The Short-Term Forecast of BeiDou Satellite Clock Bias Based on Wavelet Neural Network

Ai, Qingsong; Xu, Tianhe; Li, Jiajing; Xiong, Hongwei

doi:10.1007/978-981-10-0934-1_14

Cited by 13 publications

(9 citation statements)

References 6 publications

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“…Therefore, research on satellite clock bias (SCB) prediction has been the focus of much research. The common models of clock prediction include quadratic polynomial (QP) models (Huang et al 2011;Wang et al 2016a, b, c), grey models (GMs) (1,1) (Cui et al 2005;Liang et al 2015;Lu et al 2008), spectrum analysis (SA) models (Zheng et al 2010;Heo et al 2010), autoregressive integrated moving average (ARIMA) models (Xu et al 2009;Zhao et al 2012), Kalman filtering (KF) (Davis et al 2012;Huang et al 2012), and artificial neural network (ANN) models and their corresponding combined models (Lei et al 2014;Wang et al 2014;2016a, b, c;Ai et al 2016). At present, these models have obvious advantages and disadvantages in clock bias prediction: For example, QP models have simple structures and good timeliness, but the prediction errors will continue to accumulate with increasing prediction duration, making the prediction accuracy and stability decline significantly.…”

Section: Introductionmentioning

confidence: 99%

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

Huang

Zhai

et al. 2021

GPS Solut

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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.

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Section: Introductionmentioning

confidence: 99%

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

Huang

Zhai

et al. 2021

GPS Solut

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“…There are several traditional methods to predict satellite clock for both short-term and long-term [20], such as quadratic polynomial, grey model, spectrum analysis, and Kalman filter [21]. However, many disadvantages are exposed for these methods.…”

Section: Introductionmentioning

confidence: 99%

An Improved QZSS Satellite Clock Offsets Prediction Based on the Extreme Learning Machine Method

Zhou

Zhu

et al. 2020

IEEE Access

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The Japanese Quasi-Zenith Satellite System (QZSS) has been developed as a GPS (Global Positioning System) complementary system to improve positioning accuracy in the Asia-Pacific region. However, the accuracies of ultra-rapid predicted clocks are not high enough for real-time applications, so it is still a challenge problem. This paper focuses on the clock predictions of the new QZSS constellation. Based on the QZSS clock periodic characteristics, an improved clock prediction method combining the spectrum analysis model (SAM) and extreme learning machine (ELM) is proposed with abbreviation as iELM. The key parameters of iELM are selected carefully including the number of hidden layer nodes and activation function. Further, the input length of the iELM network is optimized and discussed thoroughly. For the purpose of assessing the performance of the proposed algorithm, the clock prediction accuracies are compared among GBU-P (the ultra-rapid predicted orbits/clocks provided by GFZ (Deutsches GeoForschungsZentrum)), SAM and iELM methods. It is demonstrated that iELM keeps in a high level of accuracy below 1.0ns with the predicted time increasing from 0 to 18h, and a little larger during the next six hours. And the QZO (Quasi-Zenith Orbit) satellites perform better than GEO (Geostationary Earth Orbit) satellite. Furthermore, precise point positioning (PPP) for both static and kinematic modes are experimentally studied for 13 IGS (International GNSS (Global Navigation Satellite System) Service) MGEX (Multi-GNSS Experiment) stations in the longitude range between 100°E and 180°E. In the static PPP mode, the iELM method is verified to be effective for the GPS/QZSS constellation as positioning accuracy is improved by 28.3%, 57.7% and 47.4% on average in the east, north and up component with respect to GPS/QZSS GBU-P results. Nearly 70.0% stations achieve sub-decimeter accuracy in the vertical component. As for the kinematic PPP, the iELM method based on GPS/QZSS observations performs much better than the others for shorter convergence time and better positioning accuracy. Compared with GPS/QZSS GBU-P, iELM takes at most a half time to get convergence, and the accuracy is enhanced by 27.6%, 23.7% and 13.9% on average in the east, north and up direction respectively.

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“…However, the estimation is not reliable if a frequency jump happens. Moreover, artificial NNs are employed by scientists to predict clock offsets [11,[20][21][22], e.g., back-propagation neural network (BPNN) and wavelet neural network (WNN), which have the ability to estimate non-linear time series by sample training. However, the topology structure of the WNN is hard to set up, while the BPNN involves an iterative procedure to determine appropriate weights, which requires considerable time consumption.…”

Section: Introductionmentioning

confidence: 99%

Improving Clock Prediction Algorithm for BDS-2/3 Satellites Based on LS-SVM Method

Zhou

Liu

et al. 2019

Remote Sensing

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The satellite clock prediction is crucial to support real-time global satellite precise positioning services. Currently, the clock prediction for the Chinese BeiDou navigation satellite system (BDS) is still challenging to satisfy the precise positioning applications. Based on the exploration of existing prediction models, an improved model combing the spectrum analysis model (SAM) and the least-squares support-vector machine (LS-SVM) is proposed especially for BDS-2/3 satellites. Considering satellite-specific characteristics, the parameters of the LS-SVM method are optimized satellite by satellite, including input length, regularization and kernel parameters. The improved model is evaluated by comparing the predicted clocks of existing methods and the improved model. The bias of the predicted clock offsets are within ±1.0 ns for most medium Earth orbits (MEOs) over three hours employing the improved model, which is better than that of the existing methods and can be applied for several real-time precise positioning applications. The predicted clock offsets are further evaluated by applying clock corrections to precise point positioning (PPP) in both static and kinematic modes for 10 international GNSS service (IGS) Multi-GNSS Experiment (MGEX) stations, including five stations in the Asia-Pacific region. According to the practical engineering experience, 2 dm and 5 dm are defined for static and kinematic PPP, respectively, as a convergence threshold. Then, in the static PPP, the improved model is demonstrated to be effective, and positioning accuracies of some stations obtain more than 15% improvements on average for each direction, which enables them to get sub-decimeter positioning, especially in the Asia-Pacific region. In the kinematic PPP, the improved model performs much better than the others in terms of both the convergence time and the positioning accuracy. The convergence time can be shortened from 1.0 h to below 0.5 h, while the positioning accuracies are enhanced by 16.3%, 10.8%, and 18.9% on average in east, north, and up direction, respectively.

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The Short-Term Forecast of BeiDou Satellite Clock Bias Based on Wavelet Neural Network

Cited by 13 publications

References 6 publications

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

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

An Improved QZSS Satellite Clock Offsets Prediction Based on the Extreme Learning Machine Method

Improving Clock Prediction Algorithm for BDS-2/3 Satellites Based on LS-SVM Method

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