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Keywords = inverse covariance intersection

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24 pages, 10477 KB  
Article
Consistent Fusion of MADOCA-PPP and PPP-B2b SSR Corrections for Robust Real-Time PPP
by Ruite Yi, Xiangwei Zhu, Mingjun Ouyang, Lu Cao, Jibing Wu and Guangteng Fan
Remote Sens. 2026, 18(12), 1973; https://doi.org/10.3390/rs18121973 (registering DOI) - 13 Jun 2026
Abstract
Real-time precise point positioning (PPP) is increasingly supported by open satellite-broadcast state-space representation (SSR) services, yet standalone operation with a single service remains vulnerable to limited constellation support, correction outages, latency variations, and service-dependent modeling inconsistencies. In the Asia-Pacific region, MADOCA-PPP and PPP-B2b [...] Read more.
Real-time precise point positioning (PPP) is increasingly supported by open satellite-broadcast state-space representation (SSR) services, yet standalone operation with a single service remains vulnerable to limited constellation support, correction outages, latency variations, and service-dependent modeling inconsistencies. In the Asia-Pacific region, MADOCA-PPP and PPP-B2b provide two publicly accessible and complementary SSR sources, but their consistent fusion before user-level PPP estimation remains insufficiently investigated. This paper proposes a correction-domain fusion framework that combines MADOCA-PPP and PPP-B2b orbit and clock corrections before PPP estimation, rather than merging final positioning solutions. Inter-service discrepancies and unknown cross-correlations are handled by a bias-state-aware structured covariance intersection strategy, in which the relative weighting is derived from the respective correction information (inverse variance), preserving statistical consistency and avoiding overconfident fusion. A unified multi-GNSS PPP scheme further supports signal-priority harmonization, broadcast-ephemeris adaptation, correction-age control, and GLONASS inter-frequency and differential code bias handling. Static-station per-epoch (pseudo-kinematic) and offshore kinematic experiments validate the framework. In the static-station test, fusion raised the mean number of valid satellites from 21.98 and 14.98 to 26.56 and improved the horizontal RMS to 0.033 m—better than either standalone service (0.037 m, 0.079 m)—confirming a genuine combination rather than source selection, while the 3D RMS (0.068 m) matched the best standalone service (0.066 m). In the offshore test, fusion achieved the best overall accuracy (0.232 m horizontal, 0.290 m 3D, versus 0.332 m and 0.313 m for the standalone services) and the most satellites (25.4). It also degraded most slowly with increasing elevation cut-off, outperforming both services about threefold at 40°. A normalized-innovation-squared check confirmed the fused covariance is consistent and not overconfident (median ≈ 1.1; within the 99% bound in 100% of epochs). Under single-service outages from 30 s to 600 s, fusion maintained 100.0% availability, confirming its advantage in redundancy, continuity, and resilience. Full article
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20 pages, 1930 KB  
Article
A Distributed Fusion Method for Underwater Multi-Sensor Passive Tracking Based on Extended Measurement Space
by Wen Zhang, Tianlin Yang, Xuanzhi Zhao, Jingmin Tang, Zengli Liu and Kang Liu
Electronics 2026, 15(8), 1589; https://doi.org/10.3390/electronics15081589 - 10 Apr 2026
Viewed by 406
Abstract
Underwater multi-sensor passive tracking faces two critical challenges: the strong nonlinearity of Doppler–bearing measurements and underwater acoustic propagation delays. To address these issues, this paper proposes a distributed fusion filtering method based on extended measurement space modeling and delay compensation. First, an extended [...] Read more.
Underwater multi-sensor passive tracking faces two critical challenges: the strong nonlinearity of Doppler–bearing measurements and underwater acoustic propagation delays. To address these issues, this paper proposes a distributed fusion filtering method based on extended measurement space modeling and delay compensation. First, an extended measurement space comprising range, Doppler frequency, bearing, and bearing rate is constructed to transform the nonlinear measurements into a linear framework. Within this space, linear prediction equations for constant velocity (CV) motion are derived to facilitate linearized local filtering. Furthermore, a closed-form linear solution for propagation delay is established within the constructed state space. To resolve the incompatibility of multi-node estimates caused by local coordinate frame discrepancies, a distributed architecture based on the Unscented Transform (UT) is designed. In this architecture, local states are transformed into a unified Cartesian coordinate system for temporal compensation and fast Covariance Intersection (FCI) fusion, followed by an inverse mapping back to the local space. Simulation results demonstrate that, compared with traditional nonlinear methods based on mixed coordinate systems, the proposed method significantly reduces nonlinear approximation errors, thereby enhancing tracking accuracy and robustness. Full article
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19 pages, 7352 KB  
Article
Track-to-Track Fusion for Cooperative Perception Using Collective Perception Messages
by Redge Melroy Castelino, Shrijal Pradhan and Axel Hahn
Sensors 2026, 26(6), 2003; https://doi.org/10.3390/s26062003 - 23 Mar 2026
Viewed by 652
Abstract
Vehicle-to-everything communication grants connected and automated road vehicles the opportunity to share their sensor information such as detected road objects for collective awareness. This paper compares various state fusion strategies within a high-level cooperative perception architecture, focusing on the fusion of object-level information [...] Read more.
Vehicle-to-everything communication grants connected and automated road vehicles the opportunity to share their sensor information such as detected road objects for collective awareness. This paper compares various state fusion strategies within a high-level cooperative perception architecture, focusing on the fusion of object-level information provided in standard Collective Perception Messages. This work compares five track-to-track fusion methods, namely Covariance Intersection, Inverse Covariance Intersection, Adapted Extended Kalman Filter, Adapted Unscented Kalman Filter and Information Matrix Fusion, using a simulation framework built with CARLA and Autoware. The methods are analyzed in a case study to assess their performance under different vehicle maneuvers and varying input information accuracy. The case study highlights trade-offs between fusion strategies and illustrate their behavior in asynchronous multi-agent scenarios. While the analysis is conducted in simulation, the architecture is designed to be extensible, and directions for future development are outlined, including the integration of classification and object confidence fusion modules. Full article
(This article belongs to the Special Issue Cooperative Perception and Control for Autonomous Vehicles)
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21 pages, 2588 KB  
Article
Distributed Consensus-Based Tracking with Inverse Covariance Intersection in Bearing-Only UAV Networks
by Guangyu Yang, Wenhui Ma, Wenxing Fu, Supeng Zhu and Tong Zhang
Drones 2026, 10(2), 107; https://doi.org/10.3390/drones10020107 - 2 Feb 2026
Viewed by 577
Abstract
High-precision and consensus tracking of a long-range maneuvering target presents a significant challenge for unmanned aerial vehicles (UAVs) in complex denied environments. Earlier studies rarely considered the fast convergence and fusion accuracy of distributed consensus tracking in bearing-only UAV networks. This article proposes [...] Read more.
High-precision and consensus tracking of a long-range maneuvering target presents a significant challenge for unmanned aerial vehicles (UAVs) in complex denied environments. Earlier studies rarely considered the fast convergence and fusion accuracy of distributed consensus tracking in bearing-only UAV networks. This article proposes a distributed consensus-based estimation (DCE) method with inverse covariance intersection (ICI) fusion rule in the framework of local estimation, consensus iteration, and fusion estimation. Combined with the contribution of measurements from neighboring UAVs, the local estimation of target tracking can be achieved by a square-root cubature information filter (SRCIF) in bearing-only UAVs. Based on local estimation and centralities in a multi-UAV network, each UAV platform can obtain consensus results in a finite number of iterations. Then, the fusion estimations are the consensus with the global ICI fusion rule. Furthermore, the fusion estimations are analyzed in consensus, finiteness, and boundedness. Numerical simulations are performed to validate the effectiveness and superiority of the proposed DCE–ICI method. Full article
(This article belongs to the Section Drone Communications)
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18 pages, 2669 KB  
Communication
The GM-JMNS-CPHD Filtering Algorithm for Nonlinear Systems Based on a Generalized Covariance Intersection
by Zhixuan Xu, Yu Wei, Xiaobao Qin and Pengfei Guo
Sensors 2024, 24(5), 1508; https://doi.org/10.3390/s24051508 - 26 Feb 2024
Cited by 1 | Viewed by 1835
Abstract
Some fusion criteria in multisensor and multitarget motion tracking cannot be directly applied to nonlinear motion models, as the fusion accuracy applied in nonlinear systems is relatively low. In response to the above issue, this study proposes a distributed Gaussian mixture cardinality jumping [...] Read more.
Some fusion criteria in multisensor and multitarget motion tracking cannot be directly applied to nonlinear motion models, as the fusion accuracy applied in nonlinear systems is relatively low. In response to the above issue, this study proposes a distributed Gaussian mixture cardinality jumping Markov-cardinalized probability hypothesis density (GM-JMNS-CPHD) filter based on a generalized inverse covariance intersection. The state estimation of the JMNS-CPHD filter combines the state evaluation of traditional CPHD filters with the state estimation of jump Markov systems, estimating the target state of multiple motion models without knowing the current motion models. The performances of the generalized covariance intersection (GCI)GCI-GM-JMNS-CPHD and generalized inverse covariance intersection (GICI)GICI-GM-JMNS-CPHD methods are evaluated via simulation results. The simulation results show that, compared with algorithms such as Sensor1, Sensor2, GCI-GM-CPHD, and GICI-GM-CPHD, this algorithm has smaller optimal subpattern assignment (OSPA) errors and a higher fusion accuracy. Full article
(This article belongs to the Section Fault Diagnosis & Sensors)
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21 pages, 5688 KB  
Article
An Efficient Implementation Method for Distributed Fusion in Sensor Networks Based on CPHD Filters
by Liu Wang and Guifen Chen
Sensors 2024, 24(1), 117; https://doi.org/10.3390/s24010117 - 25 Dec 2023
Cited by 2 | Viewed by 2643
Abstract
A highly efficient implementation method for distributed fusion in sensor networks based on CPHD filters is proposed to address the issues of unknown cross-covariance fusion estimation and long fusion times in multi-sensor distributed fusion. This method can effectively and efficiently fuse multi-node information [...] Read more.
A highly efficient implementation method for distributed fusion in sensor networks based on CPHD filters is proposed to address the issues of unknown cross-covariance fusion estimation and long fusion times in multi-sensor distributed fusion. This method can effectively and efficiently fuse multi-node information in multi-target tracking applications. Discrete gamma cardinalized probability hypothesis density (DG-CPHD) can effectively reduce the computational burden while ensuring computational accuracy similar to that of CPHD filters. Parallel inverse covariance intersection (PICI) can effectively avoid solving high-dimensional weight coefficient convex optimization problems, reduce the computational burden, and efficiently implement filtering fusion strategies. The effectiveness of the algorithm is demonstrated through simulation results, which indicate that PICI-GM-DG-CPHD can substantially reduce the computational time compared to other algorithms and is more suitable for distributed sensor fusion. Full article
(This article belongs to the Section Sensor Networks)
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17 pages, 3535 KB  
Article
Gaussian Mixture Cardinalized Probability Hypothesis Density(GM-CPHD): A Distributed Filter Based on the Intersection of Parallel Inverse Covariances
by Liu Wang, Guifen Chen and Guangjiao Chen
Sensors 2023, 23(6), 2921; https://doi.org/10.3390/s23062921 - 8 Mar 2023
Cited by 5 | Viewed by 2594
Abstract
A distributed GM-CPHD filter based on parallel inverse covariance crossover is designed to attenuate the local filtering and uncertain time-varying noise affecting the accuracy of sensor signals. First, the GM-CPHD filter is identified as the module for subsystem filtering and estimation due to [...] Read more.
A distributed GM-CPHD filter based on parallel inverse covariance crossover is designed to attenuate the local filtering and uncertain time-varying noise affecting the accuracy of sensor signals. First, the GM-CPHD filter is identified as the module for subsystem filtering and estimation due to its high stability under Gaussian distribution. Second, the signals of each subsystem are fused by invoking the inverse covariance cross-fusion algorithm, and the convex optimization problem with high-dimensional weight coefficients is solved. At the same time, the algorithm reduces the burden of data computation, and data fusion time is saved. Finally, the GM-CPHD filter is added to the conventional ICI structure, and the generalization capability of the parallel inverse covariance intersection Gaussian mixture cardinalized probability hypothesis density (PICI-GM-CPHD) algorithm reduces the nonlinear complexity of the system. An experiment on the stability of Gaussian fusion models is organized and linear and nonlinear signals are compared by simulating the metrics of different algorithms, and the results show that the improved algorithm has a smaller metric OSPA error than other mainstream algorithms. Compared with other algorithms, the improved algorithm improves the signal processing accuracy and reduces the running time. The improved algorithm is practical and advanced in terms of multisensor data processing. Full article
(This article belongs to the Section Physical Sensors)
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24 pages, 2837 KB  
Article
An Improved Multiple-Target Tracking Scheme Based on IGGM–PMBM for Mobile Aquaculture Sensor Networks
by Chunfeng Lv, Jianping Zhu, Naixue Xiong and Zhengsu Tao
Appl. Sci. 2023, 13(2), 926; https://doi.org/10.3390/app13020926 - 9 Jan 2023
Cited by 4 | Viewed by 2543
Abstract
The Poisson multi-Bernoulli Mixture (PMBM) filter, as well as its variants, is a popular and practical multitarget tracking algorithm. There are some pending problems for the standard PMBM filter, such as unknown detection probability, random target newborn distribution, and high energy consumption for [...] Read more.
The Poisson multi-Bernoulli Mixture (PMBM) filter, as well as its variants, is a popular and practical multitarget tracking algorithm. There are some pending problems for the standard PMBM filter, such as unknown detection probability, random target newborn distribution, and high energy consumption for limited computational and processing capacity in sensor networks. For the sake of accommodating these existing problems, an improved multitarget tracking method based on a PMBM filter with adaptive detection probability and adaptive newborn distribution is proposed, accompanied by an associated distributed fusion strategy to reduce the computational complexities. Firstly, gamma (GAM) distribution is introduced to present the augmented state of unknown and changing target detection probability. Secondly, the intensity of newborn targets is adaptively derived from the inverse gamma (IG) distribution based on this augmented state. Then, the measurement likelihood is presented as a gamma distribution for the augmented state. On these bases, the detailed recursion and closed-form solutions to the proposed filter are derived by means of approximating the intensity of target birth and potential targets to an inverse gamma Gaussian mixture (IGGM) form and the density of existing Bernoulli components to a single IGGM form. Moreover, the associated distributed fusion strategy generalized covariance intersection (GCI), whose target states are measured by multiple sensors according to their respective fusion weights, is applied to a large-scale aquaculture tracking network. Comprehensive experiments are presented to verify the effectiveness of this IGGM–PMBM method, and comparisons with other multitarget tracking filters also demonstrate that tracking behaviors are largely improved; in particular, tracking energy consumption is reduced sharply, and tracking accuracy is relatively enhanced. Full article
(This article belongs to the Special Issue Intelligent Control Using Machine Learning)
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17 pages, 2059 KB  
Article
SMC-CPHD Filter with Adaptive Survival Probability for Multiple Frequency Tracking
by Sun Young Kim, Chang Ho Kang and Chan Gook Park
Appl. Sci. 2022, 12(3), 1369; https://doi.org/10.3390/app12031369 - 27 Jan 2022
Cited by 6 | Viewed by 2253
Abstract
We propose a sequential Monte Carlo-based cardinalized probability hypothesis density (SMC-CPHD) filter with adaptive survival probability for multiple frequency tracking to enhance the tracking performance. The survival probability of the particles in the filter is adjusted using the pre-designed exponential function related to [...] Read more.
We propose a sequential Monte Carlo-based cardinalized probability hypothesis density (SMC-CPHD) filter with adaptive survival probability for multiple frequency tracking to enhance the tracking performance. The survival probability of the particles in the filter is adjusted using the pre-designed exponential function related to the distribution of the estimated particle points. In order to ensure whether the proposed survival probability affects the stability of the filter, the error bounds in the prediction process are analyzed. Moreover, an inverse covariance intersection-based compensation method is added to enhance cardinality tracking performance by integrating two types of cardinality information from the CPHD filter and data clustering process. To evaluate the proposed method’s performance, MATLAB-based simulations are performed. As a result, the tracking performance of the multiple frequencies has been confirmed, and the accuracy of cardinality estimates are improved compared to the existing filters. Full article
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20 pages, 1670 KB  
Article
A Bayesian Method for Dynamic Origin–Destination Demand Estimation Synthesizing Multiple Sources of Data
by Hang Yu, Senlai Zhu, Jie Yang, Yuntao Guo and Tianpei Tang
Sensors 2021, 21(15), 4971; https://doi.org/10.3390/s21154971 - 21 Jul 2021
Cited by 10 | Viewed by 4041
Abstract
In this paper a Bayesian method is proposed to estimate dynamic origin–destination (O–D) demand. The proposed method can synthesize multiple sources of data collected by various sensors, including link counts, turning movements at intersections, flows, and travel times on partial paths. Time-dependent demand [...] Read more.
In this paper a Bayesian method is proposed to estimate dynamic origin–destination (O–D) demand. The proposed method can synthesize multiple sources of data collected by various sensors, including link counts, turning movements at intersections, flows, and travel times on partial paths. Time-dependent demand for each O–D pair at each departure time is assumed to satisfy the normal distribution. The connections among multiple sources of field data and O–D demands for all departure times are established by their variance-covariance matrices. Given the prior distribution of dynamic O–D demands, the posterior distribution is developed by updating the traffic count information. Then, based on the posterior distribution, both point estimation and the corresponding confidence intervals of O–D demand variables are estimated. Further, a stepwise algorithm that can avoid matrix inversion, in which traffic counts are updated one by one, is proposed. Finally, a numerical example is conducted on Nguyen–Dupuis network to demonstrate the effectiveness of the proposed Bayesian method and solution algorithm. Results show that the total O–D variance is decreasing with each added traffic count, implying that updating traffic counts reduces O–D demand uncertainty. Using the proposed method, both total error and source-specific errors between estimated and observed traffic counts decrease by iteration. Specifically, using 52 multiple sources of traffic counts, the relative errors of almost 50% traffic counts are less than 5%, the relative errors of 85% traffic counts are less than 10%, the total error between the estimated and “true” O–D demands is relatively small, and the O–D demand estimation accuracy can be improved by using more traffic counts. It concludes that the proposed Bayesian method can effectively synthesize multiple sources of data and estimate dynamic O–D demands with fine accuracy. Full article
(This article belongs to the Topic Intelligent Transportation Systems)
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22 pages, 30480 KB  
Article
Multi-Sensor Fusion Positioning Method Based on Batch Inverse Covariance Intersection and IMM
by Yanxu Liu, Zhongliang Deng and Enwen Hu
Appl. Sci. 2021, 11(11), 4908; https://doi.org/10.3390/app11114908 - 26 May 2021
Cited by 13 | Viewed by 4120
Abstract
For mass application positioning demands, the current single positioning sensor cannot provide reliable and accurate positioning. Herein, we present batch inverse covariance intersection (BICI) and BICI with interacting multiple model (BICI-IMM) multi-sensor fusion positioning methods, which are based on the batch form of [...] Read more.
For mass application positioning demands, the current single positioning sensor cannot provide reliable and accurate positioning. Herein, we present batch inverse covariance intersection (BICI) and BICI with interacting multiple model (BICI-IMM) multi-sensor fusion positioning methods, which are based on the batch form of the sequential inverse covariance intersection (SICI) fusion method. Meanwhile, it is proved that the BICI is robust. Compared with SICI, BICI-IMM reduces estimation error variance of the motion model and has less conservativeness. The BICI-IMM algorithm improves the accuracy of local filtering by interacting with multiple models and realizes global fusion estimation based on BICI. The validity of the BICI and BICI-IMM algorithm are demonstrated by two simulations and experiments in the open and semi-open scenes, and its positioning accuracy relations are shown. In addition, it is demonstrated that the BICI-IMM algorithm can improve the positioning accuracy in the actual scenes. Full article
(This article belongs to the Section Electrical, Electronics and Communications Engineering)
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19 pages, 6154 KB  
Article
Temperature Sequential Data Fusion Algorithm Based on Cluster Hierarchical Sensor Networks
by Tianwei Yang, Xinyuan Nan and Weixu Jin
Sensors 2020, 20(16), 4533; https://doi.org/10.3390/s20164533 - 13 Aug 2020
Cited by 4 | Viewed by 3425
Abstract
The process of extracting gold by biological oxidation involves oxidizing the refractory high-sulfur and high-arsenic ore with the help of bacteria to decompose the wrapping material of gold to extract the gold. Therefore, maximizing the activity of bacteria will directly affect the efficiency [...] Read more.
The process of extracting gold by biological oxidation involves oxidizing the refractory high-sulfur and high-arsenic ore with the help of bacteria to decompose the wrapping material of gold to extract the gold. Therefore, maximizing the activity of bacteria will directly affect the efficiency of gold extraction, for which it is particularly important to maintain the pulp temperature in the oxidation tank at the optimal bacteria breeding temperature. However, gold mines are generally located in mountainous areas, and the large temperature difference between day and night in winter, coupled with the influence of wind and snow, creates variations in the temperature in the oxidation tank. The traditional temperature measurement method cannot fully reflect the temperature change of the oxidation tank. As a multi-field application method, sensor information fusion can effectively address the problem of pulp temperature measurement. First, we analyzed the heat transfer principle inside the oxidation tank, and designed the cluster hierarchical sensor network according to the spatial position of each oxidation tank and the environmental interference factors. The network structure is divided into three layers; the bottom of the sensor to collect pulp temperature data shows a spiral distribution in the inner wall of the oxidation tank. Each cluster head node sensor is used as an intermediate layer to complete local measurement fusion estimation. Finally, the fusion center is taken as the upper layer to realize the global state fusion estimation. Secondly, in the data processing of the bottom temperature sensor, the traditional unscented Kalman filter (UKF) algorithm is improved and the fading memory matrix is added to improve the identification of nonlinear modeling errors. The sequential observation fusion estimator (SOFE) algorithm is embedded in the measurement update to improve the performance of local measurement fusion. Finally, in the global state fusion estimation, the sequential analysis is combined with the inverse covariance intersection, and the sequential analysis and inverse covariance intersection-global state fusion estimation (SICI-GSFE) algorithm is proposed. Through calculation and simulation, the results show that the external interference can be reduced by combining all the temperature state estimations, and the accuracy of the best global temperature state estimation is improved. Full article
(This article belongs to the Special Issue Sensor Fusion and Signal Processing)
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16 pages, 2174 KB  
Article
1-Point RANSAC UKF with Inverse Covariance Intersection for Fault Tolerance
by Sun Young Kim, Chang Ho Kang and Jin Woo Song
Sensors 2020, 20(2), 353; https://doi.org/10.3390/s20020353 - 8 Jan 2020
Cited by 6 | Viewed by 3054
Abstract
The fault tolerance estimation method is proposed to maintain reliable correspondences between sensor data and estimation performance regardless of the number of valid measurements. The proposed method is based on the 1-point random sample consensus (RANSAC) unscented Kalman filter (UKF), and the inverse [...] Read more.
The fault tolerance estimation method is proposed to maintain reliable correspondences between sensor data and estimation performance regardless of the number of valid measurements. The proposed method is based on the 1-point random sample consensus (RANSAC) unscented Kalman filter (UKF), and the inverse covariance intersection (ICI)-based data fusion method is added to the update process in the proposed algorithm. To verify the performance of the proposed algorithm, two analyses are performed with respect to the degree of measurement error reduction and accuracy of generated information. In addition, experiments are conducted using the dead reckoning (DR)/global positioning system (GPS) navigation system with a barometric altimeter to confirm the performance of fault tolerance in the altitude. It is confirmed that the proposed algorithm maintains estimation performance when there are not enough valid measurements. Full article
(This article belongs to the Section Intelligent Sensors)
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