GPS Solutions

Abstract

GPS satellites of Block IIR-M and the subsequent Blocks have the capability to redistribute the transmit power of the individual signal components, which is called flex power. This technology is used to prevent enemy jamming by increasing the power of the designed signal. It is of great importance to detect flex power since it has great impacts on differential code biases, phase shifts, and multiple access interference. Based on geodetic stations, stepwise enhancement in their carrier-to-noise density ratios (C/N0) can reflect the power changes caused by flex power. Thus, we propose a real-time detection method for GPS flex power based on C/N0 patterns. The patterns for 100 International GNSS Service stations uniformly distributed around the world are built according to their azimuths and elevations. In order to evaluate the performance of the proposed method, daily data with 30-s sampling in 2020 and real-time data with 1-s sampling in 2023 are adopted to detect flex power with the new method. Results of experiment show that the average false positive rate for real-time detection is around 10–6, and the true positive rate is 0.999479. The results confirm the effectiveness of our method for real-time flex power detection. Meanwhile, a new flex power mode is discovered in real-time detection experiments, which has the largest coverage area between longitudes 125°W and 180°E.

Abstract

Time-relative positioning (TRP), a global navigation satellite system (GNSS) dead reckoning method with low-cost and highly autonomous characteristics, accumulates the position increments calculated by time-differenced carrier phase (TDCP) between adjacent epochs to extrapolate position. It suffers from error accumulation over time, so it is necessary to judge the availability of positioning services based on predicted accuracy. We propose a new model to predict the accuracy (the root-mean-square error, RMSE) of TRP in real time by determining systematical errors and random errors. The proposed model consists of the following two steps: first, extracting the systematic errors and correlation of position increment errors before position extrapolation; second, predicting RMSE of the positioning results based on the error propagation law during position extrapolation. The experimental results show that after considering the correlation, the predicted RMSE sequences can envelop the actual positioning error more closely. In the case of having static observation before position extrapolation, the predicted RMSEs of extrapolation position in both horizontal and vertical directions decrease by approximately 53.8% compared to the results without considering correlation; in the case where real-time kinematic (RTK) dynamic results are obtained before extrapolation, the predicted RMSE of extrapolation position can decrease by 36.7% in horizontal direction and decrease by 27.9% in vertical direction. The proposed model will be able to provide an important accuracy reference to judge the availability of positioning services when the TRP method is used to extrapolate position under the condition of the augmentation information of RTK interruption.

Abstract

Ground-based augmentation system (GBAS) is a safety of life system that supports precision approach, landing, departure and surface operations in civil aviation. To compensate the tropospheric delay difference encountered at the aircraft and ground stations, empirical tropospheric correction (TC) models are applied. Scale height is one of the key parameters in TC models, while there are various methods to estimate scale heights and their performance is not fully evaluated, which affects the integrity and poses threats to GBAS. The purpose of this study is to evaluate the performance of TC models when using different scale height estimation methods by exploiting analytical products, including the European center for medium-range weather forecasts and meteorological data from the stations deployed in the crustal movement observation network of China in 2021. Taking the effects of virtual temperature and station height anomaly into consideration, a modified ray-tracing algorithm is proposed to calculate the tropospheric delay error, which is the difference of tropospheric delay between that encountered, respectively, at the GBAS station and the aircraft. The calculated tropospheric delay error serves as a reference to evaluate the performance of TC models. Results show that the TC model bias in the zenith direction estimated by the different scale height methods is approximately equal in the GBAS approach service type C. When the elevation is lower than 20°, there is a significant bias induced by the mapping function of TC models. Additionally, the TC model bias increases with height for GBAS precision approach service. The maximum TC model bias in the zenith direction at most stations exceeds 20 mm. The occurrence probability of anomaly with TC model bias more than 10 mm with a higher than 20% at a height of 400 m. This study contributes to better understanding of the GBAS TC model performance in China. It provides valuable insights and guidance for developing more precise TC models.

Abstract

Safety-critical navigation systems often involve multiple sensor types, including global navigation satellite system (GNSS), to enhance positioning accuracy. Additionally, the systems’ reliability has been significantly improved through the application of fault detection and exclusion (FDE) techniques. An enhanced AIME (Autonomous Integrity Monitoring by Extrapolation) method is introduced in our approach to identify faulty satellites. This is accomplished by analyzing the measured Kalman filter (KF) innovations and their covariances within a sliding window. Furthermore, a strategy for fault separation, detection, and exclusion is developed for GNSS and IMU, making use of their relationship within the KF innovation vector derived from the GNSS measurement model. Similarly, the innovation vector derived from the visual measurement model is employed to detect visual faults, with the assumption that the inertial measuring unit (IMU) is fault-free. Upon detecting faults, we proceed to redesign the system noise matrix and measurement noise matrix within the KF using test statistics, effectively excluding measurement faults from satellites and IMU. In order to assess the performance of our proposed method, we conducted a field test utilizing the collected vehicle-mounted dataset. The results demonstrate the effectiveness of our FDE method in accurately identifying faulty satellites, detecting IMU faults of varying magnitudes, and excluding abnormal visual observations. Furthermore, after fault exclusion, the maximum position error during the fault time period decreased by an average of 62%.

Abstract

The national Beidou Navigation Satellite System (BDS) ground-based augmentation network (BGAN) of China is constructed with the existing GNSS observation resources of industrial sectors and local governments, based on the concept of joint building and sharing with sustainable development. This study provides a detailed introduction to the design, construction and operation of a meteorological application system based on BGAN, and validation of its water vapor products. BDS and GPS real-time observation of atmospheric water vapor is achieved nationwide in China and multi-GNSS applications. Through the application of multi-GNSS data and validation of the water vapor products from 2018 to 2020, the accuracy of precipitable water vapor (PWV) derived from BDS only is equivalent to that from GPS only. The root mean square error (RMSE) between them is about 2 mm with high correlation coefficient. Based on radiosonde data, the validation is conducted with the products of BDS-PWV, GPS-PWV, and Combined-PWV derived with multi-GNSS of BDS and GPS. The error characteristics of the three products show a consistent trend over the months. The bias is relatively small. The RMSE of the three products is in the range of 2.18–2.73 mm. The BDS-PWV has the largest RMSE, followed by GPS-PWV, and Combined-PWV has the smallest RMSE.

Abstract

Earthquakes and tsunamis can trigger acoustic and gravity waves that could reach the ionosphere, generating electron density disturbances, known as traveling ionospheric disturbances. These perturbations can be investigated as variations in ionospheric total electron content (TEC) estimated through global navigation satellite systems (GNSS) receivers. The VARION (Variometric Approach for Real-Time Ionosphere Observation) algorithm is a well-known real-time tool for estimating TEC variations. In this context, the high amount of data allows the exploration of a VARION-based machine learning classification approach for TEC perturbation detection. For this purpose, we analyzed the 2015 Illapel earthquake and tsunami for its strength and high impact. We use the VARION-generated observations (i.e., dsTEC/dt) provided by 115 GNSS stations as input features for the machine learning algorithms, namely, Random Forest and XGBoost. We manually label time frames of TEC perturbations as the target variable. We consider two elevation cut-off time series, namely, 15° and 25°, to which we apply the classifier. XGBoost with a 15° elevation cut-off dsTEC/dt time series reaches the best performance, achieving an F1 score of 0.77, recall of 0.74, and precision of 0.80 on the test data. Furthermore, XGBoost presents an average difference between the labeled and predicted middle epochs of TEC perturbation of 75 s. Finally, the model could be seamlessly integrated into a real-time early warning system, due to its low computational time. This work demonstrates high-probability TEC signature detection by machine learning for earthquakes and tsunamis, that can be used to enhance tsunami early warning systems.

Abstract

Global Navigation Satellite System (GNSS) signals are susceptible to ionospheric plasma irregularities and associated scintillations, causing large deviations in the positioning solutions. This study aims to develop statistical regression models to estimate kinematic three-dimensional (3D) precise point positioning errors associated with ionospheric plasma irregularities based on the Rate Of Total electron content Index (ROTI). By assuming that the positioning errors follow the Laplace distribution, we perform nonlinear regression using the Levenberg–Marquardt algorithm on a collection of experimental data from 700 + Trimble receivers deployed in the NOAA Continuously Operating Reference Stations (CORS) Network. Three ROTI-based regression models are identified by curve fitting with nonlinear functions, i.e., third-degree polynomial (Poly3), two-term exponential (Exp2) and two-term power (Power2) models. A goodness-of-fit test suggests the models fit well into the relationship between ROTI and the 3D positioning errors with the adjusted coefficient of determination above 0.97. The regression models are subsequently employed to predict the 3D positioning errors with a given set of ROTI. Evaluation analysis using the observations from four CORS networks across different geographical regions indicate that the Exp2 model demonstrates encouraging prediction performance, with bias and root mean square error within − 0.14 m and 0.34 m, respectively, and the correct prediction ratio consistently surpasses 60.3%. The ROTI-based regression models have great potential in predictions of the degradation in GNSS positioning due to ionospheric space weather effects.

Abstract

To mitigate multipath effects in multi-GNSS and multi-frequency precise point positioning (PPP), we constructed multi-GNSS and multi-frequency multipath models using the multipath hemispherical map (MHM) method. We investigated multi-GNSS and multi-frequency multipath effects by analyzing the impact of multipath corrections on observation residuals and PPP performance. In general, greater code rates and signal strengths lead to smaller observation residuals and multipath corrections, and signals with better anti-multipath performance are obtained. Notably, the observation residuals and multipath corrections of the GPS L5 signals are the smallest among those of the triple-frequency signals, and those of the GLONASS G1 signals are smaller than those of the G2 signals. Among the Galileo five-frequency signals, those of the E1 and E5 signals are the largest and smallest, respectively. Among the BDS-3 five-frequency signals, those of the B1I and B1C signals are greater than those of the other signals. Additionally, overlapping frequency signals with the same code rates and similar signal strengths display similar observation residuals and multipath corrections. In particular, the BDS-3 B1C signal has large phase residuals in the high-elevation region, possibly due to inaccurate receiver antenna phase center corrections applied. Surprisingly, the MHM method works well on it, possibly because the phase multipath corrections include elevation-specific errors. After multipath correction, the low-frequency multipath errors of multi-GNSS and multi-frequency observations are efficiently mitigated, significantly reducing the observation residuals and improving the observation accuracy. As a result, the three-dimensional convergence time of multi-GNSS and multi-frequency float kinematic PPP is reduced by 24.1%, with a 13.8% improvement in the positioning accuracy.

Abstract

Integer ambiguity resolution enabled precise point positioning, PPP-RTK, which is becoming one of the most popular global navigation satellite system (GNSS) positioning modes. Owing to the presence of rank deficiencies in the system of GNSS observation equations, one needs to choose some of the GNSS parameters as S-basis and let the remaining parameters absorb them. Doing so forms a full-rank PPP-RTK model whose combined parameters are estimable. To simplify the model construction, previous contributions assume that observations are tracked on common-frequency (CF) bands for all the involved receiver-satellite pairs. Such a model is referred to as CF PPP-RTK. However, the coexistence of legacy and modernized GNSS signal systems, together with the presence of outdated and updated receiver firmware, leads to not-common-frequency (NCF) cases where some of the involved receivers fail to track observations on certain frequencies. For such cases, the CF PPP-RTK model discards part of the observations so as to maintain the CF assumption. In this contribution, we refrain from making the CF assumption and extend the GNSS undifferenced and uncombined formulation to NCF cases. Such a NCF PPP-RTK model ensures that all observations contribute to the parameter estimation process, avoiding losing any information content in the data. As a result, our proposed NCF PPP-RTK avoids any potential reduction in both the availability and the precision of the corrections. To evaluate the positioning performance of the proposed model, we conducted three experiments with continuously operating reference station data in Hong Kong, Australia, and Europe. The superiority of the NCF PPP-RTK model over its conventional CF PPP-RTK version is illustrated in terms of both the time-to-first-fix and root mean square positioning errors.

Abstract

The rapid growth of the GNSS equipment market has put affordable receivers and antennas capable of receiving satellite signals into the hands of users. High positioning accuracy, previously achievable only with high-grade devices, is becoming possible with low-cost ones. However, simplifications in the design of these devices, intended to reduce the manufacturing cost, affect their capabilities. This study analyzes the positioning accuracy that may be achieved with recent low-cost antennas. We put particular stress on investigating the susceptibility of such antennas to the multipath effect and implications from the quality of the antenna phase center models. The positioning performance is assessed by employing the Precise Point Positioning method with the integer ambiguity resolution of phase observations. The results obtained with three low-cost antennas are validated against three high-grade antennas. We reveal a two-to threefold decrease in positioning performance with low-cost antennas compared to high-quality equipment. However, positioning accuracy increased when a low-cost antenna with a phase correction model was used, particularly for the eastern component of coordinate bias. In addition, a significant susceptibility of low-cost antennas to the multipath effect was confirmed, especially for GPS L2 and Galileo E5a signals.

Abstract

The application field of global navigation satellite systems continues to expand, and their security and stability have received widespread attention. Navigation spoofing has the characteristics of solid concealment and significant harm, posing a severe security threat to navigation systems. In current spoofing detection methods based on signal spatial correlation, multiple antennas/receivers or moving single antennas are required, which means high cost and complexity in implementation. To this end, we propose a spoofing detection method based on the intersection angle between two directions of arrival (IA-DOA) for single-antenna receivers. The essence of this method is to accurately estimate the IA-DOA between a pair of signals based on pseudorange observations and navigation information. The observation should be consistent with the prediction when there is no spoofing. Otherwise, due to geometric and kinematic differences between the navigation satellite and the spoofer or the pulling off of the spoofing, the spoofing may disrupt the consistency between the observation and prediction of IA-DOA. Theoretically, since the proposed method makes no assumptions about spoofing, it can detect multi-antenna spoofing. We conducted a Monte Carlo simulation to analyze the impact of different parameters on spoofing detection performance and conducted experimental verification and evaluation through open datasets. The results show that the method proposed in this article can effectively detect multi-antenna spoofing, reducing the requirements of receiver antennas for spoofing detection methods based on signal spatial correlation.

Abstract

In January 2023, the International Laser Ranging Service (ILRS) approved the tracking of 20 additional BeiDou-3 Medium Earth Orbit (BDS-3 MEO) satellites, integrating them into the ILRS tracking network. Before that, only 4 BDS-3 MEO satellites had been tracked. BDS satellites employ highly advanced GNSS components and technological solutions; however, microwave-based orbits still contain systematic errors. Satellite Laser Ranging (SLR) tracking is thus crucial for better identification and understanding of orbit modeling issues. Orbit improvements are necessary to consider BDS in future realizations of terrestrial reference frames, supporting the determination of global geodetic parameters and utilizing them for the co-location of GNSS and SLR in space. In this study, we summarize the first 6 months of SLR tracking 24 BDS-3 MEO satellites. The study indicates that the ILRS network effectively executed the request to track the entire BDS-3 MEO constellation. The number of observations is approximately 1300 and 450 for high- and low-priority BDS-3 satellites, respectively, over the 6 months. More than half of the SLR observations to BDS-3 MEO satellites were provided by 5 out of the 24 laser stations, which actively measured GNSS targets. For 14 out of 24 BDS-3 MEO satellites, the standard deviation of SLR residuals is at the level of 19–20 mm, which is comparable with the quality of the state-of-the-art Galileo orbit solutions. However, the SLR validation of the individual satellites revealed that the BDS-3 MEO constellation consists of more ambiguous groups of satellites than originally reported in the official metadata files distributed by the BDS operators. For 8 BDS-3 satellites, the quality of the orbits is noticeably inferior with a standard deviation of SLR residuals above 100 mm. Therefore, improving orbit modeling for BDS-3 MEO satellites remains an urgent challenge for the GNSS community.

Abstract

In recent years, the potential of Global Navigation Satellite System Interferometric Reflectometry (GNSS-IR) for monitoring sea-level variations has been explored extensively. However, most studies have typically selected coastal sites with optimal GNSS-IR observation conditions, often limiting verification to one or two stations and overlooking other viable sites. This study introduces a site-evaluation strategy named facilitated interferometric reflectometry evaluation (FIRE), which utilizes two constructed indices—normalized available observation time and normalized sampling deficiency—to assess the suitability of GNSS sites for sea-level retrieval. Implemented in Hong Kong, China, the strategy was applied to all 19 sites within the local reference GNSS network. In addition to the two sites previously used, we identified five additional sites conducive to tidal GNSS-IR, demonstrating precisions between 0.07 m and 0.37 m and correlations ranging from 0.986 to 0.711. With denser GNSS-IR observations, we were able to map sea-level variations during three historic typhoon storm surges in the region more precisely: 2017 Typhoon Hato, 2018 Typhoon Mangkhut, and 2023 Typhoon Saola. Typhoon Saola presented a longer duration of six days and a slightly lower sea-level peak between 2.88 m and 3.13 m. The deployment of additional tidal GNSS-IR sites revealed variations in sea levels during typhoon storm surges, with differences influenced by coastline topography of up to 1.24 m observed during Typhoon Mangkhut. These sites offer a valuable supplement to traditional tide measurements, filling gaps in historical records. The FIRE strategy demonstrates the untapped potential of existing GNSS networks globally for sea-level monitoring and can be employed to unlock further observational opportunities.

Abstract

High-accuracy GNSS positioning in urban environments is important for applications like safe autonomous driving, however, dynamic errors in complex urban environments limit positioning performances. Recently, deep learning-based (DL) approaches can obtain better GNSS positioning solutions in complex urban environments than model-based ones. However, DL-based approaches simply concentrate one-view GNSS observations as inputs, which are insufficient to model vehicle states accurately, and temporally continuous observations are highly correlated, leading to inaccurate positioning correction results. To solve the challenge, we propose a Sparse Representation-based Multiview Deep Reinforcement Learning model for positioning correction, which employs attention-based multiview fusion to process multiview observations, and uses sparse representation to alleviate disturbances from highly correlated observations. To represent the vehicle state sufficiently, we build a multiview positioning correction environment, and develop an attention-weighted multiview fusion module to fuse temporal features as belief states based on adaptively learned attention weights. To effectively process redundant and correlated multiview features, we impose the ℓ1 norm regularizer to learn sparse hidden representations and improve the precision of value estimation. Finally, we construct a sparse representation-driven multiview actor-critic positioning correction model to achieve high-accuracy GNSS positioning in complex urban environments. We validate performances in both Google Smartphone Decimeter Challenge (GSDC) datasets and our collected GNSS datasets in the Guangzhou area (GZGNSS). Experimental results show that our algorithm can improve localization performances with 27% improvements from WLS+KF in GSDC trajectories, 16% from RTK, and 6% from DL-based methods in GZGNSS trajectories.

Abstract

Troposphere augmentation is of great importance for global navigation satellite system (GNSS) real-time precise point positioning (PPP) service. This contribution focuses on the feasibility of modeling the regional troposphere by polynomial fitting and the benefits of precise tropospheric corrections for triple-frequency and multi-GNSS PPP and PPP with integer ambiguity resolution (PPP-IAR) during a period of typhoon weather. A modified optimal fitting coefficient (MOFC) method is proposed with the height-related parameters removed by a priori fitted exponential function. Two spatial scales of networks are chosen to verify the effect of the GNSS station distribution on troposphere modeling. The results show that the MOFC model can provide centimeter-level accuracy with average root mean square (RMS) of 2.1 and 2.2 cm for dense and sparse networks, respectively, while that of GPT2w and real-time VMF3-FC products are 6.6 and 3.3 cm during typhoon periods. PPP/PPP-IAR tests with zenith troposphere delay (ZTD) augmentation based on the MOFC model are conducted when a typhoon eye passes over. Accuracy improvements of 18.2 and 16.6% for vertical components are observed in BDS-only and BDS/Galileo/GPS PPP-IAR solutions with ZTD augmentation, while those for PPP float solutions are marginal. Additionally, 2-h positioning arcs for PPP float solutions and 1224 10-min arcs for PPP-IAR solutions confirm that ZTD augmentation plays an important role in convergence, especially for PPP-IAR solutions. The percentage of instantaneous convergence in BDS-only PPP-IAR solutions improves from 42.1, 44.0 and 18.9% to 51.3, 52.3 and 48.9% for the east, north and up components, respectively, indicating that decorrelation between ZTD and vertical coordinates can be achieved with MOFC ZTD corrections in the initial stage of positioning. The percentages further improved from 89.7, 89.5 and 74.6% to 94.1, 94.2 and 93.7% for BDS/Galileo/GPS PPP-IAR solutions.

Abstract

Global navigation satellite system (GNSS) data collected from Android devices have gained increasing importance in various applications, ranging from geospatial positioning to environmental monitoring. However, the lack of standardized tools for converting Android GNSS raw data into receiver independent exchange (RINEX) format poses a significant challenge for researchers and practitioners. In response to this need, we present a comprehensive Python toolbox designed to streamline the conversion process and enhance the usability of Android GNSS data. The proposed toolbox leverages Python’s versatility to provide a user-friendly interface for converting Android GNSS raw data into the widely adopted RINEX format. Key features include robust data parsing algorithms, support for multiple GNSS constellations, and compatibility with diverse Android device configurations. Furthermore, the toolbox’s open-source nature encourages community collaboration and allows for continual improvement and adaptation to emerging GNSS technologies. We anticipate that this Python toolbox will serve as a valuable resource for researchers and practitioners working with Android GNSS data, facilitating standardized data interchange and promoting reproducibility in GNSS-based studies.

Abstract

The Galileo high accuracy service (HAS) is a new capability of the European global navigation satellite system, currently providing satellite orbit and clock corrections and dispersive effects such as satellite instrumental biases for code and phase. In its full capability, Galileo HAS will also correct the ionospheric delay on a continental scale (initially over Europe). We analyze a real-time ionospheric correction system based on the fast precise point positioning (F-PPP), and its potential application to the Galileo HAS. The F-PPP ionospheric model is assessed through a 281-day campaign, confirming previously reported results, where the proof of concept was introduced. We introduce a novel real-time test that directly links the instantaneous position error with the error of the ionospheric corrections, a key point for a HAS. The test involved 15 GNSS receivers in Europe acting as user receivers at various latitudes, with distances to the nearest reference receivers ranging from tens to four hundred kilometers. In the position domain, the test results show that the 95th percentile of the instantaneous position error depends on the user-receiver distance, as expected, ranging in the horizontal and vertical components from 10 to 30 cm and from 20 to 50 cm, respectively. These figures not only meet Galileo HAS requirements but outperform them by achieving instantaneous positioning. Additionally, it is shown that formal errors of the ionospheric corrections, which are also transmitted, are typically at the decimeter level (1 sigma), protecting users against erroneous position by weighting its measurements in the navigation filter.

Abstract

European Galileo officially provided global users with the initial high accuracy service (HAS) through Galileo satellites for free on January 24, 2023. The emergence of the Galileo HAS provides the possibility of a globally stable real-time precise point positioning (PPP) time transfer that does not depend on a network. The coverage and service availability (the proportion of epochs that can support PPP solution) of the HAS, accuracy of the satellite orbit and clock offset, and accuracy of HAS time transfer were comprehensively analyzed using real-time and satellite-broadcast HAS data. Twenty-three global time links, including time-keeping laboratories, were established to assess the accuracy of time comparison using the HAS product. The results showed that the average numbers of GPS and Galileo satellites with valid HAS corrections worldwide were 9.44 and 7.95, respectively, and the average service availability of GPS-only and Galileo-only PPP using the HAS product reached 99.9% and 99.6%, respectively, in most areas. Taking post-processing satellite products from GeoForschungZentrum as a reference, the radial errors of the HAS orbit product are concentrated within 5 cm, and the accuracy of the corrected Galileo satellite clock offset was twice that of ephemeris. Further, in the 7200–12295 km-long baselines, the mean standard deviation values of HAS GPS-only, Galileo-only, and GPS/Galileo time comparison result errors were 0.19–0.29 ns, 0.13–0.24 ns, and 0.11–0.21 ns, respectively. In general, HAS time transfer is available globally.

Abstract

Satellite clock bias (SCB) is a critical factor influencing the accuracy of real-time precise point positioning. Nevertheless, the utilization of real-time service products, as supplied by the International GNSS Service, may be vulnerable to interruptions or network failures. In specific situations, users may encounter difficulties in obtaining accurate real-time corrections. Our research presents an enhanced predictive model for SCB using a long short-term memory (LSTM) neural network fused with a Self-Attention mechanism to address this challenge. This fusion enables the model to effectively balance global attention and localized feature capture, ultimately enhancing prediction accuracy and stability. We compared and analyzed our proposed model with convolutional neural network (CNN) and LSTM models. This analysis encompasses an assessment of the model's strengths and suitability for predicting SCB within the BeiDou navigation system, considering diverse satellites, orbits, and atomic clocks. Our results exhibit a substantial improvement in predictive accuracy through the LSTM-Attention model. There has been an improvement of 49.67 and 62.51% compared to the CNN and LSTM models in the 12-h prediction task. In the case of the 24-h prediction task, the improvements escalated to 68.41 and 71.16%, respectively.