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1.
Sensors (Basel) ; 24(13)2024 Jul 07.
Artigo em Inglês | MEDLINE | ID: mdl-39001187

RESUMO

As an important vehicle in road construction, the unmanned roller is rapidly advancing in its autonomous compaction capabilities. To overcome the challenges of GNSS positioning failure during tunnel construction and diminished visual positioning accuracy under different illumination levels, we propose a feature-layer fusion positioning system based on a camera and LiDAR. This system integrates loop closure detection and LiDAR odometry into the visual odometry framework. Furthermore, recognizing the prevalence of similar scenes in tunnels, we innovatively combine loop closure detection with the compaction process of rollers in fixed areas, proposing a selection method for loop closure candidate frames based on the compaction process. Through on-site experiments, it is shown that this method not only enhances the accuracy of loop closure detection in similar environments but also reduces the runtime. Compared with visual systems, in static positioning tests, the longitudinal and lateral accuracy of the fusion system are improved by 12 mm and 11 mm, respectively. In straight-line compaction tests under different illumination levels, the average lateral error increases by 34.1% and 32.8%, respectively. In lane-changing compaction tests, this system enhances the positioning accuracy by 33% in dim environments, demonstrating the superior positioning accuracy of the fusion positioning system amid illumination changes in tunnels.

2.
Sensors (Basel) ; 24(13)2024 Jul 08.
Artigo em Inglês | MEDLINE | ID: mdl-39001198

RESUMO

In GNSS/IMU integrated navigation systems, factors like satellite occlusion and non-line-of-sight can degrade satellite positioning accuracy, thereby impacting overall navigation system results. To tackle this challenge and leverage historical pseudorange information effectively, this paper proposes a graph optimization-based GNSS/IMU model with virtual constraints. These virtual constraints in the graph model are derived from the satellite's position from the previous time step, the rate of change of pseudoranges, and ephemeris data. This virtual constraint serves as an alternative solution for individual satellites in cases of signal anomalies, thereby ensuring the integrity and continuity of the graph optimization model. Additionally, this paper conducts an analysis of the graph optimization model based on these virtual constraints, comparing it with traditional graph models of GNSS/IMU and SLAM. The marginalization of the graph model involving virtual constraints is analyzed next. The experiment was conducted on a set of real-world data, and the results of the proposed method were compared with tightly coupled Kalman filtering and the original graph optimization method. In instantaneous performance testing, the method maintains an RMSE error within 5% compared with real pseudorange measurement, while in a continuous performance testing scenario with no available GNSS signal, the method shows approximately a 30% improvement in horizontal RMSE accuracy over the traditional graph optimization method during a 10-second period. This demonstrates the method's potential for practical applications.

3.
Sensors (Basel) ; 24(2)2024 Jan 15.
Artigo em Inglês | MEDLINE | ID: mdl-38257631

RESUMO

Intelligent vehicles are constrained by road, resulting in a disparity between the assumed six degrees of freedom (DoF) motion within the Visual Simultaneous Localization and Mapping (SLAM) system and the approximate planar motion of vehicles in local areas, inevitably causing additional pose estimation errors. To address this problem, a stereo Visual SLAM system with road constraints based on graph optimization is proposed, called RC-SLAM. Addressing the challenge of representing roads parametrically, a novel method is proposed to approximate local roads as discrete planes and extract parameters of local road planes (LRPs) using homography. Unlike conventional methods, constraints between the vehicle and LRPs are established, effectively mitigating errors arising from assumed six DoF motion in the system. Furthermore, to avoid the impact of depth uncertainty in road features, epipolar constraints are employed to estimate rotation by minimizing the distance between road feature points and epipolar lines, robust rotation estimation is achieved despite depth uncertainties. Notably, a distinctive nonlinear optimization model based on graph optimization is presented, jointly optimizing the poses of vehicle trajectories, LPRs, and map points. The experiments on two datasets demonstrate that the proposed system achieved more accurate estimations of vehicle trajectories by introducing constraints between the vehicle and LRPs. The experiments on a real-world dataset further validate the effectiveness of the proposed system.

4.
Neural Netw ; 170: 285-297, 2024 Feb.
Artigo em Inglês | MEDLINE | ID: mdl-38000312

RESUMO

The intricacy of the Deep Learning (DL) landscape, brimming with a variety of models, applications, and platforms, poses considerable challenges for the optimal design, optimization, or selection of suitable DL models. One promising avenue to address this challenge is the development of accurate performance prediction methods. However, existing methods reveal critical limitations. Operator-level methods, proficient at predicting the performance of individual operators, often neglect broader graph features, which results in inaccuracies in full network performance predictions. On the contrary, graph-level methods excel in overall network prediction by leveraging these graph features but lack the ability to predict the performance of individual operators. To bridge these gaps, we propose SLAPP, a novel subgraph-level performance prediction method. Central to SLAPP is an innovative variant of Graph Neural Networks (GNNs) that we developed, named the Edge Aware Graph Attention Network (EAGAT). This specially designed GNN enables superior encoding of both node and edge features. Through this approach, SLAPP effectively captures both graph and operator features, thereby providing precise performance predictions for individual operators and entire networks. Moreover, we introduce a mixed loss design with dynamic weight adjustment to reconcile the predictive accuracy between individual operators and entire networks. In our experimental evaluation, SLAPP consistently outperforms traditional approaches in prediction accuracy, including the ability to handle unseen models effectively. Moreover, when compared to existing research, our method demonstrates a superior predictive performance across multiple DL models.


Assuntos
Aprendizado Profundo , Redes Neurais de Computação
5.
Sensors (Basel) ; 23(17)2023 Aug 31.
Artigo em Inglês | MEDLINE | ID: mdl-37688035

RESUMO

Satellite signals are easily lost in urban areas, which causes difficulty in vehicles being located with high precision. Visual odometry has been increasingly applied in navigation systems to solve this problem. However, visual odometry relies on dead-reckoning technology, where a slight positioning error can accumulate over time, resulting in a catastrophic positioning error. Thus, this paper proposes a road-network-map-assisted vehicle positioning method based on the theory of pose graph optimization. This method takes the dead-reckoning result of visual odometry as the input and introduces constraints from the point-line form road network map to suppress the accumulated error and improve vehicle positioning accuracy. We design an optimization and prediction model, and the original trajectory of visual odometry is optimized to obtain the corrected trajectory by introducing constraints from map correction points. The vehicle positioning result at the next moment is predicted based on the latest output of the visual odometry and corrected trajectory. The experiments carried out on the KITTI and campus datasets demonstrate the superiority of the proposed method, which can provide stable and accurate vehicle position estimation in real-time, and has higher positioning accuracy than similar map-assisted methods.

6.
Sensors (Basel) ; 22(21)2022 Oct 30.
Artigo em Inglês | MEDLINE | ID: mdl-36366035

RESUMO

Monocular 3D human pose estimation is used to calculate a 3D human pose from monocular images or videos. It still faces some challenges due to the lack of depth information. Traditional methods have tried to disambiguate it by building a pose dictionary or using temporal information, but these methods are too slow for real-time application. In this paper, we propose a real-time method named G2O-pose, which has a high running speed without affecting the accuracy so much. In our work, we regard the 3D human pose as a graph, and solve the problem by general graph optimization (G2O) under multiple constraints. The constraints are implemented by algorithms including 3D bone proportion recovery, human orientation classification and reverse joint correction and suppression. When the depth of the human body does not change much, our method outperforms the previous non-deep learning methods in terms of running speed, with only a slight decrease in accuracy.


Assuntos
Gráficos por Computador , Imageamento Tridimensional , Humanos , Algoritmos
7.
Sensors (Basel) ; 22(19)2022 Oct 09.
Artigo em Inglês | MEDLINE | ID: mdl-36236759

RESUMO

The fusion of light detection and ranging (LiDAR) and inertial measurement unit (IMU) sensing information can effectively improve the environment modeling and localization accuracy of navigation systems. To realize the spatiotemporal unification of data collected by the IMU and the LiDAR, a two-step spatiotemporal calibration method combining coarse and fine is proposed. The method mainly includes two aspects: (1) Modeling continuous-time trajectories of IMU attitude motion using B-spline basis functions; the motion of the LiDAR is estimated by using the normal distributions transform (NDT) point cloud registration algorithm, taking the Hausdorff distance between the local trajectories as the cost function and combining it with the hand-eye calibration method to solve the initial value of the spatiotemporal relationship between the two sensors' coordinate systems, and then using the measurement data of the IMU to correct the LiDAR distortion. (2) According to the IMU preintegration, and the point, line, and plane features of the lidar point cloud, the corresponding nonlinear optimization objective function is constructed. Combined with the corrected LiDAR data and the initial value of the spatiotemporal calibration of the coordinate systems, the target is optimized under the nonlinear graph optimization framework. The rationality, accuracy, and robustness of the proposed algorithm are verified by simulation analysis and actual test experiments. The results show that the accuracy of the proposed algorithm in the spatial coordinate system relationship calibration was better than 0.08° (3δ) and 5 mm (3δ), respectively, and the time deviation calibration accuracy was better than 0.1 ms and had strong environmental adaptability. This can meet the high-precision calibration requirements of multisensor spatiotemporal parameters of field robot navigation systems.

8.
Micromachines (Basel) ; 13(9)2022 Aug 26.
Artigo em Inglês | MEDLINE | ID: mdl-36144023

RESUMO

Global navigation satellite system (GNSS) and inertial navigation system (INS) are indispensable for ground vehicle position and navigation. The Kalman filter (KF) is the first choice to integrate them and output more reliable navigation solutions. However, the GNSS signal is denied in urban areas, i.e., tunnels, and the INS position errors diverge quickly over time. Under normal conditions, the ground vehicle will not slide or jump off the ground; nonholonomic constraints (NHC) and odometers are available to aid the INS and reduce its position errors. Factor graph optimization (FGO) recently attracted attention as an advanced sensor fusion algorithm. This paper implemented the FGO method based on GNSS/INS/NHC/Odometer integration. In the FGO, state transformation, measurement model, the NHC, and the odometer were all regarded as constraints employed to construct a graph; an iterative process was utilized to find the optimal estimation results. Two experiments were carried out: firstly, the FGO-GNSS/INS performance was assessed and compared with the KF-GNSS/INS; secondly, we compared the FGO-GNSS/INS/NHC/Odometer and KF-GNSS/INS/NHC/Odometer under GNSS denied environments. Experimental results supported that the FGO improved the performance.

9.
Sensors (Basel) ; 22(15)2022 Aug 05.
Artigo em Inglês | MEDLINE | ID: mdl-35957418

RESUMO

With the increasingly widespread application of UAV intelligence, the need for autonomous navigation and positioning is becoming more and more important. To solve the problem that UAV cannot perform localization in complex scenes, a new multi-source fusion framework factor graph optimization algorithm is used for UAV localization state estimation in this paper, which is based on IMU/GNSS/VO multi-source sensors. Based on the factor graph model and the iSAM incremental inference algorithm, a multi-source fusion model of IMU/GNSS/VO is established, including the IMU pre-integration factor, IMU bias factor, GNSS factor, and VO factor. Mathematical simulations and validations on the EuRoC dataset show that, when the selected sliding window size is 30, the factor graph optimization (FGO) algorithm can not only meet the requirements of real time and accuracy at the same time, but it also achieves a plug-and-play function in the event of local sensor failures. Finally, compared with the traditional federated Kalman algorithm and the adaptive federated Kalman algorithm, the positioning accuracy of the FGO algorithm in this paper is improved by 1.5-2-fold, and can effectively improve autonomous navigation system robustness and flexibility in complex scenarios. Moreover, the multi-source fusion framework in this paper is a general algorithm framework that can satisfy other scenarios and other types of sensor combinations.

10.
Sensors (Basel) ; 22(16)2022 Aug 20.
Artigo em Inglês | MEDLINE | ID: mdl-36016025

RESUMO

The advancement of smartphones with multiple built-in sensors facilitates the development of crowdsourcing-based indoor map construction and localization. This paper proposes a crowdsourcing-based indoor semantic map construction and localization method using graph optimization. Using waypoints, semantic landmarks, and Wi-Fi landmarks as nodes and the relevance between waypoints and landmarks (i.e., waypoint-waypoint, waypoint-semantic, waypoint-Wi-Fi, semantic-semantic, and Wi-Fi-Wi-Fi) as edges, the optimization graph is constructed. Initializing the venue map is the single-track semantic map with the highest quality, as determined by a proposed map quality evaluation function. The aligned venue and candidate maps are optimized while satisfying the constraints, with the candidate map exhibiting the highest degree of similarity to the venue map. The lightweight venue map is then updated in terms of waypoint and landmark attributes, as well as the relationship between waypoints and landmarks. To determine a pedestrian's location on a venue map, similarities between a local map and a venue map are evaluated. Experiments conducted in an office building and shopping mall scenes demonstrate that crowdsourcing-based venue maps are superior to single-track semantic maps. Additionally, the landmark matching-based localization method can achieve a mean localization error of less than 0.5 m on the venue map, compared to 0.6 m in a single-track semantic map.

11.
Sensors (Basel) ; 22(11)2022 May 26.
Artigo em Inglês | MEDLINE | ID: mdl-35684669

RESUMO

To improve the user's positioning accuracy of a Wi-Fi fingerprint-based positioning algorithm, this study proposes a graph optimization model based on the framework of g2o that fuses a Wi-Fi fingerprint and Bluetooth Low Energy (BLE) ranging technologies. In our model, the improvement in positioning can be formulated as a nonlinear least-squares optimization problem that a graph can represent. The graph regards users as nodes and our self-designed error functions between users as edges. In the graph, the nodes obtain the initial coordinates through Wi-Fi fingerprint positioning, and all error functions aggregate to a total error function to be solved. To improve the solution effect of the total error function and weaken the influence of measurement error, an information matrix, an edge selection principle, and a Huber kernel function are introduced. The Levenberg-Marquardt (LM) algorithm is used to solve the total error function and the affine transformation estimation is used for the drifting solution. Through experiments, the influence of the threshold in the Huber kernel function is explored, the relationship between the number of nodes in the graph and the optimization effect is analyzed, and the impact of the distribution of nodes is researched. The experimental results show improvements in the positioning accuracy of four common Wi-Fi fingerprint-matching algorithms: KNN, WKNN, GK, and Stg.

12.
Sensors (Basel) ; 22(12)2022 Jun 09.
Artigo em Inglês | MEDLINE | ID: mdl-35746155

RESUMO

Real-time performance and global consistency are extremely important in Simultaneous Localization and Mapping (SLAM) problems. Classic lidar-based SLAM systems often consist of front-end odometry and back-end pose optimization. However, due to expensive computation, it is often difficult to achieve loop-closure detection without compromising the real-time performance of the odometry. We propose a SLAM system where scan-to-submap-based local lidar odometry and global pose optimization based on submap construction as well as loop-closure detection are designed as separated from each other. In our work, extracted edge and surface feature points are inserted into two consecutive feature submaps and added to the pose graph prepared for loop-closure detection and global pose optimization. In addition, a submap is added to the pose graph for global data association when it is marked as in a finished state. In particular, a method to filter out false loops is proposed to accelerate the construction of constraints in the pose graph. The proposed method is evaluated on public datasets and achieves competitive performance with pose estimation frequency over 15 Hz in local lidar odometry and low drift in global consistency.


Assuntos
Algoritmos , Imageamento Tridimensional , Imageamento Tridimensional/métodos
13.
Sensors (Basel) ; 22(9)2022 Apr 28.
Artigo em Inglês | MEDLINE | ID: mdl-35591079

RESUMO

Recently, generating dense maps in real-time has become a hot research topic in the mobile robotics community, since dense maps can provide more informative and continuous features compared with sparse maps. Implicit depth representation (e.g., the depth code) derived from deep neural networks has been employed in the visual-only or visual-inertial simultaneous localization and mapping (SLAM) systems, which achieve promising performances on both camera motion and local dense geometry estimations from monocular images. However, the existing visual-inertial SLAM systems combined with depth codes are either built on a filter-based SLAM framework, which can only update poses and maps in a relatively small local time window, or based on a loosely-coupled framework, while the prior geometric constraints from the depth estimation network have not been employed for boosting the state estimation. To well address these drawbacks, we propose DiT-SLAM, a novel real-time Dense visual-inertial SLAM with implicit depth representation and Tightly-coupled graph optimization. Most importantly, the poses, sparse maps, and low-dimensional depth codes are optimized with the tightly-coupled graph by considering the visual, inertial, and depth residuals simultaneously. Meanwhile, we propose a light-weight monocular depth estimation and completion network, which is combined with attention mechanisms and the conditional variational auto-encoder (CVAE) to predict the uncertainty-aware dense depth maps from more low-dimensional codes. Furthermore, a robust point sampling strategy introducing the spatial distribution of 2D feature points is also proposed to provide geometric constraints in the tightly-coupled optimization, especially for textureless or featureless cases in indoor environments. We evaluate our system on open benchmarks. The proposed methods achieve better performances on both the dense depth estimation and the trajectory estimation compared to the baseline and other systems.

14.
Sensors (Basel) ; 22(6)2022 Mar 13.
Artigo em Inglês | MEDLINE | ID: mdl-35336392

RESUMO

In recent years, multi-sensor fusion technology has made enormous progress in 3D reconstruction, surveying and mapping, autonomous driving, and other related fields, and extrinsic calibration is a necessary condition for multi-sensor fusion applications. This paper proposes a 3D LIDAR-to-camera automatic calibration framework based on graph optimization. The system can automatically identify the position of the pattern and build a set of virtual feature point clouds, and can simultaneously complete the calibration of the LIDAR and multiple cameras. To test this framework, a multi-sensor system is formed using a mobile robot equipped with LIDAR, monocular and binocular cameras, and the pairwise calibration of LIDAR with two cameras is evaluated quantitatively and qualitatively. The results show that this method can produce more accurate calibration results than the state-of-the-art method. The average error on the camera normalization plane is 0.161 mm, which outperforms existing calibration methods. Due to the introduction of graph optimization, the original point cloud is also optimized while optimizing the external parameters between the sensors, which can effectively correct the errors caused during data collection, so it is also robust to bad data.

15.
Sensors (Basel) ; 22(2)2022 Jan 11.
Artigo em Inglês | MEDLINE | ID: mdl-35062481

RESUMO

Simultaneous localization and mapping (SLAM) is one of the key technologies for coal mine underground operation vehicles to build complex environment maps and positioning and to realize unmanned and autonomous operation. Many domestic and foreign scholars have studied many SLAM algorithms, but the mapping accuracy and real-time performance still need to be further improved. This paper presents a SLAM algorithm integrating scan context and Light weight and Ground-Optimized LiDAR Odometry and Mapping (LeGO-LOAM), LeGO-LOAM-SC. The algorithm uses the global descriptor extracted by scan context for loop detection, adds pose constraints to Georgia Tech Smoothing and Mapping (GTSAM) by Iterative Closest Points (ICP) for graph optimization, and constructs point cloud map and an output estimated pose of the mobile vehicle. The test with KITTI dataset 00 sequence data and the actual test in 2-storey underground parking lots are carried out. The results show that the proposed improved algorithm makes up for the drift of the point cloud map, has a higher mapping accuracy, a better real-time performance, a lower resource occupancy, a higher coincidence between trajectory estimation and real trajectory, smoother loop, and 6% reduction in CPU occupancy, the mean square errors of absolute trajectory error (ATE) and relative pose error (RPE) are reduced by 55.7% and 50.3% respectively; the translation and rotation accuracy are improved by about 5%, and the time consumption is reduced by 2~4%. Accurate map construction and low drift pose estimation can be performed.


Assuntos
Algoritmos , Cintilografia
16.
Sensors (Basel) ; 21(8)2021 Apr 16.
Artigo em Inglês | MEDLINE | ID: mdl-33923735

RESUMO

In this work, we propose and evaluate a pose-graph optimization-based real-time multi-sensor fusion framework for vehicle positioning using low-cost automotive-grade sensors. Pose-graphs can model multiple absolute and relative vehicle positioning sensor measurements and can be optimized using nonlinear techniques. We model pose-graphs using measurements from a precise stereo camera-based visual odometry system, a robust odometry system using the in-vehicle velocity and yaw-rate sensor, and an automotive-grade GNSS receiver. Our evaluation is based on a dataset with 180 km of vehicle trajectories recorded in highway, urban, and rural areas, accompanied by postprocessed Real-Time Kinematic GNSS as ground truth. We compare the architecture's performance with (i) vehicle odometry and GNSS fusion and (ii) stereo visual odometry, vehicle odometry, and GNSS fusion; for offline and real-time optimization strategies. The results exhibit a 20.86% reduction in the localization error's standard deviation and a significant reduction in outliers when compared with automotive-grade GNSS receivers.

17.
Artigo em Inglês | MEDLINE | ID: mdl-35664445

RESUMO

We propose a novel stereo laparoscopy video-based non-rigid SLAM method called EMDQ-SLAM, which can incrementally reconstruct thee-dimensional (3D) models of soft tissue surfaces in real-time and preserve high-resolution color textures. EMDQ-SLAM uses the expectation maximization and dual quaternion (EMDQ) algorithm combined with SURF features to track the camera motion and estimate tissue deformation between video frames. To overcome the problem of accumulative errors over time, we have integrated a g2o-based graph optimization method that combines the EMDQ mismatch removal and as-rigid-as-possible (ARAP) smoothing methods. Finally, the multi-band blending (MBB) algorithm has been used to obtain high resolution color textures with real-time performance. Experimental results demonstrate that our method outperforms two state-of-the-art non-rigid SLAM methods: MISSLAM and DefSLAM. Quantitative evaluation shows an average error in the range of 0.8-2.2 mm for different cases.

18.
Sensors (Basel) ; 20(19)2020 Sep 29.
Artigo em Inglês | MEDLINE | ID: mdl-33003456

RESUMO

One of the most fundamental tasks for robots inspecting water distribution pipes is localization, which allows for autonomous navigation, for faults to be communicated, and for interventions to be instigated. Pose-graph optimization using spatially varying information is used to enable localization within a feature-sparse length of pipe. We present a novel method for improving estimation of a robot's trajectory using the measured acoustic field, which is applicable to other measurements such as magnetic field sensing. Experimental results show that the use of acoustic information in pose-graph optimization reduces errors by 39% compared to the use of typical pose-graph optimization using landmark features only. High location accuracy is essential to efficiently and effectively target investment to maximise the use of our aging pipe infrastructure.

19.
Sensors (Basel) ; 20(17)2020 Aug 20.
Artigo em Inglês | MEDLINE | ID: mdl-32825329

RESUMO

In this paper, we proposed a multi-sensor integrated navigation system composed of GNSS (global navigation satellite system), IMU (inertial measurement unit), odometer (ODO), and LiDAR (light detection and ranging)-SLAM (simultaneous localization and mapping). The dead reckoning results were obtained using IMU/ODO in the front-end. The graph optimization was used to fuse the GNSS position, IMU/ODO pre-integration results, and the relative position and relative attitude from LiDAR-SLAM to obtain the final navigation results in the back-end. The odometer information is introduced in the pre-integration algorithm to mitigate the large drift rate of the IMU. The sliding window method was also adopted to avoid the increasing parameter numbers of the graph optimization. Land vehicle tests were conducted in both open-sky areas and tunnel cases. The tests showed that the proposed navigation system can effectually improve accuracy and robustness of navigation. During the navigation drift evaluation of the mimic two-minute GNSS outages, compared to the conventional GNSS/INS (inertial navigation system)/ODO integration, the root mean square (RMS) of the maximum position drift errors during outages in the proposed navigation system were reduced by 62.8%, 72.3%, and 52.1%, along the north, east, and height, respectively. Moreover, the yaw error was reduced by 62.1%. Furthermore, compared to the GNSS/IMU/LiDAR-SLAM integration navigation system, the assistance of the odometer and non-holonomic constraint reduced vertical error by 72.3%. The test in the real tunnel case shows that in weak environmental feature areas where the LiDAR-SLAM can barely work, the assistance of the odometer in the pre-integration is critical and can effectually reduce the positioning drift along the forward direction and maintain the SLAM in the short-term. Therefore, the proposed GNSS/IMU/ODO/LiDAR-SLAM integrated navigation system can effectually fuse the information from multiple sources to maintain the SLAM process and significantly mitigate navigation error, especially in harsh areas where the GNSS signal is severely degraded and environmental features are insufficient for LiDAR-SLAM.

20.
Sensors (Basel) ; 20(3)2020 Feb 05.
Artigo em Inglês | MEDLINE | ID: mdl-32033499

RESUMO

Wi-Fi based positioning has great potential for use in indoor environments because Wi-Fi signals are near-ubiquitous in many indoor environments. With a Reference Fingerprint Map (RFM), fingerprint matching can be adopted for positioning. Much assisting information can be adopted for increasing the accuracy of Wi-Fi based positioning. One of the most adopted pieces of assisting information is the Pedestrian Dead Reckoning (PDR) information derived from inertial measurements. This is widely adopted because the inertial measurements can be acquired through a Commercial Off The Shelf (COTS) smartphone. To integrate the information of Wi-Fi fingerprinting and PDR information, many methods have adopted filters, such as Kalman filters and particle filters. A new methodology for integration of Wi-Fi fingerprinting and PDR is proposed using graph optimization in this paper. For the Wi-Fi based fingerprinting part, our method adopts the state-of-art hierarchical structure and the Penalized Logarithmic Gaussian Distance (PLGD) metric. In the integration part, a simple extended Kalman filter (EKF) is first used for integration of Wi-Fi fingerprinting and PDR results. Then, the tracking results are adopted as initial values for the optimization block, where Wi-Fi fingerprinting and PDR results are adopted to form an concentrated cost function (CCF). The CCF can be minimized with the aim of finding the optimal poses of the user with better tracking results. With both real-scenario experiments and simulations, we show that the proposed method performs better than classical Kalman filter based and particle filter based methods with both less average and maximum positioning error. Additionally, the proposed method is more robust to outliers in both Wi-Fi based and PDR based results, which is commonly seen in practical situations.

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