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Keywords = cascaded extended Kalman filter (EKF)

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15 pages, 5551 KiB  
Article
Online Nodal Demand Estimation in Branched Water Distribution Systems Using an Array of Extended Kalman Filters
by Francisco-Ronay López-Estrada, Leonardo Gómez-Coronel, Lizeth Torres, Guillermo Valencia-Palomo, Ildeberto Santos-Ruiz and Arlette Cano
Sensors 2025, 25(8), 2632; https://doi.org/10.3390/s25082632 - 21 Apr 2025
Viewed by 463
Abstract
This paper proposes a model-based methodology to estimate multiple nodal demands by using only pressure and flow rate measurements, which should be recorded at the inlet of the distribution system. The algorithm is based on an array of multiple extended Kalman filters (EKFs) [...] Read more.
This paper proposes a model-based methodology to estimate multiple nodal demands by using only pressure and flow rate measurements, which should be recorded at the inlet of the distribution system. The algorithm is based on an array of multiple extended Kalman filters (EKFs) in a cascade configuration. Each EKF functions as an unknown input observer and focuses on a section of the pipeline. The pipeline model used to design the filters is an adaptation of the well-known rigid water column model. Simulation and experimental tests on standardized pipeline systems are presented to demonstrate the proposed method’s effectiveness. Finally, for the case of the experimental validation, both steady-state and variable input conditions were considered. Full article
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18 pages, 6790 KiB  
Article
A Double Extended Kalman Filter Algorithm for Weakening Non-Line-of-Sight Errors in Complex Indoor Environments Based on Ultra-Wideband Technology
by Sheng Xu, Qianyun Liu, Min Lin, Qing Wang and Kaile Chen
Sensors 2025, 25(3), 740; https://doi.org/10.3390/s25030740 - 26 Jan 2025
Viewed by 611
Abstract
In complex indoor environments, target tracking performance is impacted by non-line-of sight (NLOS) noises and other measurement errors. In order to fix NLOS errors, a double extended Kalman filter (DEKF) algorithm is proposed, which refers to a kind of cascaded structure composed of [...] Read more.
In complex indoor environments, target tracking performance is impacted by non-line-of sight (NLOS) noises and other measurement errors. In order to fix NLOS errors, a double extended Kalman filter (DEKF) algorithm is proposed, which refers to a kind of cascaded structure composed of two Kalman filters. In the proposed algorithm, the first filter is a classic Kalman filter (KF) and the second is an extended Kalman filter (EKF). Time of arrival (TOA) measurements collected by multiple stationary ultra-wideband (UWB) sensors are used. The residual errors between the measured TOA and that of the first KF are predicted, and the covariance of the first KF is adjusted correspondingly. Then, we use the estimated distance state of the first KF as a measurement vector for the second EKF in order to obtain a smoother observation. One of the advantages of the proposed algorithm is that it is able to perform target tracking with good accuracy even without or with only one LOS TOA measurement for a period of time without prior information about the NLOS noise, which may be difficult to obtain in practical applications. Another advantage is that the accuracy does not greatly decrease when NLOS noises exist for a long period of time. Finally, the proposed DEKF can maintain the high-precision positioning characteristics in both the constant velocity (CV) model and the constant acceleration (CA) model in the LOS/NLOS environment. Our simulation and experimental results show that the proposed algorithm performs much better than other algorithms in SOTA, particularly in severe mixed LOS/NLOS environments. Full article
(This article belongs to the Section Navigation and Positioning)
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19 pages, 6803 KiB  
Article
A Novel Non-Line-of-Sight Error Mitigation Algorithm Using Double Extended Kalman Filter for Ultra-Wide Band Ranging Technology
by Sheng Xu, Qianyun Liu, Min Lin, Qing Wang and Kaile Chen
Electronics 2025, 14(3), 483; https://doi.org/10.3390/electronics14030483 - 25 Jan 2025
Cited by 1 | Viewed by 911
Abstract
In complex indoor environments, target tracking performance is impacted by non-line-of-sight (NLOS) noises and other measurement errors. In order to fix NLOS errors, a Double Extended Kalman filter (DEKF) algorithm is proposed, which refers to a kind of cascaded structure composed of two [...] Read more.
In complex indoor environments, target tracking performance is impacted by non-line-of-sight (NLOS) noises and other measurement errors. In order to fix NLOS errors, a Double Extended Kalman filter (DEKF) algorithm is proposed, which refers to a kind of cascaded structure composed of two Kalman filters. In the proposed algorithm, the first filter is a classic Kalman filter (KF) and the second is an Extended Kalman filter (EKF). The time of arrival (TOA) measurements collected by multiple stationary ultra-wide band (UWB) sensors are used. Residual errors between the measured TOA and the prediction from the first KF are used to adjust the covariance of the first KF accordingly. Then, we use the estimated distance state of the first KF as a measurement vector of the second EKF in order to obtain a smoother observation. One of the advantages of the proposed algorithm is that it is able to perform target tracking with a good accuracy even without or with only one line-of-sight(LOS) TOA measurement for a period of time without prior information of the NLOS noise, which may be difficult to obtain in practical applications. Another advantage is that the accuracy does not significantly decrease when NLOS noises persist for a long period of time. Finally, the proposed DEKF can maintain high-precision positioning characteristics in both the constant velocity (CV) model and the constant acceleration (CA) model for LOS/NLOS environments. In the case of mixed LOS/NLOS environments, the RMSE of the proposed algorithm can be kept within 5 cm, while the RMSEs of other compared algorithms are easily beyond tens of centimeters. At the same time, when the confidence of RMSE is set to 95% for 1000 MC simulations, the confidence interval of the proposed algorithm is the smallest, and the mean value is 3–5 times closer to the true value compared to other algorithms. Simulation and experimental results show that the proposed algorithm performs much better than other state-of-the-art algorithms, particularly in severe mixed LOS/NLOS environments. Full article
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16 pages, 939 KiB  
Article
State-of-Charge and State-of-Health Estimation in Li-Ion Batteries Using Cascade Electrochemical Model-Based Sliding-Mode Observers
by Yong Feng, Chen Xue, Fengling Han, Zhenwei Cao and Rebecca Jing Yang
Batteries 2024, 10(8), 290; https://doi.org/10.3390/batteries10080290 - 15 Aug 2024
Cited by 4 | Viewed by 1615
Abstract
This paper proposes a cascade approach based on a sliding mode observer (SMO) for estimating the state of charge (SoC) and state of health (SoH) of lithium-ion (Li-ion) batteries using a single particle model (SPM). After convergence, the observation error signal of the [...] Read more.
This paper proposes a cascade approach based on a sliding mode observer (SMO) for estimating the state of charge (SoC) and state of health (SoH) of lithium-ion (Li-ion) batteries using a single particle model (SPM). After convergence, the observation error signal of the current node in the cascade observer is generated from the output injection signal of the previous node’s observer. The current node’s observer generates its output injection signal, leading to its convergence. This sequential process accurately determines the observed values of each node using only the battery’s current and voltage. Subsequently, the SoC and SoH are estimated using observations of lithium-ion concentrations on the surface and inside the battery anode. The accuracy of this approach is validated using Dynamic Stress Test (DST) and Federal Urban Driving Scheme (FUDS) experimental data. A comparative analysis with conventional SMO and Extended Kalman Filter (EKF) algorithms demonstrates the approach’s effectiveness and superior performance, confirming its practical applicability. Full article
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20 pages, 14884 KiB  
Article
Current Sensor Fault-Tolerant Control Strategy for Speed-Sensorless Control of Induction Motors Based on Sequential Probability Ratio Test
by Feige Zhang, Shesheng Gao, Wenjuan Zhang, Guo Li and Chao Zhang
Electronics 2024, 13(13), 2476; https://doi.org/10.3390/electronics13132476 - 25 Jun 2024
Cited by 4 | Viewed by 1445
Abstract
In the speed-sensorless vector control of induction motors (IMs), the speed estimation accuracy suffers from the deteriorated current measurement caused by the current sensor faults, such as open circuit in one phase, DC bias, and odd harmonics. In this paper, a novel speed [...] Read more.
In the speed-sensorless vector control of induction motors (IMs), the speed estimation accuracy suffers from the deteriorated current measurement caused by the current sensor faults, such as open circuit in one phase, DC bias, and odd harmonics. In this paper, a novel speed estimation strategy based on the current sensor fault-tolerant control is proposed to improve the speed estimation accuracy under the current sensor faults. First, to detect the current sensor faults in real time, the sequential probability ratio test is introduced to the system by using the innovations of the extended Kalman filter (EKF). Second, to ensure speed estimation accuracy, a double-cascading second-order generalized integrator (DSOGI) is employed to reconstruct the faulty current information when a fault is identified. Finally, the reconstructed current information is fed back to the sequential probability extended Kalman filter (SPEKF), which estimates the rotor speed of the IM, and high-accuracy speed estimation under the condition of current sensor faults is achieved. The effectiveness of the proposed strategy is validated by a series of experiments, which were conducted on a 3 kW induction motor drive platform. Full article
(This article belongs to the Special Issue New Insights Into Smart and Intelligent Sensors)
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18 pages, 17282 KiB  
Article
A Cascaded and Adaptive Visual Predictive Control Approach for Real-Time Dynamic Visual Servoing
by Sina Sajjadi, Mehran Mehrandezh and Farrokh Janabi-Sharifi
Drones 2022, 6(5), 127; https://doi.org/10.3390/drones6050127 - 14 May 2022
Cited by 8 | Viewed by 3055
Abstract
In the past two decades, Unmanned Aerial Vehicles (UAVs) have gained attention in applications such as industrial inspection, search and rescue, mapping, and environment monitoring. However, the autonomous navigation capability of UAVs is aggravated in GPS-deprived areas such as indoors. As a result, [...] Read more.
In the past two decades, Unmanned Aerial Vehicles (UAVs) have gained attention in applications such as industrial inspection, search and rescue, mapping, and environment monitoring. However, the autonomous navigation capability of UAVs is aggravated in GPS-deprived areas such as indoors. As a result, vision-based control and guidance methods are sought. In this paper, a vision-based target-tracking problem is formulated in the form of a cascaded adaptive nonlinear Model Predictive Control (MPC) strategy. The proposed algorithm takes the kinematics/dynamics of the system, as well as physical and image constraints into consideration. An Extended Kalman Filter (EKF) is designed to estimate uncertain and/or time-varying parameters of the model. The control space is first divided into low and high levels, and then, they are parameterised via orthonormal basis network functions, which makes the optimisation- based control scheme computationally less expensive, therefore suitable for real-time implementation. A 2-DoF model helicopter, with a coupled nonlinear pitch/yaw dynamics, equipped with a front-looking monocular camera, was utilised for hypothesis testing and evaluation via experiments. Simulated and experimental results show that the proposed method allows the model helicopter to servo toward the target efficiently in real-time while taking kinematic and dynamic constraints into account. The simulation and experimental results are in good agreement and promising. Full article
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19 pages, 4696 KiB  
Article
Real-Time Terrain-Following of an Autonomous Quadrotor by Multi-Sensor Fusion and Control
by Yuan Yang, Yongjiang Huang, Haoran Yang, Tingting Zhang, Zixuan Wang and Xixiang Liu
Appl. Sci. 2021, 11(3), 1065; https://doi.org/10.3390/app11031065 - 25 Jan 2021
Cited by 7 | Viewed by 3748
Abstract
For the application of the autonomous guidance of a quadrotor from confined undulant ground, terrain-following is the major issue for flying at a low altitude. This study has modified the open-source autopilot based on the integration of a multi-sensor receiver (a Global Navigation [...] Read more.
For the application of the autonomous guidance of a quadrotor from confined undulant ground, terrain-following is the major issue for flying at a low altitude. This study has modified the open-source autopilot based on the integration of a multi-sensor receiver (a Global Navigation Satellite System (GNSS)), a Lidar-lite (a laser-range-finder device), a barometer and a low-cost inertial navigation system (INS)). These automatically control the position, attitude and height (a constant clearance above the ground) to allow terrain-following and avoid obstacles based on multi-sensors that maintain a constant height above flat ground or with obstacles. The INS/Lidar-lite integration is applied for the attitude and the height stabilization, respectively. The height control is made by the combination of an extended Kalman filter (EKF) estimator and a cascade proportional-integral-derivative (PID) controller that is designed appropriately for the noise characteristics of low accuracy sensors. The proposed terrain-following is tested by both simulations and real-world experiments. The results indicate that the quadrotor can continuously navigate and avoid obstacles at a real-time response of reliable height control with the adjustment time of the cascade PID controller improving over 50% than that of the PID controller. Full article
(This article belongs to the Special Issue Intelligent Robotics and Mechatronics)
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20 pages, 2136 KiB  
Article
Enhanced Pedestrian Navigation Based on Course Angle Error Estimation Using Cascaded Kalman Filters
by Jin Woo Song and Chan Gook Park
Sensors 2018, 18(4), 1281; https://doi.org/10.3390/s18041281 - 21 Apr 2018
Cited by 26 | Viewed by 7109
Abstract
An enhanced pedestrian dead reckoning (PDR) based navigation algorithm, which uses two cascaded Kalman filters (TCKF) for the estimation of course angle and navigation errors, is proposed. The proposed algorithm uses a foot-mounted inertial measurement unit (IMU), waist-mounted magnetic sensors, and a zero [...] Read more.
An enhanced pedestrian dead reckoning (PDR) based navigation algorithm, which uses two cascaded Kalman filters (TCKF) for the estimation of course angle and navigation errors, is proposed. The proposed algorithm uses a foot-mounted inertial measurement unit (IMU), waist-mounted magnetic sensors, and a zero velocity update (ZUPT) based inertial navigation technique with TCKF. The first stage filter estimates the course angle error of a human, which is closely related to the heading error of the IMU. In order to obtain the course measurements, the filter uses magnetic sensors and a position-trace based course angle. For preventing magnetic disturbance from contaminating the estimation, the magnetic sensors are attached to the waistband. Because the course angle error is mainly due to the heading error of the IMU, and the characteristic error of the heading angle is highly dependent on that of the course angle, the estimated course angle error is used as a measurement for estimating the heading error in the second stage filter. At the second stage, an inertial navigation system-extended Kalman filter-ZUPT (INS-EKF-ZUPT) method is adopted. As the heading error is estimated directly by using course-angle error measurements, the estimation accuracy for the heading and yaw gyro bias can be enhanced, compared with the ZUPT-only case, which eventually enhances the position accuracy more efficiently. The performance enhancements are verified via experiments, and the way-point position error for the proposed method is compared with those for the ZUPT-only case and with other cases that use ZUPT and various types of magnetic heading measurements. The results show that the position errors are reduced by a maximum of 90% compared with the conventional ZUPT based PDR algorithms. Full article
(This article belongs to the Special Issue Inertial Sensors and Systems 2018)
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24 pages, 5109 KiB  
Article
A Robust Inner and Outer Loop Control Method for Trajectory Tracking of a Quadrotor
by Dunzhu Xia, Limei Cheng and Yanhong Yao
Sensors 2017, 17(9), 2147; https://doi.org/10.3390/s17092147 - 19 Sep 2017
Cited by 24 | Viewed by 7659
Abstract
In order to achieve the complicated trajectory tracking of quadrotor, a geometric inner and outer loop control scheme is presented. The outer loop generates the desired rotation matrix for the inner loop. To improve the response speed and robustness, a geometric SMC controller [...] Read more.
In order to achieve the complicated trajectory tracking of quadrotor, a geometric inner and outer loop control scheme is presented. The outer loop generates the desired rotation matrix for the inner loop. To improve the response speed and robustness, a geometric SMC controller is designed for the inner loop. The outer loop is also designed via sliding mode control (SMC). By Lyapunov theory and cascade theory, the closed-loop system stability is guaranteed. Next, the tracking performance is validated by tracking three representative trajectories. Then, the robustness of the proposed control method is illustrated by trajectory tracking in presence of model uncertainty and disturbances. Subsequently, experiments are carried out to verify the method. In the experiment, ultra wideband (UWB) is used for indoor positioning. Extended Kalman Filter (EKF) is used for fusing inertial measurement unit (IMU) and UWB measurements. The experimental results show the feasibility of the designed controller in practice. The comparative experiments with PD and PD loop demonstrate the robustness of the proposed control method. Full article
(This article belongs to the Section Physical Sensors)
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18 pages, 7134 KiB  
Article
A Map/INS/Wi-Fi Integrated System for Indoor Location-Based Service Applications
by Chunyang Yu, Haiyu Lan, Fuqiang Gu, Fei Yu and Naser El-Sheimy
Sensors 2017, 17(6), 1272; https://doi.org/10.3390/s17061272 - 2 Jun 2017
Cited by 41 | Viewed by 6339
Abstract
In this research, a new Map/INS/Wi-Fi integrated system for indoor location-based service (LBS) applications based on a cascaded Particle/Kalman filter framework structure is proposed. Two-dimension indoor map information, together with measurements from an inertial measurement unit (IMU) and Received Signal Strength Indicator (RSSI) [...] Read more.
In this research, a new Map/INS/Wi-Fi integrated system for indoor location-based service (LBS) applications based on a cascaded Particle/Kalman filter framework structure is proposed. Two-dimension indoor map information, together with measurements from an inertial measurement unit (IMU) and Received Signal Strength Indicator (RSSI) value, are integrated for estimating positioning information. The main challenge of this research is how to make effective use of various measurements that complement each other in order to obtain an accurate, continuous, and low-cost position solution without increasing the computational burden of the system. Therefore, to eliminate the cumulative drift caused by low-cost IMU sensor errors, the ubiquitous Wi-Fi signal and non-holonomic constraints are rationally used to correct the IMU-derived navigation solution through the extended Kalman Filter (EKF). Moreover, the map-aiding method and map-matching method are innovatively combined to constrain the primary Wi-Fi/IMU-derived position through an Auxiliary Value Particle Filter (AVPF). Different sources of information are incorporated through a cascaded structure EKF/AVPF filter algorithm. Indoor tests show that the proposed method can effectively reduce the accumulation of positioning errors of a stand-alone Inertial Navigation System (INS), and provide a stable, continuous and reliable indoor location service. Full article
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32 pages, 19409 KiB  
Article
Roll and Bank Estimation Using GPS/INS and Suspension Deflections
by Lowell S. Brown and David M. Bevly
Electronics 2015, 4(1), 118-149; https://doi.org/10.3390/electronics4010118 - 29 Jan 2015
Cited by 4 | Viewed by 5997
Abstract
This article presents a method that provides an estimate of road bank by decoupling the vehicle roll due to the dynamics and the roll due to the road bank. Suspension deflection measurements were used to provide a measurement of the relative roll between [...] Read more.
This article presents a method that provides an estimate of road bank by decoupling the vehicle roll due to the dynamics and the roll due to the road bank. Suspension deflection measurements were used to provide a measurement of the relative roll between the vehicle body frame and the axle frame or between the sprung mass and the unsprung mass, respectively. A deflection scaling parameter was found via suspension geometry and dynamic analysis. The relative roll measurement was then incorporated into two different kinematic navigation models based on extended Kalman filter (EKF) architectures. Each algorithm was tested and then verified on the Prowler ATV experimental platform at the National Center for Asphalt Technology (NCAT). Experimental data showed that both the cascaded and coupled approach performed well in providing estimates of the current vehicle roll and instantaneous road bank. Full article
(This article belongs to the Special Issue Intelligent and Cooperative Vehicles)
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21 pages, 2047 KiB  
Article
A New Blondin System for Surveying and Photogrammetry
by Federico Cuesta, Francisco M. Lopez-Rodriguez and Antonio Esteban
Sensors 2013, 13(12), 16894-16914; https://doi.org/10.3390/s131216894 - 6 Dec 2013
Cited by 3 | Viewed by 8492
Abstract
The main objective of the system presented in this paper is to provide surveyors and engineers with a new photogrammetry device that can be easily integrated with surveying total stations and a global navigation satellite system (GNSS) infrastructure at a construction site, taking [...] Read more.
The main objective of the system presented in this paper is to provide surveyors and engineers with a new photogrammetry device that can be easily integrated with surveying total stations and a global navigation satellite system (GNSS) infrastructure at a construction site, taking advantage of their accuracy and overcoming limitations of aerial vehicles with respect to weight, autonomy and skilled operator requirements in aerial photogrammetry. The system moves between two mounting points, in a blondin ropeway configuration, at the construction site, taking pictures and recording the data of the position and the orientation along the cable path. A cascaded extended Kalman filter is used to integrate measurements from the on-board inertial measurement unit (IMU), a GPS and a GNSS. Experimental results taken in a construction site show the system performance, including the validation of the position estimation, with a robotic surveying total station, or the creation of a digital surface model (DSM), using the emergent structure from motion (SfM) techniques and open software. The georeferencing of the DSM is performed based on estimated camera position or using ground control points (GCPs). Full article
(This article belongs to the Special Issue State-of-the-Art Sensors Technology in Spain 2013)
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