54
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.
Loading PDF
Improving BDS-2/3 satellite clock bias prediction using a TCN-Transformer framework with cross-attention mechanism
Improving BDS-2/3 satellite clock bias prediction using a TCN-Transformer framework with cross-attention mechanism
Satellite Clock Bias Prediction Method for BeiDou-3 Satellites Based on Entropy Weight Method
In order to improve the accuracy and stability of satellite clock bias prediction, a combined satellite clock bias prediction method based on the entropy weight method is proposed. Firstly, the method adopts a quadratic polynomial model and a gray model to make a single prediction of satellite clock bias and generate two sets of prediction results. Then, by calculating the entropy of error information of the two sets of prediction results, it determines the weights of each model and realizes the optimal fusion of the models. Finally, the entropy weight combination method is used to obtain a higher precision prediction result. Four different types of BeiDou-3 satellites were randomly selected for the prediction test by using the precision satellite clock bias products released by the GNSS Analysis Center of Wuhan University. The results show that the method can provide high-precision short- and medium-term predictions of BeiDou-3 satellite clock bias, and its 6-h average prediction accuracy and stability are 0.22ns and 0.46ns, respectively, which are 72.15% and 48.84% higher than the average prediction accuracy of quadratic polynomial and gray models, and the stability is 70.00% and 20 .69% higher, respectively.
Read more16Long-term Clock Bias Prediction Based on An ARMA Model
Long-term Clock Bias Prediction Based on An ARMA Model
11A 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.
Read moreReview of Research on Satellite Clock Bias Prediction Models in GNSS
As foundational infrastructure for spatiotemporal information, the Global Navigation Satellite System (GNSS) delivers high-precision positioning, navigation, and timing (PNT) services worldwide. However, satellite atomic clock drift causes satellite clock bias, degrading PNT service quality. Compared to post-processed clock bias products and real-time estimation, satellite clock bias prediction offers a key advantage: it provides high-precision real-time clock bias even in scenarios with limited real-time data or poor communication. Through analysis and summarization of error sources in prediction models, this paper proposed generalized modeling frameworks for both classical and AI-based approaches. We reviewed current research on classical mathematical models—including polynomial, grey, Kalman filter, and time series models—and AI-based models such as machine learning (ML), multilayer perceptron (MLP), recurrent neural networks (RNN), and Transformer architectures. Technical characteristics, applicability, and limitations of each model were discussed. While AI-based models demonstrate superior flexibility and adaptability in complex scenarios compared to classical approaches, they require extensive datasets and computational resources. In conclusion, we summarized the advantages, disadvantages, and future research directions, offering insights for developing next-generation real-time high-precision GNSS PNT services.
Read more2On the Application of Long Short-Term Memory Neural Network for Daily Forecasting of PM2.5 in Dakar, Senegal (West Africa)
This study aims to optimize daily forecasts of the PM2.5 concentrations in Dakar, Senegal using a long short-term memory (LSTM) neural network model. Particulate matter, aggravated by factors such as dust, traffic, and industrialization, poses a serious threat to public health, especially in developing countries. Existing models such as the Autoregressive integrated moving average (ARIMA) have limitations in capturing nonlinear relationships and complex dynamics in environmental data. Using four years of daily data collected at the Bel Air station, this study shows that the LSTM neural network model provides more accurate forecasts with a root mean square error (RMSE) of 3.2 μg/m3, whereas the RMSE for ARIMA is about 6.8 μg/m3. The LSTM model predicts reliably up to 7 days in advance, accurately reproducing extreme values, especially during dust event outbreaks and peak travel periods. Computational analysis shows that using Graphical Processing Unit and Tensor Processing Unit processors significantly reduce the execution time, improving the model efficiency while maintaining high accuracy. Overall, these results highlight the usefulness of the LSTM network for air quality prediction and its potential for public health management in Dakar.
Read more2Simulation Research on the Optimization of Rural Tourism System Resilience Based on a Long Short-Term Memory Neural Network—Taking Well-Known Tourist Villages in Heilongjiang Province as Examples
Taking well-known tourist villages in Heilongjiang Province as the research object, we constructed a rural tourism system resilience assessment framework with the dimensions of “environment, institution, economy, society, and culture”. Using a geographical detector to analyze driving factors, an LSTM neural network model was constructed to predict the evolution trend of the rural tourism system resilience of these villages. The resulting insights included the following: ① The rural tourism system resilience of the well-known tourist villages in Heilongjiang Province is at a medium level, with a relatively good degree of development in the environmental dimension and the lowest degree in the economic dimension. ② The existence of financial support, water supply guarantee, domestic waste treatment, livestock manure treatment, and tourism development satisfaction are core driving factors for rural tourism system resilience; there is a non-linear or two-factor enhancement effect among these factors, and the interaction between domestic waste treatment and tourism development satisfaction has the strongest influence, while policy support particularly improves rural tourism system resilience and interacts most frequently with other driving factors. ③ Compared to the backpropagation (BP) neural network, the long short-term memory (LSTM) neural network has better stability and prediction accuracy.
Read more189Multi-Step Short-Term Power Consumption Forecasting with a Hybrid Deep Learning Strategy
Electric power consumption short-term forecasting for individual households is an important and challenging topic in the fields of AI-enhanced energy saving, smart grid planning, sustainable energy usage and electricity market bidding system design. Due to the variability of each household’s personalized activity, difficulties exist for traditional methods, such as auto-regressive moving average models, machine learning methods and non-deep neural networks, to provide accurate prediction for single household electric power consumption. Recent works show that the long short term memory (LSTM) neural network outperforms most of those traditional methods for power consumption forecasting problems. Nevertheless, two research gaps remain as unsolved problems in the literature. First, the prediction accuracy is still not reaching the practical level for real-world industrial applications. Second, most existing works only work on the one-step forecasting problem; the forecasting time is too short for practical usage. In this study, a hybrid deep learning neural network framework that combines convolutional neural network (CNN) with LSTM is proposed to further improve the prediction accuracy. The original short-term forecasting strategy is extended to a multi-step forecasting strategy to introduce more response time for electricity market bidding. Five real-world household power consumption datasets are studied, the proposed hybrid deep learning neural network outperforms most of the existing approaches, including auto-regressive integrated moving average (ARIMA) model, persistent model, support vector regression (SVR) and LSTM alone. In addition, we show a k-step power consumption forecasting strategy to promote the proposed framework for real-world application usage.
Read morePREDICTING FUTURE ENROLLMENT TRENDS AT UNIVERSITAS LANCANG KUNING USING ARIMA AND LSTM MODELS
Abstract: This research is driven by the challenges faced by Universitas Lancang Kuning (UNILAK) in attracting applicants amidst intense competition, especially after the government's policy opened independent pathways to State Universities (PTN) from 2022-2023, which impacted private university applicant numbers. To address this and support strategic planning, this study aims to predict the trend of prospective students applying to all study programs at UNILAK for the period 2025-2027. Two time series models were employed: ARIMA (AutoRegressive Integrated Moving Average) and LSTM (Long Short-Term Memory). Applicant data from 2019 to 2024 was used to build the model. The Augmented Dickey-Fuller (ADF) test confirmed the data's stationarity with a p-value of 0.0. ACF and PACF analyses determined the ARIMA parameters as p=1, d=1, q=1. The LSTM model was trained to capture more complex data patterns. ARIMA predictions for 2025, 2026, and 2027 are 3298.66, 3362.33, and 3371.30, respectively. LSTM predictions for the same years are 3335.64, 3476.52, and 3518.42. Evaluation using Root Mean Squared Error (RMSE) showed ARIMA (RMSE=588.72) to be more accurate than LSTM (RMSE=653.96). Nevertheless, LSTM provided a more optimistic prediction. This study concludes that ARIMA is better suited for short-term planning, while LSTM can be used for more ambitious long-term strategies. Keywords: arima; LSTM; applicants; prediction; university Abstrak: Penelitian ini didorong oleh tantangan Universitas Lancang Kuning (UNILAK) dalam menarik pendaftar di tengah persaingan ketat, khususnya setelah kebijakan pemerintah membuka jalur mandiri ke Perguruan Tinggi Negeri (PTN) sejak 2022-2023, yang menyebabkan penurunan jumlah pendaftar di universitas swasta. Untuk mendukung perencanaan strategis, studi ini bertujuan memprediksi tren jumlah calon mahasiswa yang mendaftar ke seluruh program studi di UNILAK untuk periode 2025-2027.Dua model deret waktu digunakan: ARIMA (AutoRegressive Integrated Moving Average) dan LSTM (Long Short-Term Memory). Data jumlah pendaftar dari 2019 hingga 2024 digunakan untuk membangun model. Uji Augmented Dickey-Fuller (ADF) menunjukkan data stasioner dengan p-value 0,0. Analisis ACF dan PACF menentukan parameter ARIMA sebagai p=1, d=1, q=1. Model LSTM dilatih untuk menangkap pola data yang lebih kompleks.Prediksi ARIMA untuk 2025, 2026, dan 2027 adalah 3298.66, 3362.33, dan 3371.30. Prediksi LSTM untuk tahun yang sama adalah 3335.64, 3476.52, dan 3518.42. Evaluasi menggunakan Root Mean Squared Error (RMSE) menunjukkan ARIMA (RMSE=588.72) lebih akurat daripada LSTM (RMSE=653.96). Meskipun demikian, LSTM memberikan prediksi yang lebih optimis. Studi ini menyimpulkan ARIMA lebih cocok untuk perencanaan jangka pendek, sementara LSTM dapat digunakan untuk strategi jangka panjang yang ambisius. Kata kunci: arima; LSTM; pendaftar; prediksi; universitas
Read more
13Real-Time PPP Based on the Coupling Estimation of Clock Bias and Orbit Error with Broadcast Ephemeris
Satellite orbit error and clock bias are the keys to precise point positioning (PPP). The traditional PPP algorithm requires precise satellite products based on worldwide permanent reference stations. Such an algorithm requires considerable work and hardly achieves real-time performance. However, real-time positioning service will be the dominant mode in the future. IGS is providing such an operational service (RTS) and there are also commercial systems like Trimble RTX in operation. On the basis of the regional Continuous Operational Reference System (CORS), a real-time PPP algorithm is proposed to apply the coupling estimation of clock bias and orbit error. The projection of orbit error onto the satellite-receiver range has the same effects on positioning accuracy with clock bias. Therefore, in satellite clock estimation, part of the orbit error can be absorbed by the clock bias and the effects of residual orbit error on positioning accuracy can be weakened by the evenly distributed satellite geometry. In consideration of the simple structure of pseudorange equations and the high precision of carrier-phase equations, the clock bias estimation method coupled with orbit error is also improved. Rovers obtain PPP results by receiving broadcast ephemeris and real-time satellite clock bias coupled with orbit error. By applying the proposed algorithm, the precise orbit products provided by GNSS analysis centers are rendered no longer necessary. On the basis of previous theoretical analysis, a real-time PPP system was developed. Some experiments were then designed to verify this algorithm. Experimental results show that the newly proposed approach performs better than the traditional PPP based on International GNSS Service (IGS) real-time products. The positioning accuracies of the rovers inside and outside the network are improved by 38.8% and 36.1%, respectively. The PPP convergence speeds are improved by up to 61.4% and 65.9%. The new approach can change the traditional PPP mode because of its advantages of independence, high positioning precision, and real-time performance. It could be an alternative solution for regional positioning service before global PPP service comes into operation.
Read more27Forex market forecasting with two-layer stacked Long Short-Term Memory neural network (LSTM) and correlation analysis
Since it is one of the world's most significant financial markets, the foreign exchange (Forex) market has attracted a large number of investors. Accurately anticipating the forex trend has remained a popular but difficult issue to aid Forex traders' trading decisions. It is always a question of how precise a Forex prediction can be because of the market's tremendous complexity. The fast advancement of machine learning in recent decades has allowed artificial neural networks to be effectively adapted to several areas, including the Forex market. As a result, a slew of research articles aimed at improving the accuracy of currency forecasting has been released. The Long Short-Term Memory (LSTM) neural network, which is a special kind of artificial neural network developed exclusively for time series data analysis, is frequently used. Due to its high learning capacity, the LSTM neural network is increasingly being utilized to predict advanced Forex trading based on previous data. This model, on the other hand, can be improved by stacking it. The goal of this study is to choose a dataset using the Hurst exponent, then use a two-layer stacked Long Short-Term Memory (TLS-LSTM) neural network to forecast the trend and conduct a correlation analysis. The Hurst exponent (h) was used to determine the predictability of the Australian Dollar and United States Dollar (AUD/USD) dataset. TLS-LSTM algorithm is presented to improve the accuracy of Forex trend prediction of Australian Dollar and United States Dollar (AUD/USD). A correlation study was performed between the AUD/USD, the Euro and the Australian Dollar (EUR/AUD), and the Australian Dollar and the Japanese Yen (AUD/JPY) to see how AUD/USD movement affects EUR/AUD and AUD/JPY. The model was compared with Single-Layer Long Short-Term (SL-LSTM), Multilayer Perceptron (MLP), and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise–Improved Firefly Algorithm Long Short-Term Memory. Based on the evaluation metrics Mean Square Error (MSE), Root Mean Square Error, and Mean Absolute Error, the suggested TLS-LSTM, whose data selection is based on the Hurst exponent (h) value of 0.6026, outperforms SL-LSTM, MLP, and CEEMDAN-IFALSTM. The correlation analysis conducted shows both positive and negative relations between AUD/USD, EUR/AUD, and AUD/JPY which means that a change in AUD/USD will affect EUR/AUD and AUD/JPY as recorded depending on the magnitude of the correlation coefficient (r).
Read more37Time series prediction based on LSTM neural network for top tension response of umbilical cables
Time series prediction based on LSTM neural network for top tension response of umbilical cables
48Taxi-Based Mobility Demand Formulation and Prediction Using Conditional Generative Adversarial Network-Driven Learning Approaches
In this paper, a deep learning (DL) framework was proposed to predict the taxi-passenger demand while the spatial, the temporal, and external dependencies were considered simultaneously. The proposed DL framework combined a modified density-based spatial clustering algorithm with noise (DBSCAN) and a conditional generative adversarial network (CGAN) model. More specifically, the modified DBSCAN model was applied to produce a number of sub-networks considering the spatial correlation of taxi pick-up events in the road network. And the CGAN model, fed with the historical taxi passenger demand and other conditional information, was capable to predict the taxi-passenger demands. The proposed CGAN model was made up with two long short-term memory (LSTM) neural networks, which are termed as the generative network ${G}$ and the discriminative network ${D}$ , respectively. Adversarial training process was conducted to the two LSTMs. In the numerical experiment, different model layouts were compared. It was found that different network layouts provided reasonable accuracy. With limited training data, more LSTM layers in the generator network resulted in not only higher accuracy, but also more difficulties in training. Comparisons were also conducted between the proposed prediction model and four typical approaches, including the moving average method, the autoregressive integrated moving method, the neural network model, and the LSTM neural network model. The comparison results showed that the proposed model outperformed all the other methods. And the repeated experiment indicated that the proposed CGAN model provided significant better predictions than the LSTM model did. Future research was recommended to include more datasets for testing the model and more information for improving predictive performance.
Read more19A long short-term memory neural network model for knee joint acceleration estimation using mechanomyography signals
With the growth of the number of elderly and disabled with motor dysfunction, the demand for assisted exercise is increasing. Wearable power assistance robots are developed to provide athletic ability of limbs for the elderly or the disabled who have weakened limbs to better self-care ability. Existing wearable power-assisted robots generally use surface electromyography (sEMG) to obtain effective human motion intentions. Due to the characteristics of sEMG signals, it is limited in many applications. To solve the above problems, we design a long short-term memory (LSTM) neural network model based on human mechanomyography (MMG) signals to estimate the motion acceleration of knee joint. The acceleration can be further calculated by the torque required for movement control of the wearable power assistance robots for the lower limb. We detect MMG signals on the clothed thigh, extract features of the MMG signals, and then, use principal component analysis to reduce the features’ dimensions. Finally, the dimension-reduced features are inputted into the LSTM neural network model in time series for estimating the acceleration. The experimental results show that the average correlation coefficient ( R) is 94.48 ± 1.91% for the estimation of acceleration in the process of continuously performing under approximately π/4 rad/s. This approach can be applied in the practical applications of wearable field.
Read more50Comparison of ARIMA and LSTM in Forecasting the Incidence of HFMD Combined and Uncombined with Exogenous Meteorological Variables in Ningbo, China.
Background: This study intends to identify the best model for predicting the incidence of hand, foot and mouth disease (HFMD) in Ningbo by comparing Autoregressive Integrated Moving Average (ARIMA) and Long Short-Term Memory Neural Network (LSTM) models combined and uncombined with exogenous meteorological variables. Methods: The data of daily HFMD incidence in Ningbo from January 2014 to November 2017 were set as the training set, and the data of December 2017 were set as the test set. ARIMA and LSTM models combined and uncombined with exogenous meteorological variables were adopted to fit the daily incidence of HFMD by using the data of the training set. The forecasting performances of the four fitted models were verified by using the data of the test set. Root mean square error (RMSE) was selected as the main measure to evaluate the performance of the models. Results: The RMSE for multivariate LSTM, univariate LSTM, ARIMA and ARIMAX (Autoregressive Integrated Moving Average Model with Exogenous Input Variables) was 10.78, 11.20, 12.43 and 14.73, respectively. The LSTM model with exogenous meteorological variables has the best performance among the four models and meteorological variables can increase the prediction accuracy of LSTM model. For the ARIMA model, exogenous meteorological variables did not increase the prediction accuracy but became the interference factor of the model. Conclusions: Multivariate LSTM is the best among the four models to fit the daily incidence of HFMD in Ningbo. It can provide a scientific method to build the HFMD early warning system and the methodology can also be applied to other communicable diseases.
Read more
Copyright 2026 Cactus Communications. All rights reserved.
