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19 pages, 1958 KiB  
Article
Visual-Inertial-Wheel Odometry with Slip Compensation and Dynamic Feature Elimination
by Niraj Reginald, Omar Al-Buraiki, Thanacha Choopojcharoen, Baris Fidan and Ehsan Hashemi
Sensors 2025, 25(5), 1537; https://doi.org/10.3390/s25051537 - 1 Mar 2025
Viewed by 210
Abstract
Inertial navigation systems augmented with visual and wheel odometry measurements have emerged as a robust solution to address uncertainties in robot localization and odometry. This paper introduces a novel data-driven approach to compensate for wheel slippage in visual-inertial-wheel odometry (VIWO). The proposed method [...] Read more.
Inertial navigation systems augmented with visual and wheel odometry measurements have emerged as a robust solution to address uncertainties in robot localization and odometry. This paper introduces a novel data-driven approach to compensate for wheel slippage in visual-inertial-wheel odometry (VIWO). The proposed method leverages Gaussian process regression (GPR) with deep kernel design and long short-term memory (LSTM) layers to model and mitigate slippage-induced errors effectively. Furthermore, a feature confidence estimator is incorporated to address the impact of dynamic feature points on visual measurements, ensuring reliable data integration. By refining these measurements, the system utilizes a multi-state constraint Kalman filter (MSCKF) to achieve accurate state estimation and enhanced navigation performance. The effectiveness of the proposed approach is demonstrated through extensive simulations and experimental validations using real-world datasets. The results highlight the ability of the method to handle challenging terrains and dynamic environments by compensating for wheel slippage and mitigating the influence of dynamic objects. Compared to conventional VIWO systems, the integration of GPR and LSTM layers significantly improves localization accuracy and robustness. This work paves the way for deploying VIWO systems in diverse and unpredictable environments, contributing to advancements in autonomous navigation and multi-sensor fusion technologies. Full article
(This article belongs to the Section Physical Sensors)
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<p>Overall structure of the proposed VIWO scheme.</p>
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<p>Slip compensation scheme.</p>
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<p>Robot kinematic schematic.</p>
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<p>Deep kernel architecture using CNN.</p>
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<p>Test sequence 1 odometry trajectories comparison. VIWO: visual-inertial-wheel odometry, DPE: dynamic point elimination, WSC with CNN: wheel-slip compensation with CNN for kernel design, WSC with RNN: wheel-slip compensation with RNN for kernel design.</p>
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<p>Test sequence 2 odometry trajectories comparison.</p>
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<p>MATE error for test sequences.</p>
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<p>Experimental setup.</p>
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<p>Comparison of wheel speeds of the robot.</p>
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<p>Experiment sequence 1 odometry trajectory comparison.</p>
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<p>Experiment sequence 2 odometry trajectory comparison.</p>
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<p>RMSE for the experimental trajectories.</p>
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<p>Experiment sequence 3 odometry trajectories comparison in gravel/sand-based terrain.</p>
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29 pages, 4682 KiB  
Article
LSAF-LSTM-Based Self-Adaptive Multi-Sensor Fusion for Robust UAV State Estimation in Challenging Environments
by Mahammad Irfan, Sagar Dalai, Petar Trslic, James Riordan and Gerard Dooly
Machines 2025, 13(2), 130; https://doi.org/10.3390/machines13020130 - 9 Feb 2025
Viewed by 584
Abstract
Unmanned aerial vehicle (UAV) state estimation is fundamental across applications like robot navigation, autonomous driving, virtual reality (VR), and augmented reality (AR). This research highlights the critical role of robust state estimation in ensuring safe and efficient autonomous UAV navigation, particularly in challenging [...] Read more.
Unmanned aerial vehicle (UAV) state estimation is fundamental across applications like robot navigation, autonomous driving, virtual reality (VR), and augmented reality (AR). This research highlights the critical role of robust state estimation in ensuring safe and efficient autonomous UAV navigation, particularly in challenging environments. We propose a deep learning-based adaptive sensor fusion framework for UAV state estimation, integrating multi-sensor data from stereo cameras, an IMU, two 3D LiDAR’s, and GPS. The framework dynamically adjusts fusion weights in real time using a long short-term memory (LSTM) model, enhancing robustness under diverse conditions such as illumination changes, structureless environments, degraded GPS signals, or complete signal loss where traditional single-sensor SLAM methods often fail. Validated on an in-house integrated UAV platform and evaluated against high-precision RTK ground truth, the algorithm incorporates deep learning-predicted fusion weights into an optimization-based odometry pipeline. The system delivers robust, consistent, and accurate state estimation, outperforming state-of-the-art techniques. Experimental results demonstrate its adaptability and effectiveness across challenging scenarios, showcasing significant advancements in UAV autonomy and reliability through the synergistic integration of deep learning and sensor fusion. Full article
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<p>Proposed architecture for LSTM-based self-adaptive multi-sensor fusion (LSAF).</p>
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<p>An illustration of the proposed LSAF framework. The global estimator combines local estimations from various global sensors to achieve precise local accuracy and globally drift free pose estimation, which builds upon our previous work [<a href="#B28-machines-13-00130" class="html-bibr">28</a>].</p>
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<p>Proposed LSTM-based multi-sensor fusion architecture for UAV state estimation.</p>
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<p>LSTM cell architecture for adaptive multi-sensor fusion.</p>
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<p>Training and validation loss of the proposed LSTM-based self-adaptive multi-sensor fusion (LSAF) framework over 1000 epochs.</p>
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<p>Training and validation MAE of the proposed LSTM-based self-adaptive multi-sensor fusion (LSAF) framework over 1000 epochs.</p>
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<p>Proposed block diagram for LSTM-based self-adaptive multi-sensor fusion (LSAF).</p>
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<p>The experimental environment in different scenarios during the data collection. Panel (<b>a</b>,<b>b</b>) represent the UAV hardware along with sensor integration and panel (<b>c</b>,<b>d</b>) are the open-field dataset environment view from stereo and LiDAR sensors, respectively, which build upon our previous work [<a href="#B28-machines-13-00130" class="html-bibr">28</a>].</p>
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<p>Trajectory plots of the proposed LSAF method and comparison with FASTLIO2 and VINS-Fusion.</p>
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<p>Box plots showing the overall APE of each strategy.</p>
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<p>Absolute estimated position of x, y, and z axes showing plots of various methods on the UAV car parking dataset.</p>
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<p>Absolute position error of roll, yaw, and pitch showing the plots of various methods on the UAV car parking dataset.</p>
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<p>Trajectory plots of the proposed LSAF method and comparison with FASTLIO2 and VINS-Fusion on the UL outdoor handheld dataset.</p>
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<p>Box plots showing the overall APE of each strategy.</p>
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<p>Absolute estimated position of x, y, and z axes showing the plots of various methods on the UL outdoor handheld dataset.</p>
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<p>Absolute position error of roll, yaw, and pitch showing the plots of various methods on the UL outdoor handheld dataset.</p>
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<p>Trajectory plots of the proposed LSAF method and comparison with FASTLIO2 and VINS-Fusion.</p>
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<p>Absolute estimated position of the x, y, and z axes showing the plots of various methods on the UAV car bridge dataset.</p>
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<p>Absolute position error of roll, yaw, and pitch showing plots of various methods on the UAV car bridge dataset.</p>
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<p>Box plots showing the overall APE of each strategy.</p>
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17 pages, 13227 KiB  
Article
Robot Localization Method Based on Multi-Sensor Fusion in Low-Light Environment
by Mengqi Wang, Zengzeng Lian, María Amparo Núñez-Andrés, Penghui Wang, Yalin Tian, Zhe Yue and Lingxiao Gu
Electronics 2024, 13(22), 4346; https://doi.org/10.3390/electronics13224346 - 6 Nov 2024
Viewed by 1133
Abstract
When robots perform localization in indoor low-light environments, factors such as weak and uneven lighting can degrade image quality. This degradation results in a reduced number of feature extractions by the visual odometry front end and may even cause tracking loss, thereby impacting [...] Read more.
When robots perform localization in indoor low-light environments, factors such as weak and uneven lighting can degrade image quality. This degradation results in a reduced number of feature extractions by the visual odometry front end and may even cause tracking loss, thereby impacting the algorithm’s positioning accuracy. To enhance the localization accuracy of mobile robots in indoor low-light environments, this paper proposes a visual inertial odometry method (L-MSCKF) based on the multi-state constraint Kalman filter. Addressing the challenges of low-light conditions, we integrated Inertial Measurement Unit (IMU) data with stereo vision odometry. The algorithm includes an image enhancement module and a gyroscope zero-bias correction mechanism to facilitate feature matching in stereo vision odometry. We conducted tests on the EuRoC dataset and compared our method with other similar algorithms, thereby validating the effectiveness and accuracy of L-MSCKF. Full article
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<p>Algorithm procedure.</p>
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<p>Selection of image enhancement algorithm parameters. (<b>a</b>) Fixed low-frequency gain at 0.5, sharpening coefficient at 1, and contrast threshold set to 4. (<b>b</b>) Fixed high-frequency gain at 1.6, sharpening coefficient of 1, and contrast threshold of 4. (<b>c</b>) High-frequency gain is set to 1.6, low-frequency gain to 0.3, and the contrast threshold to 4. (<b>d</b>) The fixed high-frequency gain is 1.6, the low-frequency gain is 0.3, and the sharpening coefficient is 1.5.</p>
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<p>Comparison of feature point extraction effect. (<b>a</b>) The feature point extraction result of the original image. (<b>b</b>) The feature point extraction result after CLAHE processing. (<b>c</b>) The feature point extraction result after homomorphic filtering processing. (<b>d</b>) The feature point extraction result after both CLAHE processing and homomorphic filtering processing.</p>
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<p>Estimation of gyroscope bias coefficients on the MH02 and V203 sequences. (<b>a</b>) Variation in gyroscope bias for L-MSCKF and MSCKF-VIO on the MH02 sequence. (<b>b</b>) Estimated gyroscope bias values by L-MSCKF and MSCKF-VIO on the V203 sequence.</p>
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<p>The trajectory of the algorithm on sequences V103 and V203 of the EuRoC dataset. (<b>a</b>) The trajectory on the V103 sequence. (<b>b</b>) The X, Y, and Z triaxial values on the V103 sequence. (<b>c</b>) The trajectory on the V203 sequence. (<b>d</b>) The X, Y, and Z triaxial values on the V203 sequence.</p>
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<p>Comparison of absolute trajectory errors of each algorithm on weak light sequence V203.</p>
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<p>Comparison of the computational efficiency of each algorithm. (<b>a</b>) Average CPU usage in % of the total available CPU, by the algorithms running the same experiment. (<b>b</b>) Total running time of each algorithm on the same dataset.</p>
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20 pages, 6961 KiB  
Article
High-Accuracy Positioning in GNSS-Blocked Areas by Using the MSCKF-Based SF-RTK/IMU/Camera Tight Integration
by Qiaozhuang Xu, Zhouzheng Gao, Cheng Yang and Jie Lv
Remote Sens. 2023, 15(12), 3005; https://doi.org/10.3390/rs15123005 - 8 Jun 2023
Cited by 8 | Viewed by 2917
Abstract
The integration of global navigation satellite system (GNSS) single-frequency (SF) real-time kinematics (RTKs) and inertial navigation system (INS) has the advantages of low-cost and low-power consumption compared to the multiple-frequency GNSS RTK/INS integration system. However, due to the vulnerability of GNSS signal reception, [...] Read more.
The integration of global navigation satellite system (GNSS) single-frequency (SF) real-time kinematics (RTKs) and inertial navigation system (INS) has the advantages of low-cost and low-power consumption compared to the multiple-frequency GNSS RTK/INS integration system. However, due to the vulnerability of GNSS signal reception, the application of the GNSS SF-RTK/INS integration is limited in complex environments. To improve the positioning accuracy of SF-RTK/INS integration in GNSS-blocked environments, we present a low-cost tight integration system based on BDS/GPS SF-RTK, a low-cost inertial measurement unit (IMU), and a monocular camera. In such a system, a multi-state constraint Kalman filter (MSCKF) is adopted to integrate the single-frequency pseudo-range, phase-carrier, inertial measurements, and visual data tightly. A wheel robot dataset collected under satellite signal-blocked conditions is used to evaluate its performance in terms of position, attitude, and run time, respectively. Results illustrated that the presented model can provide higher position accuracy compared to those provided by the RTK/INS tight integration system and visual-inertial tight integration system. Moreover, the average running time presents the potential of the presented method in real-time applications. Full article
(This article belongs to the Special Issue Remote Sensing in Urban Positioning and Navigation)
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Graphical abstract

Graphical abstract
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<p>Overview of the camera projection model.</p>
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<p>Implementation of the presented GNSS/INS/vision-tight integration.</p>
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<p>Filed trajectory of the wheel robot test.</p>
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<p>Typical scenarios in the test.</p>
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<p>Sky-plot of tracked satellites during the test.</p>
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<p>Satellite numbers (<b>a</b>) and the corresponding PDOP (<b>b</b>) during the test.</p>
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<p>Satellite numbers (<b>a</b>) and the corresponding PDOP (<b>b</b>) during the test.</p>
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<p>Sensors-aided cycle-slip detection results in the simulation test. The red line denotes the detection threshold, the blue line represents the detection term, and the green cycle denotes the detected cycle-slips value.</p>
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<p>Time series of the detected cycle-slips value during the measured test. The red line denotes the detection threshold and the blue dot represents the detection term.</p>
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<p>Time series of position differences of the single-frequency GNSS RTK mode (SF RTK), single -frequency GNSS RTK/INS tight integration mode, (SF RI), and visual-inertial tight integration mode (MSCKF VIO).</p>
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<p>Time series of position differences of the dual-frequency GNSS RTK/INS/vision tight integration mode (DF RIV) and single-frequency GNSS RTK/INS/vision tight integration mode (SF RIV).</p>
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<p>3D trajectories of different modes.</p>
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<p>Horizontal position error density of different modes.</p>
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<p>Cumulative distribution function (CDF) of horizontal position differences of different modes.</p>
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<p>(<b>a</b>) Time series and (<b>b</b>) cumulative distribution function (CDF) of attitude differences for the modes of SF RI, MSCKF VIO, DF RIV, and SF RIV.</p>
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<p>(<b>a</b>) Time series and (<b>b</b>) cumulative distribution function (CDF) of attitude differences for the modes of SF RI, MSCKF VIO, DF RIV, and SF RIV.</p>
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21 pages, 5139 KiB  
Article
An Enhanced Hybrid Visual–Inertial Odometry System for Indoor Mobile Robot
by Yanjie Liu, Changsen Zhao and Meixuan Ren
Sensors 2022, 22(8), 2930; https://doi.org/10.3390/s22082930 - 11 Apr 2022
Cited by 13 | Viewed by 3168
Abstract
As mobile robots are being widely used, accurate localization of the robot counts for the system. Compared with position systems with a single sensor, multi-sensor fusion systems provide better performance and increase the accuracy and robustness. At present, camera and IMU (Inertial Measurement [...] Read more.
As mobile robots are being widely used, accurate localization of the robot counts for the system. Compared with position systems with a single sensor, multi-sensor fusion systems provide better performance and increase the accuracy and robustness. At present, camera and IMU (Inertial Measurement Unit) fusion positioning is extensively studied and many representative Visual–Inertial Odometry (VIO) systems have been produced. Multi-State Constraint Kalman Filter (MSCKF), one of the tightly coupled filtering methods, is characterized by high accuracy and low computational load among typical VIO methods. In the general framework, IMU information is not used after predicting the state and covariance propagation. In this article, we proposed a framework which introduce IMU pre-integration result into MSCKF framework as observation information to improve the system positioning accuracy. Additionally, the system uses the Helmert variance component estimation (HVCE) method to adjust the weight between feature points and pre-integration to further improve the positioning accuracy. Similarly, this article uses the wheel odometer information of the mobile robot to perform zero speed detection, zero-speed update, and pre-integration update to enhance the positioning accuracy of the system. Finally, after experiments carried out in Gazebo simulation environment, public dataset and real scenarios, it is proved that the proposed algorithm has better accuracy results while ensuring real-time performance than existing mainstream algorithms. Full article
(This article belongs to the Section Sensors and Robotics)
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<p>The system framework.</p>
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<p>The Gazebo simulation environment.</p>
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<p>Comparison of the proposed method versus OpenVINS: (<b>a</b>) OpenVINS; (<b>c</b>) OpenVINS+IMU Pre-integration; (<b>e</b>) OpenVINS+IMU Pre-integration + Odom; (<b>b</b>,<b>d</b>,<b>f</b>) are the corresponding errors.</p>
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<p>Comparison of the proposed method versus OpenVINS: (<b>a</b>) OpenVINS; (<b>c</b>) OpenVINS+IMU Pre-integration; (<b>e</b>) OpenVINS+IMU Pre-integration + Odom; (<b>b</b>,<b>d</b>,<b>f</b>) are the corresponding errors.</p>
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<p>Comparison of the proposed method versus OpenVINS: (<b>a</b>) OpenVINS; (<b>c</b>) OpenVINS+IMU Pre-integration; (<b>e</b>) OpenVINS+IMU Pre-integration +Odom; (<b>b</b>,<b>d</b>,<b>f</b>) are the corresponding errors.</p>
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<p>Comparison of the proposed method versus OpenVINS: (<b>a</b>) OpenVINS; (<b>c</b>) OpenVINS+IMU Pre-integration; (<b>e</b>) OpenVINS+IMU Pre-integration +Odom; (<b>b</b>,<b>d</b>,<b>f</b>) are the corresponding errors.</p>
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<p>The comparison of estimated trajectory between OpenVINS and the proposed method for the (<b>a</b>) MH-04-difficult and (<b>b</b>) MH-05-difficult sequences.</p>
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<p>(<b>a</b>) The experiment platform; (<b>b</b>) localization of the robot on the established environment map; (<b>c</b>) camera view (the blue points are SLAM tracking points); (<b>d</b>) estimated trajectory of the robot (red points indicate SLAM feature points).</p>
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<p>Comparison of the proposed method versus OpenVINS: (<b>a</b>) OpenVINS; (<b>c</b>) OpenVINS+IMU Pre-integration; (<b>e</b>) OpenVINS+IMU Pre-integration +Odom; (<b>b</b>,<b>d</b>,<b>f</b>) are the corresponding errors.</p>
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<p>Comparison of the proposed method versus OpenVINS: (<b>a</b>) OpenVINS; (<b>c</b>) OpenVINS+IMU Pre-integration; (<b>e</b>) OpenVINS+IMU Pre-integration +Odom; (<b>b</b>,<b>d</b>,<b>f</b>) are the corresponding errors.</p>
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24 pages, 4599 KiB  
Article
Robust Stereo Visual Inertial Navigation System Based on Multi-Stage Outlier Removal in Dynamic Environments
by Dinh Van Nam and Kim Gon-Woo
Sensors 2020, 20(10), 2922; https://doi.org/10.3390/s20102922 - 21 May 2020
Cited by 29 | Viewed by 5499
Abstract
Robotic mapping and odometry are the primary competencies of a navigation system for an autonomous mobile robot. However, the state estimation of the robot typically mixes with a drift over time, and its accuracy is degraded critically when using only proprioceptive sensors in [...] Read more.
Robotic mapping and odometry are the primary competencies of a navigation system for an autonomous mobile robot. However, the state estimation of the robot typically mixes with a drift over time, and its accuracy is degraded critically when using only proprioceptive sensors in indoor environments. Besides, the accuracy of an ego-motion estimated state is severely diminished in dynamic environments because of the influences of both the dynamic objects and light reflection. To this end, the multi-sensor fusion technique is employed to bound the navigation error by adopting the complementary nature of the Inertial Measurement Unit (IMU) and the bearing information of the camera. In this paper, we propose a robust tightly-coupled Visual-Inertial Navigation System (VINS) based on multi-stage outlier removal using the Multi-State Constraint Kalman Filter (MSCKF) framework. First, an efficient and lightweight VINS algorithm is developed for the robust state estimation of a mobile robot by practicing a stereo camera and an IMU towards dynamic indoor environments. Furthermore, we propose strategies to deal with the impacts of dynamic objects by using multi-stage outlier removal based on the feedback information of estimated states. The proposed VINS is implemented and validated through public datasets. In addition, we develop a sensor system and evaluate the VINS algorithm in the dynamic indoor environment with different scenarios. The experimental results show better performance in terms of robustness and accuracy with low computation complexity as compared to state-of-the-art approaches. Full article
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<p>Experimental results in a dynamic environment influenced by illumination and a dynamic object. Herein, yellow rectangles present affected areas, small red squares indicate robust features. (<b>a</b>) the VINS-fusion [<a href="#B13-sensors-20-02922" class="html-bibr">13</a>], and (<b>b</b>–<b>d</b>) show the proposed method.</p>
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<p>The proposed navigation system architecture is based on a robust visual-inertial fusion with a multi-stage outlier removal. Herein, the features are classified into three classes which are represented by blue, yellow, and red.</p>
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<p>The transformations between the global frame <math display="inline"><semantics> <mrow> <mo>{</mo> <mi mathvariant="normal">G</mi> <mo>}</mo> </mrow> </semantics></math>, Inertial Measurement Unit (IMU) frame <math display="inline"><semantics> <mrow> <mo>{</mo> <mi mathvariant="normal">I</mi> <mo>}</mo> </mrow> </semantics></math>, right camera frame <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">R</mi> </msub> <mo>}</mo> </mrow> </semantics></math>, and left camera reference frame <math display="inline"><semantics> <mrow> <mo>{</mo> <msub> <mi mathvariant="normal">C</mi> <mi mathvariant="normal">L</mi> </msub> <mo>}</mo> </mrow> </semantics></math>. The IMU frame <math display="inline"><semantics> <mrow> <mo>{</mo> <mi mathvariant="normal">I</mi> <mo>}</mo> </mrow> </semantics></math> is the navigation coordinate. <math display="inline"><semantics> <mi mathvariant="normal">f</mi> </semantics></math> illustrates the position of a visual feature. <math display="inline"><semantics> <mrow> <msup> <mrow/> <mi>A</mi> </msup> <msub> <mi mathvariant="bold">T</mi> <mi>B</mi> </msub> <mo>=</mo> <mfenced separators="" open="[" close="]"> <msup> <mrow/> <mi>A</mi> </msup> <msub> <mi mathvariant="bold">R</mi> <mi>B</mi> </msub> <mspace width="0.166667em"/> <mspace width="0.166667em"/> <mspace width="0.166667em"/> <msup> <mrow/> <mi>A</mi> </msup> <msub> <mi mathvariant="bold">p</mi> <mi>B</mi> </msub> </mfenced> </mrow> </semantics></math> represents the homogeneous transformation from frame <math display="inline"><semantics> <mi mathvariant="normal">B</mi> </semantics></math> to frame <math display="inline"><semantics> <mi mathvariant="normal">A</mi> </semantics></math> on <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">E</mi> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </semantics></math>, where <math display="inline"><semantics> <mi mathvariant="bold">R</mi> </semantics></math> is the rotation matrix on <math display="inline"><semantics> <mrow> <mi mathvariant="normal">S</mi> <mi mathvariant="normal">O</mi> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </semantics></math> and <math display="inline"><semantics> <mi mathvariant="bold">p</mi> </semantics></math> is the translation.</p>
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<p>The demonstration of stereo camera and IMU clock. The left and the right camera are synchronized by software while having a time offset between the camera clock and the closest IMU clock.</p>
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<p>A demonstration of the transform between a 3D and 2D visual feature representation. The dark blue arrows indicate how to convert 3D feature representation to 2D data on the distorted image plane, and the green arrows show the processes to compute the Jacobian concerning a variable by using the chain rule of differentiation. Inside the brown circle presents the Anchored Inverse Depth model [<a href="#B7-sensors-20-02922" class="html-bibr">7</a>] of a visual feature.</p>
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<p>The demonstration of the proposed matching strategies for the stereo camera on the image plane using forward-backward-up-down tracking. The star shape represents a visual feature extracted by the FAST algorithm, and the arrow indicates the feature matching process.</p>
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<p>The illustration of the outlier removal strategy of a dynamic visual feature. (<b>a</b>) 2D feature tracking of the feature within a sliding window from time steps <math display="inline"><semantics> <mrow> <mi>N</mi> <mo>−</mo> <mi>k</mi> </mrow> </semantics></math> to <span class="html-italic">N</span>, where each green arrow indicates the optical flow of the feature observed in the image plane and dark green arrow represents the estimation movement of the feature in each period. (<b>b</b>) The geometrical method based-outlier removal from start to end time step of the sliding window, the results are inferred from (<b>a</b>). (<b>c</b>) The half above represents the tracking in the 3D environment, and the half bellow demonstrates the projection of the feature on the image plane.</p>
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<p>A comparison between the estimated trajectory (blue line) and the ground-truth (magenta line) by the proposed method on sequence V1_02, V1_03, V2_02, and V2_03 are expressed following the gravity direction.</p>
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<p>The comparison of the relative translation error of Basalt and our method on sequence V2_02. (<b>a</b>) The relative translation error of our proposed method and (<b>b</b>) the relative translation error of Basalt.</p>
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<p>State estimation errors (red-line) and 3 <math display="inline"><semantics> <mi>σ</mi> </semantics></math> bounds (green-dashed line) for the proposed method in the EuROC dataset with sequences V1_02, V1_03, V2_02, and V2_03.</p>
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<p>The hardware setup consists of a stereo Zed camera and an inertial sensor 3DM-GX3-25.</p>
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<p>Screen snapshots using the Robot Operating System (ROS) image toolbox during the indoor lab test with a dynamic pattern. (<b>a</b>) In this case, the pattern is static and many features identified the robust feature. (<b>b</b>) When the pattern begins moving, the robust feature turns to the normal feature.</p>
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<p>The estimated trajectory (blue line) drifts over time compared with VINS-Fusion [<a href="#B13-sensors-20-02922" class="html-bibr">13</a>] (red dash line) in a very high dynamic environment.</p>
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<p>The comparison between the proposed method and VINS-Fusion [<a href="#B13-sensors-20-02922" class="html-bibr">13</a>] when moving inside a lab room around 6 × 6 m<sup>2</sup> with a dynamic person moving ahead. (<b>a</b>) The comparison between the proposed method and VINS-Fusion [<a href="#B13-sensors-20-02922" class="html-bibr">13</a>]. (<b>b</b>) The visualization of our method trajectory shown in Rviz.</p>
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<p>The estimated trajectories in a stochastic environment along the hallway outside our lab around <math display="inline"><semantics> <mrow> <mn>7</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">m</mi> <mo>×</mo> <mn>25</mn> <mspace width="3.33333pt"/> <mi mathvariant="normal">m</mi> </mrow> </semantics></math> with various scenarios are illustrated. Line 1 is a path without the dynamic object; Line 2 is with the moving person but sparse, Line 3 is with a very dense active person; all cases are under the influence of illumination. Point S1, S2, and S3 are start poses of all paths while E1, E2, and E3 are end positions of scenario 1, 2, and 3, respectively.</p>
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<p>The comparison of estimated trajectories between our proposed method with VINS-Fusion and Zed SLAM in various situations, as described in <a href="#sensors-20-02922-f015" class="html-fig">Figure 15</a>. (<b>a</b>) The result in scenario 1. (<b>b</b>) The result in scenario 2, where L1 lost the tracking area. (<b>c</b>) The result in scenario 3.</p>
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<p>The comparison of estimated trajectories between our proposed method with VINS-Fusion and Zed SLAM in various situations, as described in <a href="#sensors-20-02922-f015" class="html-fig">Figure 15</a>. (<b>a</b>) The result in scenario 1. (<b>b</b>) The result in scenario 2, where L1 lost the tracking area. (<b>c</b>) The result in scenario 3.</p>
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20 pages, 6350 KiB  
Article
ACK-MSCKF: Tightly-Coupled Ackermann Multi-State Constraint Kalman Filter for Autonomous Vehicle Localization
by Fangwu Ma, Jinzhu Shi, Yu Yang, Jinhang Li and Kai Dai
Sensors 2019, 19(21), 4816; https://doi.org/10.3390/s19214816 - 5 Nov 2019
Cited by 33 | Viewed by 7762
Abstract
Visual-Inertial Odometry (VIO) is subjected to additional unobservable directions under the special motions of ground vehicles, resulting in larger pose estimation errors. To address this problem, a tightly-coupled Ackermann visual-inertial odometry (ACK-MSCKF) is proposed to fuse Ackermann error state measurements and the Stereo [...] Read more.
Visual-Inertial Odometry (VIO) is subjected to additional unobservable directions under the special motions of ground vehicles, resulting in larger pose estimation errors. To address this problem, a tightly-coupled Ackermann visual-inertial odometry (ACK-MSCKF) is proposed to fuse Ackermann error state measurements and the Stereo Multi-State Constraint Kalman Filter (S-MSCKF) with a tightly-coupled filter-based mechanism. In contrast with S-MSCKF, in which the inertial measurement unit (IMU) propagates the vehicle motion and then the propagation is corrected by stereo visual measurements, we successively update the propagation with Ackermann error state measurements and visual measurements after the process model and state augmentation. This way, additional constraints from the Ackermann measurements are exploited to improve the pose estimation accuracy. Both qualitative and quantitative experimental results evaluated under real-world datasets from an Ackermann steering vehicle lead to the following demonstration: ACK-MSCKF can significantly improve the pose estimation accuracy of S-MSCKF under the special motions of autonomous vehicles, and keep accurate and robust pose estimation available under different vehicle driving cycles and environmental conditions. This paper accompanies the source code for the robotics community. Full article
(This article belongs to the Collection Positioning and Navigation)
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<p>The basic workflow of Ackermann visual-inertial odometry (ACK-MSCKF).</p>
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<p>Geometric relation between {B} and {C} frames from time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mrow> <mi>j</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> to time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mi>j</mi> </msub> </mrow> </semantics></math>. The symbol <math display="inline"><semantics> <mrow> <mmultiscripts> <mstyle mathvariant="bold" mathsize="normal"> <mi>T</mi> </mstyle> <none/> <none/> <mprescripts/> <mrow> <msub> <mi>B</mi> <mrow> <mi>j</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> <mi>W</mi> </mmultiscripts> </mrow> </semantics></math> denotes the vehicle pose at time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mrow> <mi>j</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> in {W}, <math display="inline"><semantics> <mrow> <mmultiscripts> <mstyle mathvariant="bold" mathsize="normal"> <mi>T</mi> </mstyle> <none/> <none/> <mprescripts/> <mrow> <msub> <mi>B</mi> <mi>j</mi> </msub> </mrow> <mi>W</mi> </mmultiscripts> </mrow> </semantics></math> denotes the vehicle pose at time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mi>j</mi> </msub> </mrow> </semantics></math> in {W},<math display="inline"><semantics> <mrow> <mmultiscripts> <mstyle mathvariant="bold" mathsize="normal"> <mi>T</mi> </mstyle> <none/> <none/> <mprescripts/> <mrow> <msub> <mi>B</mi> <mi>j</mi> </msub> </mrow> <mrow> <msub> <mi>B</mi> <mrow> <mi>j</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </mmultiscripts> </mrow> </semantics></math> represents the homogeneous coordinate transformation from time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mi>j</mi> </msub> </mrow> </semantics></math> to time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mrow> <mi>j</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <mmultiscripts> <mstyle mathvariant="bold" mathsize="normal"> <mi>T</mi> </mstyle> <none/> <none/> <mprescripts/> <mi>B</mi> <mi>C</mi> </mmultiscripts> </mrow> </semantics></math> represents the homogeneous coordinate transformation from {B} to {C}, <math display="inline"><semantics> <mrow> <mmultiscripts> <mstyle mathvariant="bold" mathsize="normal"> <mi>T</mi> </mstyle> <none/> <none/> <mprescripts/> <mrow> <msub> <mi>C</mi> <mrow> <mi>j</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> <mi>G</mi> </mmultiscripts> </mrow> </semantics></math> denotes the camera pose at time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mrow> <mi>j</mi> <mo>−</mo> <mn>1</mn> </mrow> </msub> </mrow> </semantics></math> in {G} and finally <math display="inline"><semantics> <mrow> <mmultiscripts> <mstyle mathvariant="bold" mathsize="normal"> <mi>T</mi> </mstyle> <none/> <none/> <mprescripts/> <mrow> <msub> <mi>C</mi> <mi>j</mi> </msub> </mrow> <mi>G</mi> </mmultiscripts> </mrow> </semantics></math> denotes the camera pose at time <math display="inline"><semantics> <mrow> <msub> <mi>t</mi> <mi>j</mi> </msub> </mrow> </semantics></math> in {G}.</p>
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<p>Ackermann steering geometry used in car-like wheeled mobile robots. <math display="inline"><semantics> <mi>B</mi> </semantics></math> is the distance between the king pins, <math display="inline"><semantics> <mi>L</mi> </semantics></math> is the wheel base (distance between the two axles), <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>i</mi> </msub> </mrow> </semantics></math> is the steering angle of the inner wheel from straight ahead, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>c</mi> </msub> </mrow> </semantics></math> is the steering angle of the virtual wheel at the midpoint between the front wheels, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>o</mi> </msub> </mrow> </semantics></math> is the steering angle of the outer wheel from straight ahead and <math display="inline"><semantics> <mi>R</mi> </semantics></math> is the steering radius (distance between the Instantaneous Center of Rotation (ICR) and the centerline of the vehicle). The sign of <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>i</mi> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>c</mi> </msub> </mrow> </semantics></math>, <math display="inline"><semantics> <mrow> <msub> <mi>α</mi> <mi>o</mi> </msub> </mrow> </semantics></math> and <math display="inline"><semantics> <mi>R</mi> </semantics></math> follows the rule that a left turn assumes a positive value and a right turn a negative value in the coordinate system {B}.</p>
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<p>Experimental vehicle setup: (<b>a</b>) The Ackermann steering vehicle built by our research group; (<b>b</b>) MYNTEYE-S1030; (<b>c</b>) dual-antenna Spatial NAV982-RG; (<b>d</b>) telematic box ( (communicating with the smart phone application (APP) and Vehicle Control Unit (VCU)); (<b>e</b>) smart phone APP; (<b>f</b>) Controller Area Network (CAN) interface card; (<b>g</b>) mini-computer for the data acquisition.</p>
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<p>Acquired images in the experimental datasets. (<b>a</b>) AM_01; (<b>b</b>) AM_02; (<b>c</b>) AM_03; (<b>d</b>) AM_04.</p>
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<p>The performance from the Stereo Multi-State Constraint Kalman Filter (S-MSCKF)(s) (blue line), S-MSCKF(m) (green line) and ground truth (magenta line) on the AM_05 dataset. (<b>a</b>) Top-view of estimated trajectory; (<b>b</b>) Side-view of estimated trajectory; (<b>c</b>) The relative translation error; (<b>d</b>) The relative yaw error. Relative errors are measured over different sub-trajectories of length {1, 5, 20, 50, 100, 160} m.</p>
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<p>The top-views of estimated trajectory from ACK-MSCKF (blue line), S-MSCKF (green line), Open Keyframe-based Visual-Inertial SLAM (OKVIS) (red line) and ground truth (magenta line) of the dataset: (<b>a</b>) AM_01; (<b>b</b>) AM_02; (<b>c</b>) AM_03; (<b>d</b>) AM_04.</p>
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<p>The estimated trajectories aligned to Google Earth from ACK-MSCKF (blue line), S-MSCKF (green line), OKVIS (red line) and ground truth (magenta line) of the dataset: (<b>a</b>) AM_01; (<b>b</b>) AM_02; (<b>c</b>) AM_03; (<b>d</b>) AM_04.</p>
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<p>The estimated trajectories aligned to Google Earth from ACK-MSCKF (blue line), S-MSCKF (green line), OKVIS (red line) and ground truth (magenta line) of the dataset: (<b>a</b>) AM_01; (<b>b</b>) AM_02; (<b>c</b>) AM_03; (<b>d</b>) AM_04.</p>
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<p>The relative translation error from ACK-MSCKF (blue line), S-MSCKF (green line) and OKVIS (red line) of the dataset: (<b>a</b>) AM_01; (<b>b</b>) AM_02; (<b>c</b>) AM_03; (<b>d</b>) AM_04.</p>
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<p>The relative yaw error from ACK-MSCKF (blue line), S-MSCKF (green line) and OKVIS (red line) of the dataset: (<b>a</b>) AM_01; (<b>b</b>) AM_02; (<b>c</b>) AM_03; (<b>d</b>) AM_04.</p>
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<p>The relative yaw error from ACK-MSCKF (blue line), S-MSCKF (green line) and OKVIS (red line) of the dataset: (<b>a</b>) AM_01; (<b>b</b>) AM_02; (<b>c</b>) AM_03; (<b>d</b>) AM_04.</p>
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24 pages, 6203 KiB  
Article
Tight Fusion of a Monocular Camera, MEMS-IMU, and Single-Frequency Multi-GNSS RTK for Precise Navigation in GNSS-Challenged Environments
by Tuan Li, Hongping Zhang, Zhouzheng Gao, Xiaoji Niu and Naser El-sheimy
Remote Sens. 2019, 11(6), 610; https://doi.org/10.3390/rs11060610 - 13 Mar 2019
Cited by 121 | Viewed by 8342
Abstract
Precise position, velocity, and attitude is essential for self-driving cars and unmanned aerial vehicles (UAVs). The integration of global navigation satellite system (GNSS) real-time kinematics (RTK) and inertial measurement units (IMUs) is able to provide high-accuracy navigation solutions in open-sky conditions, but the [...] Read more.
Precise position, velocity, and attitude is essential for self-driving cars and unmanned aerial vehicles (UAVs). The integration of global navigation satellite system (GNSS) real-time kinematics (RTK) and inertial measurement units (IMUs) is able to provide high-accuracy navigation solutions in open-sky conditions, but the accuracy will be degraded severely in GNSS-challenged environments, especially integrated with the low-cost microelectromechanical system (MEMS) IMUs. In order to navigate in GNSS-denied environments, the visual–inertial system has been widely adopted due to its complementary characteristics, but it suffers from error accumulation. In this contribution, we tightly integrate the raw measurements from the single-frequency multi-GNSS RTK, MEMS-IMU, and monocular camera through the extended Kalman filter (EKF) to enhance the navigation performance in terms of accuracy, continuity, and availability. The visual measurement model from the well-known multistate constraint Kalman filter (MSCKF) is combined with the double-differenced GNSS measurement model to update the integration filter. A field vehicular experiment was carried out in GNSS-challenged environments to evaluate the performance of the proposed algorithm. Results indicate that both multi-GNSS and vision contribute significantly to the centimeter-level positioning availability in GNSS-challenged environments. Meanwhile, the velocity and attitude accuracy can be greatly improved by using the tightly-coupled multi-GNSS RTK/INS/Vision integration, especially for the yaw angle. Full article
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Graphical abstract

Graphical abstract
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<p>Algorithm structure of the tightly coupled integration of the monocular camera, MEMS-IMU, and multi-GNSS RTK. GNSS: global navigation satellite system; GPS: global positioning system; BDS: BeiDou navigation satellite system; GLONASS: GLObal NAvigation Satellite System; INS: inertial navigation system; DD: double-differencing; IMU: inertial measurement units; PVA: position, velocity, and attitude; MEMS: microelectromechanical system; RTK: real-time kinematics; <math display="inline"><semantics> <mrow> <mo>∇</mo> <mo>Δ</mo> <mi>P</mi> </mrow> </semantics></math>: DD code measurements; and <math display="inline"><semantics> <mrow> <mo>∇</mo> <mo>Δ</mo> <mi>φ</mi> </mrow> </semantics></math>: DD phase measurements.</p>
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<p>Field trajectory (blue line) in the campus of Wuhan University. Section A: with tall trees and buildings; Section B: with wide road and short trees; Section C: with narrow road and short trees and buildings.</p>
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<p>Typical scenarios in tree-lined roads.</p>
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<p>Test description. (<b>a</b>) Test platform and equipment; (<b>b</b>) Velocity of the vehicle.</p>
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<p>Satellite visibility of the GPS (<b>top</b>), BeiDou (<b>middle</b>), and GLONASS (<b>bottom</b>) systems during the test at a 15° cutoff elevation angle.</p>
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<p>Number of visible satellites (<b>top</b>) and the corresponding PDOP (<b>bottom</b>) for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems.</p>
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<p>Position difference of single-frequency RTK results calculated using the commercial software GrafNav 8.7 with respect to the reference: (<b>a</b>) GPS; (<b>b</b>) GPS + BDS.</p>
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<p>Position error in the north (N), east (E), and down (D) directions. (<b>a</b>) INS-only solution; (<b>b</b>) Vision-aided INS solution.</p>
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<p>Position difference of the tightly coupled RTK/INS integration with respect to the reference for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems.</p>
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<p>Position difference of the tightly coupled RTK/INS/Vision integration with respect to the reference for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems.</p>
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<p>The position standard deviation (STD) series of the GPS + BDS + GLONASS RTK/INS integration and the corresponding RTK/INS/Vision integration in the north, east, and down directions. The STDs are the square roots of the corresponding diagonal elements of the state covariance matrix and the values have been transformed from the e-frame into the north–east–down frame.</p>
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<p>Distribution of the position differences of the tightly coupled RTK/INS integration for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems. (<b>a</b>) Horizontal; (<b>b</b>) Vertical.</p>
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<p>Distribution of the position differences of the tightly coupled RTK/INS/Vision integration for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems. (<b>a</b>) Horizontal; (<b>b</b>) Vertical.</p>
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<p>Velocity error in the north (V<sub>N</sub>), east (V<sub>E</sub>), and down (V<sub>D</sub>) directions. (<b>a</b>) INS-only solution; (<b>b</b>) Vision-aided INS solution.</p>
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<p>Velocity error of the tightly coupled RTK/INS integration for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems.</p>
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<p>Velocity error of the tightly coupled RTK/INS/Vision integration for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems.</p>
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<p>The velocity STD series of the GPS + BDS + GLONASS RTK/INS integration and the corresponding RTK/INS/Vision integration in the north, east, and down directions. The STDs are the square roots of the corresponding diagonal elements of the state covariance matrix and the values have been transformed from the <span class="html-italic">e</span>-frame to the north–east–down frame.</p>
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<p>Attitude error. (<b>a</b>) INS-only solution; (<b>b</b>) Vision-aided INS solution.</p>
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<p>Attitude error of the tightly coupled RTK/INS integration for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems.</p>
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<p>Attitude error of the tightly coupled RTK/INS/Vision integration for the GPS, GPS + BDS (G + C), and GPS + BDS + GLONASS (G + C + R) systems.</p>
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<p>The attitude STD series of the GPS + BDS + GLONASS RTK/INS integration and the corresponding RTK/INS/Vision integration. The STDs are the square roots of the corresponding diagonal elements of the state covariance matrix.</p>
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14406 KiB  
Article
A Robust Indoor/Outdoor Navigation Filter Fusing Data from Vision and Magneto-Inertial Measurement Unit
by David Caruso, Alexandre Eudes, Martial Sanfourche, David Vissière and Guy Le Besnerais
Sensors 2017, 17(12), 2795; https://doi.org/10.3390/s17122795 - 4 Dec 2017
Cited by 19 | Viewed by 5400
Abstract
Visual-inertial Navigation Systems (VINS) are nowadays used for robotic or augmented reality applications. They aim to compute the motion of the robot or the pedestrian in an environment that is unknown and does not have specific localization infrastructure. Because of the low quality [...] Read more.
Visual-inertial Navigation Systems (VINS) are nowadays used for robotic or augmented reality applications. They aim to compute the motion of the robot or the pedestrian in an environment that is unknown and does not have specific localization infrastructure. Because of the low quality of inertial sensors that can be used reasonably for these two applications, state of the art VINS rely heavily on the visual information to correct at high frequency the drift of inertial sensors integration. These methods struggle when environment does not provide usable visual features, such than in low-light of texture-less areas. In the last few years, some work have been focused on using an array of magnetometers to exploit opportunistic stationary magnetic disturbances available indoor in order to deduce a velocity. This led to Magneto-inertial Dead-reckoning (MI-DR) systems that show interesting performance in their nominal conditions, even if they can be defeated when the local magnetic gradient is too low, for example outdoor. We propose in this work to fuse the information from a monocular camera with the MI-DR technique to increase the robustness of both traditional VINS and MI-DR itself. We use an inverse square root filter inspired by the MSCKF algorithm and describe its structure thoroughly in this paper. We show navigation results on a real dataset captured by a sensor fusing a commercial-grade camera with our custom MIMU (Magneto-inertial Measurment Unit) sensor. The fused estimate demonstrates higher robustness compared to pure VINS estimate, specially in areas where vision is non informative. These results could ultimately increase the working domain of mobile augmented reality systems. Full article
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<p>Reference coordinate frames at play in the problem, with associated typical measurements.</p>
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<p>Schematic view of on-board sensors. In addition to accelerometers and gyrometers, the MIMU includes several magnetometers: a central one and at least three peripheral ones in order to compute the full <math display="inline"> <semantics> <mrow> <mn>3</mn> <mo>×</mo> <mn>3</mn> </mrow> </semantics> </math> matrix of magnetic field gradients. The camera is rigidly attached to the MIMU sensor.</p>
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<p>Illustration of state augmentation and marginalization across time as described in <a href="#sec4dot2-sensors-17-02795" class="html-sec">Section 4.2</a>.</p>
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<p>The sensor setup used in this work. The white box on the left side contains the MIMU sensor, the camera is on the right side. Both sensors are rigidly attached through a non-magnetic, non conductive material (wood).</p>
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<p>Image processing pipeline. (<b>Left</b>): Raw input images. (<b>Right</b>): after rectification, intensity normalization, and corner detection. On the second example, the normalization reveals a faint signal, but it is too noisy for corner detection to works.</p>
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<p>(<b>a</b>) Overview of trajectory Traj2 as reconstructed by the three filters. (<b>b</b>) Visualisation of dark areas and low-gradient areas over the entire trajectory surimposed on MI-MSCKF estimate. (<b>c</b>) Height profile of the three estimators on this trajectory.</p>
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<p>Details of estimation results on Traj2 showing a different behavior between the MSCKF and MI-MSCKF filter. <b>Left and middle plots</b>: while transitioning from dark area to lit environment some strong filter correction happen for the MSCKF and lead to discontinuities of the position estimate. In the same areas, MI-MSCKF stays smoother. <b>Right plot</b>: here the device is laid on the ground at the end of the trajectory. A large drift of MSCKF occurs, as visual information does not provide any feedback on position. Here again, the MI-MSCKF appears more stable.</p>
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<p>(<b>a</b>) Overview of trajectory Traj2 as reconstructed by the three filters. (<b>b</b>) Visualisation of dark areas and low-gradient areas over the entire trajectory surimposed on MI-MSCKF estimate. (<b>c</b>) Height profile of the three estimators on this trajectory.</p>
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<p>Summary of trajectories on the remaining sequences of the dataset. (<b>Left</b>): Estimate of the three configuration of our filter. (<b>Right</b>) Color coded MI-MSCKF trajectory showing areas of weak gradient and weak illumination. (<b>a</b>) <b>Traj1</b> Length: ∼530 m; (<b>b</b>) <b>Traj3</b> Length: ∼368 m; (<b>c</b>) <b>Traj4</b> Length: ∼180 m.</p>
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