. This paper presents a prediction model and algorithm for the clock bias of the BP neural network based on the optimization of the mind evolutionary algorithm (MEA), which is used to optimize the initial weights and thresholds of the BP neural network. The accuracy of the comparison between clock bias data is verified with and without one-time difference processing. Compared with grey model (GM (1,1)) and BP neural network, this paper discusses the advantages and general applicability of this method from different constellation satellites, different atomic clock type satellites, and the amount of modeling data. The accuracy of the grey model (GM(1,1)), BP, and MEA-BP models for satellite clock bias prediction is analyzed and the root mean square error, range difference error, and the mean of the clock bias data compared. The results demonstrate that the prediction accuracy of the three satellites significantly increased after one-time difference processing and that they have good stability. The prediction accuracy of four sessions of 2 h, 3 h, 6 h, and 12 h obtained using the MEA-BP model was better than 0.74, 0.80, 1.12, and 0.87 ns, respectively. The MEA-BP model has a specific degree of improvement in the prediction accuracy of the different sessions. Additionally, the prediction accuracy of different models has a specific relationship with the length of the original modeling sequence, of which BP model is the most affected, and MEABP is relatively less affected by the length of the modeling sequence, indicating that the MEA-BP model has strong anti-interference ability.

A new GM (1,1) model suitable for short‐term prediction of satellite clock bias

Due to the sensitivity of spaceborne atomic clock to many factors, the variation law of satellite clock bias (SCB) can be regarded as a grey system. The GM (1,1) model is a most classical and basic model of grey system, which has been successfully applied in SCB prediction. Moreover, many improved models have been proposed and widely used in various forecasts since GM (1,1) was generated. However, the prediction performance of these models is not obviously improved compared with the classical models in clock bias prediction. In view of this, a new GM (1,1) model has been come up with in this paper by optimising fitting model and initial condition. The new fitting model is obtained by differentiating time response function of winterisation, and the new initial condition is generated through one or more components of the original clock bias sequence. The authors employ GPS rapid and precise SCB provided by the International GNSS Service (IGS) for prediction experiments. The results show that the new GM (1,1) model is effective and feasible, and its prediction accuracy and stability are enormously better than that of the classical GM (1,1) model, especially for ultra-short-term prediction.

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

The variation law of satellite clock bias (SCB) can be regarded as a grey system because the spaceborne atomic clock is very sensitive and vulnerable to many factors. GM (1,1) model is the core and foundation of the grey system, which has been highly valued and successfully applied in SCB prediction since its production. However, there are still some problems to be further studied such as the lack of stability of its prediction effect in practical application. In view of this, an improved GM (1,1) model by optimizing the initial condition has been proposed in this paper so as to increase the prediction performance. The new initial condition is obtained by the weighted combination of the latest and oldest components of the original clock bias sequence. And the weight values of these two components are acquired from a method of minimizing the sum of squares of fitting errors. We adopt GPS rapid precision SCB data provided by the International GNSS Service (IGS) for 15 mins, 30 mins, 1 h, 3 h, 6 h, 12 h, and 24 h prediction experiments. The results show that the improved GM (1,1) model is effective and feasible, and its prediction accuracy and stability are significantly better than those of the traditional GM (1,1) model, ARIMA model, and QP model, even for the SCB signal with obvious fluctuation.

Enhancing Short-Term Prediction of BDS-3 Satellite Clock Bias Based with BSO Optimized BP Neural Network

The satellite clock bias (SCB) prediction plays an important role in high-accuracy and real-time navigation and positioning. When predicting the SCB, the performance of the BP neural network is affected by the local optimum due to inaccurate initial parameters. Therefore, we propose an improved BP neural network based on the beetle swarm optimization (BSO-BP) algorithm to improve the performance of SCB prediction in third-generation Beidou satellite navigation system (BDS-3). The proposed model takes advantage of group learning strategy to optimize the initialization parameters of the BP neural network and obtains globally optimized parameters. In order to verify the proposed BSO-BP model, 15 BDS satellites are analyzed in terms of prediction accuracy and stability of SCB. The experimental results show that when predicting 1 hour SCB based on a 12 hours SCB data, the prediction accuracy of the BSO-BP model is the best, with an average accuracy of 0.064 ns. As compared with the LP, QP, and GM models, the average prediction accuracy of the proposed BSO-BP model increases by about 72.6%, 43.4%, and 86%, respectively. As the prediction time increases, the influence of the inaccurate initial parameters on SCB prediction gradually decreases, and the prediction accuracy improves. The proposed BSO-BP model has the best accuracy and stability when predicting the 1 h SCB based on the same data. The prediction stability of the proposed BSO-BP model improves by more than 36% as compared with LP, QP, and GM models. In addition, the prediction accuracies of PHM clock and Rb-II clock improved by more than 47%, as compared with that of the Rb clock. Therefore, the overall performance of the atomic clock based on BDS-3 is better than BDS-2. The positioning accuracy of the BSO-BP model can reach the centimeter level in east, north, and up directions.

Clock bias prediction algorithm for navigation satellites based on a supervised learning long short-term memory neural network

In a satellite navigation system, high-precision prediction of satellite clock bias directly determines the accuracy of navigation, positioning, and time synchronization and is the key to realizing autonomous navigation. To further improve satellite clock bias prediction accuracy, we establish a satellite clock bias prediction model by using long short-term memory (LSTM) that can accurately express the nonlinear characteristics of the navigation satellite clock bias. Outliers in the original clock bias should be preprocessed before using the clock bias for prediction. By analyzing the working principle of the traditional median absolute deviations method, the ambiguity of the mathematical model of that method was improved. Experimental results show that the improved method is better than the traditional method at detecting gross errors. The single difference sequence of the preprocessed satellite clock bias was taken as the research object. First, a quadratic polynomial model was fit to the trend term of the single difference sequence. Second, based on the LSTM neural network model and the basic principles of supervised learning, a supervised learning LSTM network model (SL-LSTM) was proposed that models cyclic and random terms. Finally, the prediction function of the satellite clock bias was realized by extrapolating the model by adding a trend term. We adopt the GPS precision satellite clock bias of International GNSS Service data forecast experiments and apply wavelet neural network (WNN), autoregressive integrated moving average (ARIMA), and quadratic polynomial (QP) models to compare their prediction effects. The average prediction RMSE for 3 h, 6 h, 12 h, 1 d, and 3 d based on the SL-LSTM improved by approximately −21.80, −1.85, 8.57, 2.27, and 40.79%, respectively, compared with the results of the WNN. The average prediction RMSE based on the SL-LSTM improved by approximately 38.23, 65.48, 80.22, 85.18, and 94.51% compared with the ARIMA results. The average prediction RMSE based on the SL-LSTM improved by approximately 82.37, 75.88, 67.24, 45.71, and 58.22% compared with the QP results. Compared with the WNN, the SL-LSTM method has no obvious advantages in the prediction accuracy and stability in short-term prediction but achieves a better long-term prediction accuracy and stability. With an increased prediction duration, the SL-LSTM method is clearly better than the other three methods in terms of the prediction accuracy and stability. The results indicated that the quality of satellite clock bias prediction by the SL-LSTM method is better than that of the above three methods and is more suitable for the middle- and long-term prediction of satellite clock bias.

Improving precise point positioning performance based on Prophet model.

Precision point positioning (PPP) is widely used in maritime navigation and other scenarios because it does not require a reference station. In PPP, the satellite clock bias (SCB) cannot be eliminated by differential, thus leading to an increase in positioning error. The prediction accuracy of SCB has become one of the key factors restricting positioning accuracy. Although International GNSS Service (IGS) provides the ultra-rapid ephemeris prediction part (IGU-P), its quality and real-time performance can not meet the practical application. In order to improve the accuracy of PPP, this paper proposes to use the Prophet model to predict SCB. Specifically, SCB sequence is read from the observation part in the ultra-rapid ephemeris (IGU-O) released by IGS. Next, the SCB sequence between adjacent epochs are subtracted to obtain the corresponding SCB single difference sequence. Then using the Prophet model to predict SCB single difference sequence. Finally, the prediction result is substituted into the PPP positioning observation equation to obtain the positioning result. This paper uses the final ephemeris (IGF) published by IGS as a benchmark and compares the experimental results with IGU-P. For the selected four satellites, compared with the results of the IGU-P, the accuracy of SCB prediction of the model in this paper is improved by about 50.3%, 61.7%, 60.4%, and 48.8%. In terms of PPP positioning results, we use Real-time kinematic (RTK) measurements as a benchmark in this paper. Positioning accuracy has increased by 26%, 35%, and 19% in the N, E, and U directions, respectively. The results show that the Prophet model can improve the performance of PPP.

A New BDS-2 Satellite Clock Bias Prediction Algorithm with an Improved Exponential Smoothing Method

High-accuracy and dependable prediction of the bias of space-borne atomic clocks is extremely crucial for the normal operation of the satellites in the case of interrupted communication. Currently, the clock bias prediction for the Chinese BeiDou Navigation Satellite System (BDS) remains still a huge challenge. To develop a high-precision approach for forecasting satellite clock bias (SCB) in allusion to analyze the shortcomings of the exponential smoothing (ES) model, a modified ES model is proposed hereof, especially for BDS-2 satellites. Firstly, the basic ES models and their prediction mechanism are introduced. As the smoothing coefficient is difficult to determine, this leads to increasing fitting errors and poor forecast results. This issue is addressed by introducing a dynamic “thick near thin far (TNTF)” principle based on the sliding windows (SW) to optimize the best smoothing coefficient. Furthermore, to enhance the short-term forecasted accuracy of the ES model, the gray model (GM) is adopted to learn the fitting residuals of the ES model and combine the forecasted results of the ES model with the predicted results of the GM model from error learning (ES + GM). Compared with the single ES models, the experimental results show that the short-term forecast based on the ES + GM models is improved remarkably, especially for the combination of the three ES model and GM model (ES3 + GM). To further improve the medium-term prediction accuracy of the ES model, the new algorithms in ES with GM error learning based on the SW (ES + GM + SW) are presented. Through examples analysis, compared with the single ES2 (ES3) model, results indicate that (1) the average forecast precision of the new algorithms ES2 + GM + SW (ES3 + GM + SW) can be dramatically enhanced by 49.10% (56.40%) from 5.56 ns (6.77 ns) to 2.83 ns (2.95 ns); (2) the average forecast stability of the new algorithms ES2 + GM + SW (ES3 + GM + SW) is also observably boosted by 53.40% (49.60%) from 8.99 ns (16.13 ns) to 4.19 ns (8.13 ns). These new coupling forecast models proposed in this contribution are more effective in clock bias prediction both forecast accuracy and forecast stability.

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

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.

Fusion-based Satellite Clock Bias Prediction Considering Characteristics and Fitted Residue

As Satellite Clock Bias (SCB) prediction may be affected by various factors such as periodic items, sampling length, and stochastic items, a fusion-based prediction method is proposed by considering characteristics of SCB and fitted residue. On this basis, an instance algorithm is presented by fusing four typical prediction models. First, we use Empirical Mode Decomposition (EMD) to pre-process and decompose the SCB series into multiple components with various characteristics. Then, we analyse the fitting performance of each model for different components and prediction length, namely short-, mid- and long-term prediction, and select models with the best performance. Next, we analyse fitted residue of the reconstructed SCB, and select the model with the best fitting results. Finally, we fuse the multiple selected models for SCB prediction. The method is tested using Global Positioning System (GPS) precise clock products provided by the International Global Navigation Satellite System Service (IGS). Experimental results show that, compared with single prediction models and existing combination models, the proposed fusion-based prediction method improves accuracy and stability. In particular, the proposed method is more stable and has better performance for mid- and long-term prediction.

A Grey Model Based on First Differences in the Application of Satellite Clock Bias Prediction

In consideration of the characteristics of satellite clock bias (SCB), a grey GM(1,1) model based on the first difference method is proposed. The first differences between the SCB values of two adjacent epoches are firstly derived to obtain the corresponding first difference sequence. Then, a grey model is made based on the sequence to predict the first difference values for the time following. Finally, the predicted first difference sequence is recovered to be the corresponding predicted SCB. The clock bias data provided by the IGS (International GNSS Service) are used as the experimental data, and the cases with different lengths of modeling data and different prediction step lengths are compared and analyzed. The result shows that the prediction accuracy of this method is higher than that of traditional grey GM(1,1) model, especially for the PRN01 satellite clock, whose forecast effect is the best. With the first difference method, the model prediction accuracy and stability can be effectively improved and enhanced. This method is feasible and reliable for the relatively long term SCB prediction.

Long-term Clock Bias Prediction Based on An ARMA Model

The long-term and reliable prediction of satellite clock bias (SCB) is an important prerequisite for realizing the satellite autonomous navigation and orbit determination. Considering the shortcomings of the quadratic polynomial model (PM) and gray system model (GM) in the long-term prediction of SCB, a new prediction method of SCB based on an ARMA (Auto-Regressive Moving Average) model is proposed to represent the variation characteristics of SCB more accurately. In this paper, a careful precision analysis of the 90-day SCB prediction is made to verify the feasibility and validity of this proposed method by using the IGS (International GNSS Service) clock data. According to the variation characteristics of each satellite clock, the pattern recognition, modeling and prediction of SCB are conducted, and the detailed comparison is made with the other three models at the same time. The results show that adopting the ARMA model can effectively improve the accuracy of long-term SCB prediction.

Application of a Novel Data Mining Method Based on Wavelet Analysis and Chaotic Neural Network on Satellite Clock Bias Prediction

A novel four-stage data mining method for clock bias prediction based on wavelet analysis and chaotic neural networks is proposed. The basic ideas, prediction models and steps of clock bias prediction based on wavelet analysis and chaotic neural network are discussed respectively. And then, to validate the feasibility and validity of the proposed method, make a careful precision analysis for satellite clock bias prediction with the performance parameters of GPS satellite clock, and make comparison and analysis with Grey system model and neural network model. The results of simulation shows that the prediction precision of the novel four-stage model based on wavelet analysis and chaotic neural networks is more better, can afford high precise satellite clock bias prediction for real-time GPS precise point positioning.