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Search Results (1,249)

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Keywords = extended kalman filter

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20 pages, 1038 KiB  
Article
Accelerometer Bias Estimation for Unmanned Aerial Vehicles Using Extended Kalman Filter-Based Vision-Aided Navigation
by Djedjiga Belfadel and David Haessig
Electronics 2025, 14(6), 1074; https://doi.org/10.3390/electronics14061074 - 7 Mar 2025
Viewed by 166
Abstract
Accurate estimation of accelerometer biases in Inertial Measurement Units (IMUs) is crucial for reliable Unmanned Aerial Vehicle (UAV) navigation, particularly in GPS-denied environments. Uncompensated biases lead to an unbounded accumulation of position error and increased velocity error, resulting in significant navigation inaccuracies. This [...] Read more.
Accurate estimation of accelerometer biases in Inertial Measurement Units (IMUs) is crucial for reliable Unmanned Aerial Vehicle (UAV) navigation, particularly in GPS-denied environments. Uncompensated biases lead to an unbounded accumulation of position error and increased velocity error, resulting in significant navigation inaccuracies. This paper examines the effects of accelerometer bias on UAV navigation accuracy and introduces a vision-aided navigation system. The proposed system integrates data from an IMU, altimeter, and optical flow sensor (OFS), employing an Extended Kalman Filter (EKF) to estimate both the accelerometer biases and the UAV position and velocity. This approach reduces the accumulation of velocity and positional errors. The efficiency of this approach was validated through simulation experiments involving a UAV navigating in circular and straight-line trajectories. Simulation results show that the proposed approach significantly enhances UAV navigation performance, providing more accurate estimates of both the state and accelerometer biases while reducing error growth through the use of vision aiding from an Optical Flow Sensor. Full article
(This article belongs to the Special Issue Precision Positioning and Navigation Communication Systems)
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<p>Basic block diagram for a strapdown inertial navigation system, courtesy [<a href="#B16-electronics-14-01074" class="html-bibr">16</a>].</p>
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<p>Strapdown inertial navigation with IMU acceleration input corrected for IMU bias.</p>
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<p>System and Simulation Block Diagram.</p>
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<p>Position Errors, Dead-Reckoning, biases not present.</p>
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<p>Velocity Errors, Dead-Reckoning, biases not present.</p>
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<p>Position Errors, Dead-Reckoning, biases present.</p>
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<p>Velocity Errors, Dead-Reckoning, biases present.</p>
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<p>Position Errors, Kalman Est. on, biases not present, bias est. off.</p>
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<p>Velocity Errors, Kalman Est. on, biases not present, bias est. off.</p>
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<p>Position Errors, Kalman est. on, biases present, bias est. off.</p>
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<p>Velocity Errors, Kalman est. on, biases present, bias est. off.</p>
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<p>Position Errors, Kalman est. on, biases present, bias est. on.</p>
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<p>Velocity Errors, Kalman est. on, biases present, bias est. on.</p>
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<p>Bias Estimates during Scheme 4.</p>
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<p>Position Errors, Kalman est. on, biases present, bias est. off.</p>
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<p>Velocity Errors, Kalman est. on, biases present, bias est. off.</p>
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<p>Position Errors, Kalman est. on, biases present, bias est. on.</p>
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<p>Velocity Errors, Kalman est. on, biases present, bias est. on.</p>
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24 pages, 4712 KiB  
Article
Accurate Localization Method Combining Optimized Hybrid Neural Networks for Geomagnetic Localization with Multi-Feature Dead Reckoning
by Suqing Yan, Baihui Luo, Xiyan Sun, Jianming Xiao, Yuanfa Ji and Kamarul Hawari bin Ghazali
Sensors 2025, 25(5), 1304; https://doi.org/10.3390/s25051304 - 20 Feb 2025
Viewed by 234
Abstract
Location-based services provide significant economic and social benefits. The ubiquity, low cost, and accessibility of geomagnetism are highly advantageous for localization. However, the existing geomagnetic localization methods suffer from location ambiguity. To address these issues, we propose a fusion localization algorithm based on [...] Read more.
Location-based services provide significant economic and social benefits. The ubiquity, low cost, and accessibility of geomagnetism are highly advantageous for localization. However, the existing geomagnetic localization methods suffer from location ambiguity. To address these issues, we propose a fusion localization algorithm based on particle swarm optimization. First, we construct a five-dimensional hybrid LSTM (5DHLSTM) neural network model, and the 5DHLSTM network structure parameters are optimized via particle swarm optimization (PSO) to achieve geomagnetic localization. The eight-dimensional BiLSTM (8DBiLSTM) algorithm is subsequently proposed for heading estimation in dead reckoning, which effectively improves the heading accuracy. Finally, fusion localization is achieved by combining geomagnetic localization with an improved pedestrian dead reckoning (IPDR) based on an extended Kalman filter (EKF). To validate the localization performance of the proposed PSO-5DHLSTM-IPDR method, several extended experiments using Xiaomi 10 and Hi Nova 9 are conducted in two different scenarios. The experimental results demonstrate that the proposed method improves localization accuracy and has good robustness and flexibility. Full article
(This article belongs to the Special Issue Multi‐sensors for Indoor Localization and Tracking: 2nd Edition)
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<p>Overall structure of the fusion localization algorithm.</p>
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<p>Geomagnetic signals at the same location on 20 December 2023 and 17 October 2023: (<b>a</b>) geomagnetic x-direction vector; (<b>b</b>) geomagnetic y-direction vector; (<b>c</b>) geomagnetic z-direction vector.</p>
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<p>Geomagnetism captured using a mobile phone with different postures: (<b>a</b>) Pose 1; (<b>b</b>) Pose 2.</p>
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<p>Geomagnetic magnitudes of different postures with the same phone.</p>
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<p>PSO-5DHLSTM model.</p>
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<p>Localization errors of the LSTM, MaLoc, PDR, DTW, and PSO-5DHLSTM methods: (<b>a</b>) Xiaomi 10, (<b>b</b>) Hi Nova 9.</p>
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<p>Data collected via mobile phone: (<b>a</b>) triaxial component of the azimuth; (<b>b</b>) triaxial component of the geomagnetic field.</p>
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<p>Cumulative distribution function of the heading error in Scene 1.</p>
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<p>Cumulative distribution function of the heading error in Scene 2.</p>
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<p>Floorplans of the experimental sites: (<b>a</b>) Scene 1; (<b>b</b>) Scene 2.</p>
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<p>Average errors of LSTM, MaLoc, PDR, DTW, and the PSO-5DHLSTM-IPDR with different step numbers in Scene 1: (<b>a</b>) Xiaomi 10; (<b>b</b>) Hi Nova 9.</p>
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<p>Average errors of LSTM, MaLoc, PDR, DTW, and the PSO-5DHLSTM-IPDR with different step numbers in Scene 2. (<b>a</b>) Xiaomi 10; (<b>b</b>) Hi Nova 9.</p>
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<p>Localization errors of the LSTM, MaLoc, PDR, DTW, and PSO-5DHLSTM-IPDR methods in Scene 1 when different cell phones are used: (<b>a</b>) Xiaomi 10; (<b>b</b>) Hi Nova 9.</p>
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<p>Localization errors of the LSTM, MaLoc, PDR, DTW, and PSO-5DHLSTM-IPDR methods in Scene 2: (<b>a</b>) Xiaomi 10; (<b>b</b>) Hi Nova 9.</p>
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<p>Cumulative distribution functions of the LSTM, MaLoc, PDR, DTW, and PSO-5DHLSTM-IPDR methods in Scene 1: (<b>a</b>) Xiaomi 10, (<b>b</b>) Hi Nova 9.</p>
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<p>Cumulative distribution functions of the LSTM, MaLoc, PDR, DTW, and PSO-5DHLSTM-IPDR methods in Scene 2: (<b>a</b>) Xiaomi 10; (<b>b</b>) Hi Nova 9.</p>
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26 pages, 2295 KiB  
Article
Robust Adaptive Cascade Trajectory Tracking Control for an Aircraft Towing and Taxiing System
by Weining Huang, Pengjie Xu, Tianrui Zhao, Wei Zhang and Yanzheng Zhao
Actuators 2025, 14(3), 105; https://doi.org/10.3390/act14030105 - 20 Feb 2025
Viewed by 220
Abstract
With the rapid growth of the civil aviation industry, the aircraft towing and taxiing (ATT) system has gained significant attention in the literature. Due to its nonlinear and underactuated characteristics, the path tracking and control of the ATT system is a challenging issue. [...] Read more.
With the rapid growth of the civil aviation industry, the aircraft towing and taxiing (ATT) system has gained significant attention in the literature. Due to its nonlinear and underactuated characteristics, the path tracking and control of the ATT system is a challenging issue. Therefore, in this paper, a robust adaptive cascade control structure is proposed for the path tracking of the ATT system. Firstly, the system description is established via kinematic and dynamics modeling, and the lumped system disturbance is derived for the controller design. Next, the robust adaptive cascade control structure consisting of the adaptive MPC and the CSMC or the RASMC-based dynamics controller is designed with the application of the extended Kalman filter. The system stability in the dynamics loop is verified through the Lyapunov method. The simulation results reveal that the combination of the adaptive MPC and the RASMC can provide a more accurate tracking performance and smoother trajectories under the given disturbances and uncertainties, while both ensuring passenger comfort and meeting the civil aviation regulations, indicating its potential in practical applications. Full article
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<p>Illustration of the aircraft towing and taxiing operation.</p>
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<p>Schematic diagram of the ATT system.</p>
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<p>The designed robust adaptive cascade control structure for the ATT system.</p>
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<p>Path tracking performance of the two control strategies.</p>
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<p>Path tracking error of the ATT system.</p>
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<p>Trajectory tracking errors of the ATT system.</p>
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<p>Trajectories of the control inputs.</p>
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<p>Trajectories of the aircraft velocities.</p>
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<p>Trajectories of the hitch angles.</p>
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<p>Torques of rear wheel motors on the tractor.</p>
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27 pages, 11986 KiB  
Article
Robust Regression and Redundant Measurement Noise Estimation Adaptive Filtering for Localization in Urban Environments
by Li Zha, Hai Zhang, Aiping Wang and Cancan Tao
Electronics 2025, 14(5), 826; https://doi.org/10.3390/electronics14050826 - 20 Feb 2025
Viewed by 228
Abstract
This paper focuses on a solution of target self-positioning when a Global Navigation Satellite System (GNSS) is denied. It is composed of Inertial Navigation Systems (INS), Signals of Opportunities (SOPs), and a navigation prototype. One of the options for navigation via SOP (NAVSOP) [...] Read more.
This paper focuses on a solution of target self-positioning when a Global Navigation Satellite System (GNSS) is denied. It is composed of Inertial Navigation Systems (INS), Signals of Opportunities (SOPs), and a navigation prototype. One of the options for navigation via SOP (NAVSOP) is to utilize cellular signals, such as Long Time Evolution (LTE). When the prior information is insufficient, the location of the base station (BS) is obtained by collecting the demodulation of the downlink signal, and the synchronization signal is used for static time offset correction. In view of the large positioning error of the trilateral positioning method based on Received Signal Strength (RSS), a multi-station positioning optimization method is proposed by introducing the robust regression. Monte Carlo simulation experiments indicate that the method has improved the positioning failure and insufficient accuracy. Aiming at the influence of the state estimation errors on filtering results, the Second Order Mutual Difference (SOMD) method with the noise covariance R, which is independent of the existing Extended Kalman Filter (EKF) framework and combined with Redundant Measurement Noise Covariance Estimation (RMNCE), is applied to the model. The simulation results show that the average error of the robust model is 10.28 m, which is better than the EKF method. Finally, a vehicle test in constant speed has been carried out. The results show that the proposed model can realize self-positioning with limited BS location information, and the positioning accuracy can reach 11.68 m over a 283 m trajectory. Full article
(This article belongs to the Special Issue Sensor Technologies for Intelligent Transportation Systems)
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<p>NAVSOP application scenario.</p>
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<p>Vehicle-mounted NAVSOP.</p>
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<p>LTE downlink demodulation.</p>
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<p>Failure of trilateral positioning.</p>
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<p>Received signal clock offset: (<b>a</b>) time-offset extraction; (<b>b</b>) pseudo-range extraction.</p>
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<p>Correction based on static data: (<b>a</b>) signal frame header offset correction; (<b>b</b>) signal pseudo-distance difference correction.</p>
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<p>Comparison of simulation effects of three positioning methods: (<b>a</b>) positioning-error analysis; (<b>b</b>) positioning-error probability distribution.</p>
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<p>Sample estimation based on sliding window.</p>
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<p>Measurement noise covariance of different types: (<b>a</b>) the case of Gaussian distribution noise; (<b>b</b>) the case of time-varying noise.</p>
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<p>Measurement noise covariance of different factors: (<b>a</b>) the case of Gaussian distribution noise; (<b>b</b>) the case of time-varying noise.</p>
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<p>The filtering effect based on RMNCE: (<b>a</b>) true track and filter estimation; (<b>b</b>) X-Y positioning RMSE.</p>
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<p>LTE positioning: (<b>a</b>) motion track and BS position; (<b>b</b>) EKF and RMNCE EKF positioning RMSE; (<b>c</b>) INS and fusionpositioning RMSE.</p>
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<p>On-board experiment of NAVSOP.</p>
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<p>On-board test route.</p>
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<p>On-board test results: (<b>a</b>) average RSS indicators of each BS; (<b>b</b>) motion trajectories and positioning errors.</p>
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<p>LTE downlink signal solution: (<b>a</b>) timing synchronization; (<b>b</b>) CP type detection; (<b>c</b>) frequency offset estimation; (<b>d</b>) channel estimation; (<b>e</b>) downlink demodulation.</p>
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<p>Multilateral positioning based on distance: Trilateral location algorithm (red); Least squares positioning algorithm (blue); Robust regression positioning algorithm (green).</p>
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<p>Tightly SOP/INS navigation model: SOP signal pre-processing, filtering update, INS filtering value prediction, and other links.</p>
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<p>Robust NAVSOP model: BS location calculation, clock bias correction, pseudo-range calculation, and RMNCE EKF update.</p>
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27 pages, 7925 KiB  
Article
A Distributed Collaborative Navigation Strategy Based on Adaptive Extended Kalman Filter Integrated Positioning and Model Predictive Control for Global Navigation Satellite System/Inertial Navigation System Dual-Robot
by Wanqiang Chen, Yunpeng Jing, Shuo Zhao, Lei Yan, Quancheng Liu and Zichang He
Remote Sens. 2025, 17(4), 721; https://doi.org/10.3390/rs17040721 - 19 Feb 2025
Viewed by 210
Abstract
In the field of multi-robot cooperative localization and task planning, traditional filtering algorithms encounter synchronization and consistency issues during multi-source data fusion. These challenges result in cumulative localization errors and inefficient information sharing, which limits the system’s collaborative capabilities and control accuracy. To [...] Read more.
In the field of multi-robot cooperative localization and task planning, traditional filtering algorithms encounter synchronization and consistency issues during multi-source data fusion. These challenges result in cumulative localization errors and inefficient information sharing, which limits the system’s collaborative capabilities and control accuracy. To overcome these limitations, a distributed cooperative navigation strategy is introduced. Initially, a Distributed Adaptive Extended Kalman Filter (DAEKF) is implemented, which adaptively adjusts the noise covariance matrix to effectively manage nonlinearities and multi-source noise conditions. Subsequently, a Distributed Model Predictive Control (DMPC) framework is introduced. This framework predicts and optimizes each robot’s kinematic model, thereby improving the system’s collaborative operations and dynamic decision-making capabilities. Finally, the efficacy of this strategy is confirmed through detailed simulations and robotic experiments. The simulation results for cooperative localization demonstrate that DAEKF outperforms Kalman Filter (KF) and Extended Kalman Filter (EKF) in terms of localization accuracy. In the straight-line path-tracking experiments, DAEKF effectively reduced both lateral and heading errors for both robots. For Robot 1, DAEKF reduced the lateral error Root Mean Squared Error (RMSE) by 68.87%, 27.80%, and 25.76%, compared to No Filtering, KF, and EKF. In heading error, DAEKF reduced the RMSE by 52.29%, 41.89%, and 36.47%. For Robot 2, DAEKF reduced the lateral error RMSE by 51.30%, 22.88%, and 11.60%, compared to No Filtering, KF, and EKF. In heading error, DAEKF reduced the RMSE by 39.55%, 37.15%, and 26.00%. In the curved path-tracking experiments, both robots demonstrated high trajectory conformity while traveling along a predefined path combining straight-line and circular arc segments, with lateral errors in the straight-line segments all below 0.05 m. The strategy proposed in this study significantly enhanced the precision and stability of multi-robot collaborative navigation, demonstrating strong practicality and scalability. Full article
(This article belongs to the Special Issue Satellite Navigation and Signal Processing (Second Edition))
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<p>Schematic diagram of the DAEKF framework for dual-robot systems.</p>
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<p>Schematic diagram of DMPC framework for dual-robot systems.</p>
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<p>Structure and information flow diagram of the dual-robot system.</p>
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<p>RTK–GNSS base station and robotic control hardware configuration. (<b>a</b>) RTK–GNSS base station setup; (<b>b</b>) hardware composition of the experimental robots.</p>
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<p>Analysis of front wheel steering tracking performance and experimental pathways. (<b>a</b>) steering angle tracking for robot 1; (<b>b</b>) steering angle tracking for robot 2.</p>
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<p>Experimental robots in operation and path tracking. (<b>a</b>) Experimental robots in field operation; (<b>b</b>) dual straight-line and curved experimental pathways.</p>
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<p>Simulation-based path tracking performance of robot 1 and robot 2 under different filtering strategies.</p>
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<p>Noise matrix variation during the DAEKF adaptive noise estimation process. (<b>a</b>) Adaptive adjustment of process noise covariance matrix Q; (<b>b</b>) adaptive adjustment of measurement noise covariance matrix R.</p>
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<p>Localization error analysis under different filtering strategies. (<b>a</b>) X-axis error of robot 1; (<b>b</b>) Y-axis error of robot 1; (<b>c</b>) X-axis error of robot 2; (<b>d</b>) Y-axis error of robot 2.</p>
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<p>Localization error comparison of different filtering methods. (<b>a</b>) X-axis error comparison; (<b>b</b>) Y-axis error comparison.</p>
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<p>Experimental path-tracking performance of robot 1 and robot 2 along a subset of the trajectory under different filtering strategies.</p>
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<p>Control performance and coordination of robot 1 and robot 2 during path tracking. (<b>a</b>) Steering angle of robot 1; (<b>b</b>) steering angle of robot 1; (<b>c</b>) offset distance between robot 1 and robot 2; (<b>d</b>) velocity of robot 1 and robot 2.</p>
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<p>Dynamic adjustment of noise in DAEKF filtering. (<b>a</b>) Measurement noise R<sub>d</sub>; (<b>b</b>) process noise Q<sub>d</sub>; (<b>c</b>) measurement noise R<sub>d</sub>; (<b>d</b>) process noise Q<sub>a</sub>.</p>
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<p>Experimental localization performance analysis under different filtering strategies. (<b>a</b>) Lateral error of robot 1; (<b>b</b>) lateral error of robot 2; (<b>c</b>) heading error of robot 1; (<b>d</b>) heading error of robot 2.</p>
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<p>Comparison of lateral and heading errors for robot 1 and robot 2. (<b>a</b>) Lateral error comparison; (<b>b</b>) heading error comparison.</p>
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<p>Comparison of lateral and heading errors for robot 1 and robot 2 across different control methods. (<b>a</b>) Lateral error comparison; (<b>b</b>) heading error comparison.</p>
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<p>Experimental dual-loop path-tracking performance of robot 1 and robot 2. (<b>a</b>) Path tracking of robot 1; (<b>b</b>) path tracking of robot 2; (<b>c</b>) lateral error of robot 1 during path tracking; (<b>d</b>) lateral error of robot 2 during path tracking.</p>
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25 pages, 7292 KiB  
Article
Flexible Optimal Control of the CFBB Combustion System Based on ESKF and MPC
by Lei Han, Lingmei Wang, Enlong Meng, Yushan Liu and Shaoping Yin
Sensors 2025, 25(4), 1262; https://doi.org/10.3390/s25041262 - 19 Feb 2025
Viewed by 223
Abstract
In order to deeply absorb the power generation of new energy, coal-fired circulating fluidized bed units are widely required to participate in power grid dispatching. However, the combustion system of the units faces problems such as decreased control performance, strong coupling of controlled [...] Read more.
In order to deeply absorb the power generation of new energy, coal-fired circulating fluidized bed units are widely required to participate in power grid dispatching. However, the combustion system of the units faces problems such as decreased control performance, strong coupling of controlled signals, and multiple interferences in measurement signals during flexible operation. To this end, this paper proposes a model predictive control (MPC) scheme based on the extended state Kalman filter (ESKF). This scheme optimizes the MPC control framework. The ESKF is used to filter the collected output signals and jointly estimate the state and disturbance quantities in real time, thus promptly establishing a prediction model that reflects the true state of the system. Subsequently, taking the minimum output signal deviation of the main steam pressure and bed temperature and the control signal increment as objectives, a coordinated receding horizon optimization is carried out to obtain the optimal control signal of the control system within each control cycle. Tracking, anti-interference, and robustness experiments were designed to compare the control effects of ESKF-MPC, ID-PI, ID-LADRC, and MPC. The research results show that, when the system parameters had a ±30% perturbation, the adjustment time range of the main steam pressure and bed temperature loops of this method were 770~1600 s and 460~1100 s, respectively, and the ITAE indicator ranges were 0.615 × 105~1.74 × 105 and 3.9 × 106~6.75 × 106, respectively. The overall indicator values were smaller and more concentrated, and the robustness was stronger. In addition, the test results of the actual continuous variable condition process of the unit show that, compared with the PI strategy, after adopting the ESKF-MPC strategy, the overshoot of the main steam pressure loop of the combustion system was small, and the output signal was stable; the fluctuation range of the bed temperature loop was small, and the signal tracking was smooth; the overall control performance of the system was significantly improved. Full article
(This article belongs to the Section Industrial Sensors)
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<p>Simplified schematic diagram of CFBB combustion process.</p>
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<p>MPC algorithm flow of ESKF fusion.</p>
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<p>This ESKF-MPC control architecture diagram of the CFBB combustion system.</p>
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<p>Inverted decoupling control block diagram of CFBB combustion system.</p>
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<p>System output with variable prediction time domains.</p>
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<p>System output with variable control time domains.</p>
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<p>System output with variable discrete times.</p>
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<p>System output with variable adjusting weights.</p>
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<p>System output with variable error weights.</p>
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<p>System output with variable control weights.</p>
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<p>Step response curve of main steam pressure.</p>
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<p>Step response curve of bed temperature.</p>
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<p>Main steam pressure disturbance process curve.</p>
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<p>Bed temperature disturbance process curve.</p>
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<p>Monte Carlo test results of the main steam pressure circuit.</p>
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<p>Monte Carlo test results of bed temperature circuit.</p>
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<p>Operating curve of the unit under working conditions.</p>
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<p>Main steam pressure test results.</p>
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<p>Bed temperature test results.</p>
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<p>Effect of main steam pressure control circuit.</p>
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<p>Effect of bed temperature control circuit.</p>
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13 pages, 9723 KiB  
Article
Demagnetization Fault Diagnosis for PMSM Drive System with Dual Extended Kalman Filter
by Jiahan Wang, Chen Li and Zhanqing Zhou
World Electr. Veh. J. 2025, 16(2), 112; https://doi.org/10.3390/wevj16020112 - 18 Feb 2025
Viewed by 271
Abstract
Aiming at the irreversible demagnetization of permanent magnet synchronous motors (PMSMs) under extreme working conditions, a fault diagnosis method for permanent magnet demagnetization based on multi-parameter estimation is proposed in this paper. This scheme aims to provide technical support for enhancing the safety [...] Read more.
Aiming at the irreversible demagnetization of permanent magnet synchronous motors (PMSMs) under extreme working conditions, a fault diagnosis method for permanent magnet demagnetization based on multi-parameter estimation is proposed in this paper. This scheme aims to provide technical support for enhancing the safety and reliability of permanent magnet motor drive systems. In the proposed scheme, multiple operating states of the motor are acquired by injecting sinusoidal current signals into the d-axis, ensuring that the parameter estimation equation satisfies the full rank condition. Furthermore, the accurate dq-axis inductance parameters are obtained based on a recursive least square method. Subsequently, a dual extended Kalman filter is employed to acquire real-time permanent magnet flux linkage data of PMSMs, and the estimation data between the two algorithms are transferred to each other to eliminate the bias of permanent magnet flux estimation caused by a parameter mismatch. Finally, accurate evaluation of the remanence level of the rotor permanent magnet and demagnetization fault diagnosis can be achieved based on the obtained permanent magnet flux linkage parameters. The experimental results show that the relative estimation errors of the dq-axis inductance and permanent magnet flux linkage are within 5%, which can realize the effective diagnosis of demagnetization fault and high-precision condition monitoring of a permanent magnet health. Full article
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<p>Block diagram of the demagnetization fault diagnosis based on DEKF.</p>
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<p>Control block diagram of the proposed demagnetization fault diagnosis method.</p>
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<p>Experimental platform.</p>
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<p>Experimental waveforms of the stator current and its spectrum. (<b>a</b>) M1. (<b>b</b>) M2. (<b>c</b>) M3.</p>
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<p>Experimental results of the proposed diagnosis method in M1.</p>
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<p>Experimental results of the proposed diagnosis method in M2.</p>
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<p>Experimental results of the proposed diagnosis method in M3.</p>
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<p>Experimental results of the proposed diagnosis method at 1.2 N·m (<b>a</b>) M1 (<b>b</b>) M2, (<b>c</b>) M3.</p>
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21 pages, 7555 KiB  
Article
Control of Multiple Mobile Robots Based on Data Fusion from Proprioceptive and Actuated Exteroceptive Onboard Sensors
by Arpit Joon, Wojciech Kowalczyk and Przemyslaw Herman
Electronics 2025, 14(4), 776; https://doi.org/10.3390/electronics14040776 - 17 Feb 2025
Viewed by 271
Abstract
This paper introduces a team of Automated Guided Vehicles (AGVs) equipped with open-source, perception-enhancing rotating devices. Each device has a set of ArUco markers, employed to compute the relative pose of other AGVs. These markers also serve as landmarks, delineating a path for [...] Read more.
This paper introduces a team of Automated Guided Vehicles (AGVs) equipped with open-source, perception-enhancing rotating devices. Each device has a set of ArUco markers, employed to compute the relative pose of other AGVs. These markers also serve as landmarks, delineating a path for the robots to follow. The authors combined various control methodologies to track the ArUco markers on another rotating device mounted on the AGVs. Behavior trees are implemented to facilitate task-switching or to respond to sudden disturbances, such as environmental obstacles. The Robot Operating System (ROS) is installed on the AGVs to manage high-level controls. The efficacy of the proposed solution is confirmed through a real experiment. This research contributes to the advancement of AGV technology and its potential applications in various fields for example in a warehouse with a restricted and known environment where AGVs can transport goods while avoiding other AGVs in the same environment. Full article
(This article belongs to the Special Issue Recent Advances in Robotics and Automation Systems)
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<p>Robots with rotating platform.</p>
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<p>Behavior tree for rotating platform movement.</p>
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<p>Exploded view of rotating platform assembly.</p>
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<p>Axis representations between the camera and the ArUco marker.</p>
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<p>Corner points of ArUco markers.</p>
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<p>Top view of the rotating device.</p>
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<p>When robots are too close to observe the markers on the cuboidal part.</p>
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<p>Side-by-side comparison of (<b>a</b>) ArUco Diamond Marker and (<b>b</b>) Environment with landmarks.</p>
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<p>Experiment result 1. (<b>a</b>) (x,y)—plot of all robots including OptiTrack data of robots. (<b>b</b>) (x,y)—plot of robot 1 with static robot 4. (<b>c</b>) (x,y)—plot of all robots with activation regions. (<b>d</b>) Sum of collision avoidance components of robot 1 on the x-axis. (<b>e</b>) Sum of collision avoidance components of robot 1 on the y-axis. (<b>f</b>) Global error <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>x</mi> </mrow> </msub> </semantics></math> with respect to time of robot 1. (<b>g</b>) Global error <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>y</mi> </mrow> </msub> </semantics></math> with respect to time of robot 1. (<b>h</b>) Global error <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>θ</mi> </mrow> </msub> </semantics></math> with respect to time of robot 1. (<b>i</b>) Linear velocity (<math display="inline"><semantics> <msub> <mi>v</mi> <mn>1</mn> </msub> </semantics></math>) with respect to time. (<b>j</b>) Angular velocity (<math display="inline"><semantics> <msub> <mi>w</mi> <mn>1</mn> </msub> </semantics></math>) with respect to time. (<b>k</b>) Sum of collision avoidance components of robot 2 on the x-axis. (<b>l</b>) Sum of collision avoidance components of robot 2 on the y-axis. (<b>m</b>) <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </msub> </semantics></math> with respect to time of robot 2. (<b>n</b>) <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>y</mi> </mrow> </msub> </semantics></math> with respect to time of robot 2. (<b>o</b>) <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>θ</mi> </mrow> </msub> </semantics></math> with respect to time of robot 2. (<b>p</b>) Linear velocity <math display="inline"><semantics> <msub> <mi>v</mi> <mn>2</mn> </msub> </semantics></math> with respect to time. (<b>q</b>) Angular velocity <math display="inline"><semantics> <msub> <mi>w</mi> <mn>2</mn> </msub> </semantics></math> with respect to time. (<b>r</b>) Landmarks and other robots detected by robot 1. (<b>s</b>) Landmarks and other robots detected by robot 2.</p>
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<p>Experiment result 1. (<b>a</b>) (x,y)—plot of all robots including OptiTrack data of robots. (<b>b</b>) (x,y)—plot of robot 1 with static robot 4. (<b>c</b>) (x,y)—plot of all robots with activation regions. (<b>d</b>) Sum of collision avoidance components of robot 1 on the x-axis. (<b>e</b>) Sum of collision avoidance components of robot 1 on the y-axis. (<b>f</b>) Global error <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>x</mi> </mrow> </msub> </semantics></math> with respect to time of robot 1. (<b>g</b>) Global error <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>y</mi> </mrow> </msub> </semantics></math> with respect to time of robot 1. (<b>h</b>) Global error <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>1</mn> <mi>θ</mi> </mrow> </msub> </semantics></math> with respect to time of robot 1. (<b>i</b>) Linear velocity (<math display="inline"><semantics> <msub> <mi>v</mi> <mn>1</mn> </msub> </semantics></math>) with respect to time. (<b>j</b>) Angular velocity (<math display="inline"><semantics> <msub> <mi>w</mi> <mn>1</mn> </msub> </semantics></math>) with respect to time. (<b>k</b>) Sum of collision avoidance components of robot 2 on the x-axis. (<b>l</b>) Sum of collision avoidance components of robot 2 on the y-axis. (<b>m</b>) <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>x</mi> </mrow> </msub> </semantics></math> with respect to time of robot 2. (<b>n</b>) <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>y</mi> </mrow> </msub> </semantics></math> with respect to time of robot 2. (<b>o</b>) <math display="inline"><semantics> <msub> <mi>p</mi> <mrow> <mn>2</mn> <mi>θ</mi> </mrow> </msub> </semantics></math> with respect to time of robot 2. (<b>p</b>) Linear velocity <math display="inline"><semantics> <msub> <mi>v</mi> <mn>2</mn> </msub> </semantics></math> with respect to time. (<b>q</b>) Angular velocity <math display="inline"><semantics> <msub> <mi>w</mi> <mn>2</mn> </msub> </semantics></math> with respect to time. (<b>r</b>) Landmarks and other robots detected by robot 1. (<b>s</b>) Landmarks and other robots detected by robot 2.</p>
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24 pages, 26629 KiB  
Article
Optimization Model-Based Robust Method and Performance Evaluation of GNSS/INS Integrated Navigation for Urban Scenes
by Dashuai Chai, Shijie Song, Kunlin Wang, Jingxue Bi, Yunlong Zhang, Yipeng Ning and Ruijie Yan
Electronics 2025, 14(4), 660; https://doi.org/10.3390/electronics14040660 - 8 Feb 2025
Viewed by 466
Abstract
The robust and high-precision estimation of position and attitude information using a combined global navigation satellite system/inertial navigation system (GNSS/INS) model is essential to a wide range of applications in intelligent driving and smart transportation. GNSS systems are susceptible to inaccuracies and signal [...] Read more.
The robust and high-precision estimation of position and attitude information using a combined global navigation satellite system/inertial navigation system (GNSS/INS) model is essential to a wide range of applications in intelligent driving and smart transportation. GNSS systems are susceptible to inaccuracies and signal interruptions in occluded environments, which lead to unreliable parameter estimations in GNSS/INS based on filter models. To address this issue, in this paper, a GNSS/INS combination model based on factor graph optimization (FGO) is investigated and the robustness of this optimization model is evaluated in comparison to the traditional extended Kalman filter (EKF) model and robust Kalman filter (RKF) model. In this paper, both high- and low-accuracy GNSS/INS combination data are used and the two sets of urban scene data are collected using high- and low-precision consumer-grade inertial guidance systems and an in-vehicle setup. The experimental results demonstrate that the position, velocity, and attitude estimates obtained using the GNSS/INS and the FGO model are superior to those obtained using the traditional EKF and robust EKF methods. In the simulated scenarios involving gross interference and GNSS signal loss, the FGO model achieves optimal results. The maximum improvement rates of the position, velocity, and attitude estimates are 81.1%, 73.8%, and 75.1% compared to the EKF method and 79.8%, 72.1%, and 57.1% compared to the RKF method, respectively. Full article
(This article belongs to the Special Issue Recent Advance of Auto Navigation in Indoor Scenarios)
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<p>Loosely coupled PPP/INS model based on factor graph.</p>
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<p>Experiment acquisition scenario and platform.</p>
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<p>Position, velocity, and attitude errors of three estimation methods for high precision inertial guidance.</p>
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<p>Position, velocity, and attitude errors of three estimation methods for high precision inertial guidance.</p>
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<p>Simulated gross three parameter estimation methods position, velocity, and attitude errors.</p>
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<p>Position, velocity, and attitude errors estimated by the three methods of the GNSS lost lock 30 s scenario.</p>
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<p>Position, velocity, and attitude errors estimated by the three methods in the GNSS lost lock 60 s scenario.</p>
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<p>Error position velocity attitude RMS values for different GNSS lost lock conditions.</p>
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<p>Experiment area and experiment acquisition platform.</p>
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<p>Consumer inertial guidance three methods of combining model position, velocity, and attitude errors.</p>
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<p>Consumer inertial guidance three methods of combining model position, velocity, and attitude errors.</p>
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<p>The position, velocity, and attitude errors of the three parameter estimation methods under simulated gross errors.</p>
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<p>GNSS loss of lock for 30 s three methods to combine system position, velocity, and attitude errors.</p>
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<p>GNSS loss of lock for 30 s three methods to combine system position, velocity, and attitude errors.</p>
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<p>GNSS loss of lock for 60 s three methods to combine system position, velocity, and attitude errors.</p>
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<p>GNSS loss of lock for 60 s three methods to combine system position, velocity, and attitude errors.</p>
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<p>GNSS error position, velocity and attitude RMS statistics for three methods with different loss-of-lock durations.</p>
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<p>GNSS error position, velocity and attitude RMS statistics for three methods with different loss-of-lock durations.</p>
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13 pages, 5279 KiB  
Article
Nonlinear Control of a Permanent Magnet Synchronous Motor Based on State Space Neural Network Model Identification and State Estimation by Using a Robust Unscented Kalman Filter
by Sergio Velarde-Gomez and Eduardo Giraldo
Eng 2025, 6(2), 30; https://doi.org/10.3390/eng6020030 - 7 Feb 2025
Viewed by 446
Abstract
This work proposes a nonlinear modeling of a permanent magnet synchronous motor (PMSM) based on state space neural networks. The state space neural network is trained and the state variables (currents in a direct–quadrature frame and the rotational speed) are estimated by considering [...] Read more.
This work proposes a nonlinear modeling of a permanent magnet synchronous motor (PMSM) based on state space neural networks. The state space neural network is trained and the state variables (currents in a direct–quadrature frame and the rotational speed) are estimated by considering a robust Unscented Kalman Filter (UKF). Two contributions are presented in this work: the fist one is a nonlinear modeling structure for a PMSM based on a state space neural network that allows real-time parameter identification, and the second one is PMSM neural network training and state estimation based on a robust UKF. The robustness of the UKF is obtained by using a singular value decomposition of the covariance matrix. A comparison analysis is performed over a real PMSM motor by considering the proposed approach and a linear approximation of the nonlinear model where the states and parameters are computed by using an Extended Kalman Filter. The identified model is validated in closed loop by considering a nonlinear control strategy based on state feedback linearization. Full article
(This article belongs to the Special Issue Artificial Intelligence for Engineering Applications)
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<p>Block diagram that summarizes the proposed approach.</p>
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<p>Outputs of UKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 5 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100.</p>
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<p>States of UKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 5 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100.</p>
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<p>Inputs of UKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 5 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100.</p>
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<p>Parameters of UKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 5 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100.</p>
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<p>Outputs of EKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 5 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100.</p>
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<p>States of EKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 5 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100.</p>
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<p>Inputs of EKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 5 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100.</p>
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<p>Parameters of EKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 5 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100.</p>
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<p>Noise comparison for the output UKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 10, 25, 50, and 100 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100, 250, 500, and 1000.</p>
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<p>Noise comparison for the parameters UKF considering <math display="inline"><semantics> <mi>η</mi> </semantics></math> variance of 10, 25, 50, and 100 and <math display="inline"><semantics> <mi>ε</mi> </semantics></math> variance of 100, 250, 500, and 1000.</p>
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<p>High-speed reference tracking test from 800 to 1000 RPM.</p>
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46 pages, 12966 KiB  
Article
VRDeepSafety: A Scalable VR Simulation Platform with V2X Communication for Enhanced Accident Prediction in Autonomous Vehicles
by Mohammad BaniSalman, Mohammad Aljaidi, Najat Elgeberi, Ayoub Alsarhan and Rabia Emhamed Al Mamlook
World Electr. Veh. J. 2025, 16(2), 82; https://doi.org/10.3390/wevj16020082 - 6 Feb 2025
Viewed by 742
Abstract
Safe real-world navigation for autonomous vehicles (AVs) requires robust perception and decision-making, especially in complex, multi-agent scenarios. Existing AV datasets are limited by their inability to capture diverse V2X communication scenarios, lack of synchronized multi-sensor data, and insufficient coverage of critical edge cases [...] Read more.
Safe real-world navigation for autonomous vehicles (AVs) requires robust perception and decision-making, especially in complex, multi-agent scenarios. Existing AV datasets are limited by their inability to capture diverse V2X communication scenarios, lack of synchronized multi-sensor data, and insufficient coverage of critical edge cases in multi-vehicle interactions. This paper introduces VRDeepSafety, a novel and scalable VR simulation platform that overcomes these limitations by integrating Vehicle-to-Everything (V2X) communication, including realistic latency, packet loss, and signal prioritization, to enhance AV accident prediction and mitigation. VRDeepSafety generates comprehensive datasets featuring synchronized multi-vehicle interactions, coordinated V2X scenarios, and diverse sensor data, including visual, LiDAR, radar, and V2X streams. Evaluated with our novel deep-learning model, VRFormer, which uniquely fuses VR sensor data with V2X using a probabilistic Bayesian inference, as well as a hierarchical Kalman and particle filter structure, VRDeepSafety achieved an 85% accident prediction accuracy (APA) at a 2 s horizon, a 17% increase in 3D object detection precision (mAP), and a 0.3 s reduction in response time, outperforming a single-vehicle baseline. Furthermore, V2X integration increased APA by 15%. Extending the prediction horizon to 3–4 s reduced APA to 70%, highlighting the trade-off between prediction time and accuracy. The VRDeepSafety high-fidelity simulation and integrated V2X provide a valuable and rigorous tool for developing safer and more responsive AVs. Full article
(This article belongs to the Special Issue Vehicular Communications for Cooperative and Automated Mobility)
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<p>VRDeepSafety data generation philosophy diagram.</p>
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<p>Vehicle kinematics with Ackermann steering.</p>
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<p>V2X communication data flow in VRDeepSafety.</p>
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<p>Engineered accident scenarios within VRDeepSafety.</p>
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<p>Distribution of scenarios within the proposed VRDeepSafety dataset.</p>
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<p>Distribution of VRDeepSafety dataset subsets in feature space, represented by confidence ellipsoids.</p>
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<p>VRFormer deep-learning model architecture.</p>
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<p>VRFormer’s multi-source prediction system for movement and accident risk.</p>
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<p>The architecture and workflow of our proposed movement and accident prediction framework.</p>
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<p>Increased visibility accuracy comparison.</p>
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<p>Performance gains with increasing V2X intermediaries.</p>
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<p>VRFormer performance under different weather conditions.</p>
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<p>Trade-off between prediction horizon and accuracy for VRFormer.</p>
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<p>Accident prediction accuracy comparison.</p>
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<p>V2X-enhanced pedestrian detection in VRDeepSafety using VRFormer.</p>
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<p>System robustness to pose error and latency.</p>
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25 pages, 5677 KiB  
Article
Dynamic Modeling and Its Impact on Estimation Accuracy for GPS Navigation Filters
by Dah-Jing Jwo, Ta-Shun Cho and Birhanu Ayalew Demssie
Sensors 2025, 25(3), 972; https://doi.org/10.3390/s25030972 - 6 Feb 2025
Viewed by 552
Abstract
This study addresses the divergence issues in GPS navigation systems caused by inaccuracies in dynamic modeling and explores solutions using the extended Kalman filter (EKF). Since algorithms such as the Kalman filter (KF) and EKF rely on assumed process models that often deviate [...] Read more.
This study addresses the divergence issues in GPS navigation systems caused by inaccuracies in dynamic modeling and explores solutions using the extended Kalman filter (EKF). Since algorithms such as the Kalman filter (KF) and EKF rely on assumed process models that often deviate from real-world conditions, their performance in real-time applications can degrade. This paper introduces fictitious process noise as an effective remedy to mitigate divergence, demonstrating its benefits through covariance estimation and tuning factors to enhance observability and controllability, particularly for continuous differential GPS (DGPS) access. The study evaluates several motion scenarios, including stationary receivers, straight-line trajectories with constant and varying speeds, and turning trajectories. The inclusion of process noise allows the EKF to adapt to changes in direction and speed without explicitly modeling turning or acceleration dynamics. To ensure robustness, the simulations incorporate a variety of scenarios to assess the statistical reliability and real-world performance of the EKF, ensuring the findings are statistically robust and widely applicable. Simulated receivers were used to evaluate the position (P), position–velocity (PV), and position–velocity–acceleration (PVA) models. The results from both the Ordinary Least-Squares (OLS) and EKF simulations show improved vehicle trajectory tracking and demonstrate the EKF’s potential for broader navigation system applications. This paper’s novel contribution lies in its thorough analysis of the divergence issues in GPS navigation filter designs due to dynamic modeling inaccuracies, providing a systematic approach to addressing these challenges and offering new insights to improve estimation accuracy. Full article
(This article belongs to the Section Navigation and Positioning)
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<p>Flow chart for implementation of the extended Kalman filter.</p>
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<p>Configuration of the GPS extended Kalman filter.</p>
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<p>Position errors and the associated predicted 1-σ bound for a stationary receiver using the EKF, all with zero process noise covariance matrix <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mi>Q</mi> </mstyle> <mi>k</mi> </msub> <mrow> <mo>=</mo> <mn>0</mn> </mrow> </mrow> </semantics></math>. The blue, green, and red plots are results based on the P, PV, and PVA models, respectively: (<b>a</b>) east; (<b>b</b>) north.</p>
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<p>Test trajectory of the moving vehicle.</p>
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<p>Position errors using the EKF for a vehicle traveling along a straight-line path at a constant speed. The green, blue, and red plots are the results based on P, PV, and PVA models, respectively. (PV and PVA models with zero process noise covariance matrix <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mi>Q</mi> </mstyle> <mi>k</mi> </msub> <mrow> <mo>=</mo> <mn>0</mn> </mrow> </mrow> </semantics></math>; P model with tuning factor <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math>): (<b>a</b>) east; (<b>b</b>) north.</p>
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<p>Position errors for a vehicle traveling along a straight-line path at a constant speed. The EKF using P model with increasing <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mi>Q</mi> </mstyle> <mi>k</mi> </msub> </mrow> </semantics></math> values is presented. The green, red, and blue plots are results based on the tuning factor <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>, 100, and 1000, respectively: (<b>a</b>) east; (<b>b</b>) north; (<b>c</b>) 2D position errors.</p>
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<p>Position errors for a vehicle traveling along a straight-line path at a constant speed are analyzed using the EKF with the PV model and varying <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mi>Q</mi> </mstyle> <mi>k</mi> </msub> </mrow> </semantics></math> values. The green, blue, red, and black plots are the OLS and the EKF with tuning factors <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>0.1</mn> </mrow> </semantics></math>, 10, and 1000, respectively: (<b>a</b>) east; (<b>b</b>) north; (<b>c</b>) 2D position errors.</p>
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<p>The acceleration, velocity, and displacement of a vehicle along the straight-line trajectory with time-varying speed: (<b>a</b>) acceleration; (<b>b</b>) velocity; (<b>c</b>) displacement.</p>
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<p>Position estimation errors for a vehicle moving along a straight-line trajectory at time-varying speed. The EKF using the PV model with increasing <math display="inline"><semantics> <mrow> <msub> <mstyle mathvariant="bold" mathsize="normal"> <mi>Q</mi> </mstyle> <mi>k</mi> </msub> </mrow> </semantics></math> is presented. The green, black, red, and blue plots are the OLS and the EKF with small (<math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>) versus medium (<math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>10</mn> </mrow> </semantics></math>) and large (<math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math>), respectively: (<b>a</b>) east; (<b>b</b>) north; and (<b>c</b>) 2D position errors.</p>
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<p>Two test trajectories, straight-line and S-shape trajectories, of the moving vehicle with constant speed.</p>
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<p>Position errors based on the PV model applied to two trajectories of a moving vehicle. The green and blue plots are the position errors for the S-shape trajectory with <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>0.01</mn> </mrow> </semantics></math>, respectively: (<b>a</b>) east error (<b>left</b>) and a closer look on the interval 0 to 100 s (<b>right</b>); (<b>b</b>) north error (<b>left</b>) and a closer look on the interval 0 to 100 s (<b>right</b>).</p>
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<p>Position errors based on the PV model applied to two test trajectories of the moving vehicle. The green, blue, and red plots are S-shape trajectory with <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> versus straight-line trajectory with <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math> and <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>0</mn> </mrow> </semantics></math>, respectively: (<b>a</b>) east; (<b>b</b>) north.</p>
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<p>The motion along a straight line with two circular segments: (<b>a</b>) the trajectory; (<b>b</b>) angular velocity.</p>
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<p>Position errors for a trajectory of straight line with two circles are shown. The green, blue, red, and black plots are the solutions using EKF with tuning factors <math display="inline"><semantics> <mrow> <mi>ξ</mi> <mo>=</mo> <mn>1</mn> </mrow> </semantics></math>, 10, 100, and OLS, respectively: (<b>a</b>) east; (<b>b</b>) north; (<b>c</b>) 2D position errors.</p>
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32 pages, 4386 KiB  
Article
Multi-Source, Fault-Tolerant, and Robust Navigation Method for Tightly Coupled GNSS/5G/IMU System
by Zhongliang Deng, Zhichao Zhang, Zhenke Ding and Bingxun Liu
Sensors 2025, 25(3), 965; https://doi.org/10.3390/s25030965 - 5 Feb 2025
Viewed by 676
Abstract
The global navigation satellite system (GNSS) struggles to deliver the precision and reliability required for positioning, navigation, and timing (PNT) services in environments with severe interference. Fifth-generation (5G) cellular networks, with their low latency, high bandwidth, and large capacity, offer a robust communication [...] Read more.
The global navigation satellite system (GNSS) struggles to deliver the precision and reliability required for positioning, navigation, and timing (PNT) services in environments with severe interference. Fifth-generation (5G) cellular networks, with their low latency, high bandwidth, and large capacity, offer a robust communication infrastructure, enabling 5G base stations (BSs) to extend coverage into regions where traditional GNSSs face significant challenges. However, frequent multi-sensor faults, including missing alarm thresholds, uncontrolled error accumulation, and delayed warnings, hinder the adaptability of navigation systems to the dynamic multi-source information of complex scenarios. This study introduces an advanced, tightly coupled GNSS/5G/IMU integration framework designed for distributed PNT systems, providing all-source fault detection with weighted, robust adaptive filtering. A weighted, robust adaptive filter (MCC-WRAF), grounded in the maximum correntropy criterion, was developed to suppress fault propagation, relax Gaussian noise constraints, and improve the efficiency of observational weight distribution in multi-source fusion scenarios. Moreover, we derived the intrinsic relationships of filtering innovations within wireless measurement models and proposed a time-sequential, observation-driven full-source FDE and sensor recovery validation strategy. This approach employs a sliding window which expands innovation vectors temporally based on source encoding, enabling real-time validation of isolated faulty sensors and adaptive adjustment of observational data in integrated navigation solutions. Additionally, a covariance-optimal, inflation-based integrity protection mechanism was introduced, offering rigorous evaluations of distributed PNT service availability. The experimental validation was carried out in a typical outdoor scenario, and the results highlight the proposed method’s ability to mitigate undetected fault impacts, improve detection sensitivity, and significantly reduce alarm response times across step, ramp, and multi-fault mixed scenarios. Additionally, the dynamic positioning accuracy of the fusion navigation system improved to 0.83 m (1σ). Compared with standard Kalman filtering (EKF) and advanced multi-rate Kalman filtering (MRAKF), the proposed algorithm achieved 28.3% and 53.1% improvements in its 1σ error, respectively, significantly enhancing the accuracy and reliability of the multi-source fusion navigation system. Full article
(This article belongs to the Section Navigation and Positioning)
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<p>A weighted robust adaptive filtering and all-source fault detection framework for GNSS/5G/IMU tightly coupled navigation.</p>
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<p>GNSS/5G/IMU seamless and continuous indoor and outdoor positioning solution.</p>
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<p>State estimation procedure for different fault modes.</p>
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<p>(<b>a</b>) Experimental data acquisition path. (<b>b</b>) Experimental data acquisition equipment.</p>
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<p>Sky plot showing observable satellites. The pentagrams represent satellites.</p>
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<p>Step fault detection statistic and positioning error curves for GNSS/5G: (<b>a</b>) Case 1, (<b>b</b>) Case 2, (<b>c</b>) Case 4.</p>
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<p>Fault detection rate statistics for the two stages in case 4.</p>
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<p>Fault detection rate of SAT-17 under varying step errors.</p>
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<p>IMU step fault detection statistic and positioning error curves: (<b>a</b>) case 3.1, (<b>b</b>) case 3.2, and (<b>c</b>) case 3.3.</p>
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<p>Ramp fault detection statistics and positioning error curves for case 5. (<b>a</b>) Comparison of test statistics using different methods. (<b>b</b>) East-north-up positioning errors before and after FDE.</p>
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<p>Ramp fault detection statistics and positioning error curves for case 6. (<b>a</b>) Comparison of test statistics using different methods. (<b>b</b>) East-north-up positioning errors before and after FDE.</p>
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<p>Boxplot distribution of east-north-up positioning errors before and after FDE in ramp fault conditions.</p>
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<p>FDRs and RMSEs for various ramp fault conditions.</p>
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<p>Ramp fault detection statistics and positioning error curves for case 7. (<b>a</b>) Comparison of test statistics using different methods. (<b>b</b>) East-north-up positioning errors before and after FDE.</p>
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<p>Protection level curves: (<b>a</b>) before FDE and (<b>b</b>) after FDE.</p>
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<p>Stanford chart before and after FDE: (<b>a</b>) before FDE and (<b>b</b>) after FDE.</p>
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<p>Comparison of fusion localization errors of different navigation sources.</p>
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<p>Fusion Methods for Failure-Free Scenarios: (<b>a</b>) Position Error and (<b>b</b>) CDF Curves.</p>
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19 pages, 3542 KiB  
Article
A Hybrid Approach for Predictive Control of Oil Well Production Using Dynamic System Identification and Real-Time Parameter Estimation
by Anton Gryzlov, Eugene Magadeev and Muhammad Arsalan
Computation 2025, 13(2), 36; https://doi.org/10.3390/computation13020036 - 3 Feb 2025
Viewed by 495
Abstract
A significant part of modern natural sciences aims to establish a model-based approach to describe the behavior of physical systems and forecast their dynamics in different scenarios. The successful application of model-based analysis of transport phenomena is driven by several components, such as [...] Read more.
A significant part of modern natural sciences aims to establish a model-based approach to describe the behavior of physical systems and forecast their dynamics in different scenarios. The successful application of model-based analysis of transport phenomena is driven by several components, such as the consistency of a model and the uncertainty associated with its parameters. The unsatisfactory results of simulations can be caused by an improper choice of numerical methods used, but more importantly, it can be a result of wrong assumptions while establishing the model and a poor choice of closure parameters such as physical properties of fluids. This motivated the development of a hybrid approach that combines model identification directly from the data and subsequent real-time parameter estimation, which eventually minimizes the uncertainty of the developed model. This essentially brings a new model-based approach for an optimal simulation of physical phenomena by incorporating stringent interactions between all the stages of the modeling process. The identification of the governing equation from the data is achieved by a regression technique, while the model refinement is performed using the extended Kalman filter algorithm. The obtained in such a way model is then applied for control-oriented analysis. This paper discusses the deployment of such an integrated approach on a step-to-step basis and demonstrates its application to the problem of a single-phase oil inflow to the producing well. Full article
(This article belongs to the Section Computational Engineering)
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<p>Schematic description of the problem for radial inflow of oil in a vertical well from a heterogeneous reservoir.</p>
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<p>A general workflow for reconstructing equations and model refinement.</p>
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<p>Discretized simulation domain with model states and parameters. The dynamic variables are defined in the centers of grid blocks and the parameters at the interfaces.</p>
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<p>General approach for equation reconstruction.</p>
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<p>A process of reconstructing the Darcy–Forchheimer equation and detailing the absolute value of the inertial coefficient.</p>
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<p>A process of reconstructing the Darcy equation and detailing the absolute values of permeability.</p>
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<p>A general workflow for reconstructing equations from the data and subsequent model refinement.</p>
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<p>A process of reconstructing the permeability field. Figures represent different time instants: 2000 s, 4000 s, 6000 s, and 8000 s (final) of simulation.</p>
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<p>Pressure and flow rate as a function of time at target rate of <span class="html-italic">Q</span><sub>0</sub> = 2. Base inner and outer pressures correspond to the scenario without any wellbore pressure control. Actual inner and outer pressures correspond to the scenario with wellbore pressure control. Target, base, and actual production rates refer to target flow rate <span class="html-italic">Q</span><sub>0</sub> and flow rate values without and with optimal control, respectively.</p>
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<p>Pressure and flow rate as a function of time at a target rate of <span class="html-italic">Q</span><sub>0</sub> = 10. The same notation as in <a href="#computation-13-00036-f009" class="html-fig">Figure 9</a> applies.</p>
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<p>Pressure and flow rate as a function of time at a target rate of <span class="html-italic">Q</span><sub>0</sub> = 10. The same notation as in <a href="#computation-13-00036-f009" class="html-fig">Figure 9</a> applies. Dashed lines correspond to single-time optimization strategy.</p>
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15 pages, 9933 KiB  
Article
Nanosatellite Autonomous Navigation via Extreme Learning Machine Using Magnetometer Measurements
by Gilberto Goracci, Fabio Curti and Mark Anthony de Guzman
Aerospace 2025, 12(2), 117; https://doi.org/10.3390/aerospace12020117 - 3 Feb 2025
Viewed by 542
Abstract
This work presents an algorithm to perform autonomous navigation in spacecraft using onboard magnetometer data during GPS outages. An Extended Kalman Filter (EKF) exploiting magnetic field measurements is combined with a Single-Hidden-Layer Feedforward Neural Network (SLFN) trained via the Extreme Learning Machine to [...] Read more.
This work presents an algorithm to perform autonomous navigation in spacecraft using onboard magnetometer data during GPS outages. An Extended Kalman Filter (EKF) exploiting magnetic field measurements is combined with a Single-Hidden-Layer Feedforward Neural Network (SLFN) trained via the Extreme Learning Machine to improve the accuracy of the state estimate. The SLFN is trained using GPS data when available and predicts the state correction to be applied to the EKF estimates. The CHAOS-7 magnetic field model is used to generate the magnetometer measurements, while a 13th-order IGRF model is exploited by the EKF. Tests on simulated data showed that the algorithm improved the state estimate provided by the EKF by a factor of 2.4 for a total of 51 days when trained on 5 days of GPS data. Full article
(This article belongs to the Special Issue Deep Space Exploration)
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<p>ELM Neural Network structure.</p>
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<p>The tuning process of the measurement noise matrix <math display="inline"><semantics> <mrow> <msub> <mi mathvariant="bold">R</mi> <mi>B</mi> </msub> <mo>=</mo> <msup> <mi>α</mi> <mn>2</mn> </msup> <mo>·</mo> <msub> <mi mathvariant="bold">I</mi> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </msub> </mrow> </semantics></math>. The position (<b>left</b>) and velocity (<b>right</b>) mean (blue) and maximum (red) RSSE of different EKF runs are shown against the corresponding value of <math display="inline"><semantics> <msub> <mi mathvariant="bold">R</mi> <mi>B</mi> </msub> </semantics></math>. The best configuration is obtained for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>=</mo> <mn>1000</mn> </mrow> </semantics></math> nT. Each EKF run has a duration of 100,000 s, corresponding to 10,000 iterations.</p>
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<p>SLFN training process.</p>
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<p>Locations of ground magnetic observatories providing data for derivation of CHAOS-7 from [<a href="#B16-aerospace-12-00117" class="html-bibr">16</a>], published under license CC BY 4.0.</p>
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<p>The geomagnetic field magnitude difference between the CHAOS-7 and IGRF-13 models at a fixed altitude of 567 km with a 5° resolution. The red line represents the satellite ground track from the beginning to the end of the simulation (from 3 January to 3 May 2019).</p>
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<p>EKF-SLFN algorithm prediction scheme.</p>
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<p>The EKF (red) and SLFN (blue) position (<b>top</b>) and velocity (<b>bottom</b>) RSSE over time. The yellow and green backgrounds distinguish between the training and prediction phases of the SLFN, respectively. The horizontal dashed lines correspond to the mean RSSE values over the whole run.</p>
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<p>The daily EKF (red) and SLFN (blue) position (<b>top</b>) and velocity (<b>bottom</b>) mean RSSE over time, obtained from an extended 120-day simulation. Daily standard deviations are represented as error bars.</p>
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