Graph Optimization Approach to Range-Based Localization

In this article, we propose a general graph optimization-based framework for localization, which can accommodate different types of measurements with varying measurement time intervals. Special emphasis will be on range-based localization. Range and trajectory smoothness constraints are constructed in a position graph, then the robot trajectory over a sliding window is estimated by a graph-based optimization algorithm. Moreover, convergence analysis of the algorithm is provided, and the effects of the number of iterations and window size in the optimization on the localization accuracy are analyzed. Extensive experiments on quadcopter under a variety of scenarios verify the effectiveness of the proposed algorithm and demonstrate a much higher localization accuracy than the existing range-based localization methods, especially in the altitude direction.

Related papers:

title: Vision-Based Target Detection and Localization via a Team of Cooperative UAV and UGVs
abstract: Unmanned vehicles (UVs) play a key role in autonomous surveillance scenarios. A major task needed by these UVs in undertaking autonomous patrol missions is to detect the targets and find their locations in real-time. In this paper, a new vision-based target detection and localization system is presented to make use of different capabilities of UVs as a cooperative team. The scenario considered in this paper is a team of an unmanned aerial vehicle (UAV) and multiple unmanned ground vehicles (UGVs) tracking and controlling crowds on a border area. A customized motion detection algorithm is applied to follow the crowd from the moving camera mounted on the UAV. Due to UAVs lower resolution and broader detection range, UGVs with higher resolution and fidelity are used as the individual human detectors, as well as moving landmarks to localize the detected crowds with unknown independently moving patterns at each time point. The UAVs localization algorithm, proposed in this paper, then converts the crowds' image locations into their real-world positions, using perspective transformation. A rule-of-thumb localization method by a UGV is also presented, which estimates the geographic locations of the detected individuals. Moreover, an agent-based simulation model is developed for system verification, with different parameters, such as flight altitude, number of landmarks, and landmark assignment method. The performance measure considered in this paper is the average Euclidean distance between the estimated locations and simulated geographic waypoints of the crowd. Experimental results demonstrate the effectiveness of the proposed framework for autonomous surveillance by UVs.

title: Interval Observer Design for Discrete-Time Uncertain Takagi–Sugeno Fuzzy Systems
abstract: This paper proposes a novel interval observer design method for discrete-time Takagi–Sugeno fuzzy systems with parametric uncertainty, disturbances, and measurement noise. We present a new structure of interval observer with more design parameters, which can be used to broaden the application scope of interval observer design. For improving the accuracy of interval estimation, an $L_{\infty }$ norm-based approach is used in the design of interval observer to attenuate the effect of the unknown disturbances, noise, and parametric uncertainty. Furthermore, the design conditions are formulated into a set of linear matrix inequalities, which can be efficiently solved. Numerical simulations are given to illustrate the effectiveness of the proposed method.

title: LSD-SLAM: Large-Scale Direct Monocular SLAM
abstract: We propose a direct (feature-less) monocular SLAM algorithm which, in contrast to current state-of-the-art regarding direct methods, allows to build large-scale, consistent maps of the environment. Along with highly accurate pose estimation based on direct image alignment, the 3D environment is reconstructed in real-time as pose-graph of keyframes with associated semi-dense depth maps. These are obtained by filtering over a large number of pixelwise small-baseline stereo comparisons. The explicitly scale-drift aware formulation allows the approach to operate on challenging sequences including large variations in scene scale. Major enablers are two key novelties: (1) a novel direct tracking method which operates on \(\mathfrak{sim}(3)\), thereby explicitly detecting scale-drift, and (2) an elegant probabilistic solution to include the effect of noisy depth values into tracking. The resulting direct monocular SLAM system runs in real-time on a CPU.

title: Fusion of WiFi, Smartphone Sensors and Landmarks Using the Kalman Filter for Indoor Localization
abstract: Location-based services (LBS) have attracted a great deal of attention recently. Outdoor localization can be solved by the GPS technique, but how to accurately and efficiently localize pedestrians in indoor environments is still a challenging problem. Recent techniques based on WiFi or pedestrian dead reckoning (PDR) have several limiting problems, such as the variation of WiFi signals and the drift of PDR. An auxiliary tool for indoor localization is landmarks, which can be easily identified based on specific sensor patterns in the environment, and this will be exploited in our proposed approach. In this work, we propose a sensor fusion framework for combining WiFi, PDR and landmarks. Since the whole system is running on a smartphone, which is resource limited, we formulate the sensor fusion problem in a linear perspective, then a Kalman filter is applied instead of a particle filter, which is widely used in the literature. Furthermore, novel techniques to enhance the accuracy of individual approaches are adopted. In the experiments, an Android app is developed for real-time indoor localization and navigation. A comparison has been made between our proposed approach and individual approaches. The results show significant improvement using our proposed framework. Our proposed system can provide an average localization accuracy of 1 m.

title: A platform for aerial robotics research and demonstration: The Flying Machine Arena
abstract: The Flying Machine Arena is a platform for experiments and demonstrations with fleets of small flying vehicles. It utilizes a distributed, modular architecture linked by robust communication layers. An estimation and control framework along with built-in system protection components enable prototyping of new control systems concepts and implementation of novel demonstrations. More recently, a mobile version has been featured at several eminent public events. We describe the architecture of the Arena from the viewpoint of system robustness and its capability as a dual-purpose research and demonstration platform.

title: A Novel Biomechanical Model-Aided IMU/UWB Fusion for Magnetometer-Free Lower Body Motion Capture
abstract: The available human body inertial motion capture (MoCap) systems are aided by magnetometers to remove the drift error in yaw angle estimation, which in turn limits their application in the presence of long-lasting magnetic disturbances in indoor environments. This paper introduces a magnetometer-free algorithm for lower-body MoCap including 3-D localization and posture tracking by fusing inertial sensors with an ultrawideband (UWB) localization system and a biomechanical model of the human lower body. Using our novel Kalman filter-based fusion algorithm, the UWB localization data aided by the biomechanical model can eliminate the drift in inertial yaw angle estimation of the lower-body segments. This magnetometer-free yaw angle estimation makes the algorithm insensitive to the magnetic disturbances. The algorithm is benchmarked against the optical MoCap system for various indoor activities including walking, jogging, jumping, and stairs ascending/descending. The results show that the proposed algorithm outperforms the available magnetometer-aided algorithms in yaw angle tracking under magnetic disturbances. In a uniform magnetic field, the algorithm shows similar accuracies in localization and joint angle tracking when compared with the magnetometer-aided methods. The localization accuracy of the proposed method is better than 4.5 cm in a 3-D space and its accuracy for knee angle tracking is about 3.5° and 4.5° in low and high dynamic motions, respectively.

title: Generalized geometric triangulation algorithm for mobile robot absolute self-localization
abstract: Triangulation with active beacons is widely used in the absolute localization of mobile robots. The geometric triangulation algorithm allows the self-localization of a robot on a plane. However, the three beacons it uses must be "properly ordered" and the algorithm works consistently only when these beacons within the triangle form the robot. This paper presents an improved version of the algorithm, which does not require beacon ordering and works over the whole navigation plane except for a few well-determined lines where localization is not possible.

title: Fast Moving Horizon State Estimation for Discrete-Time Systems Using Single and Multi Iteration Descent Methods
abstract: Descent algorithms based on the gradient, conjugate gradient, and Newton methods are investigated to perform optimization in moving horizon state estimation for discrete-time linear and nonlinear systems. Conditions that ensure the stability of the estimation error are established for single and multi iteration schemes with a least-squares cost function that takes into account only a batch of most recent information. Simulation results show the effectiveness of the proposed approaches also in comparison with techniques based on the Kalman filter.

title: A robot self-localization system using one-way ultra-wideband communication
abstract: A robot localization system is presented that enables a robot to estimate its position within some space by passively receiving ultra-wideband radio signals from fixed-position modules. Communication from the fixed-position modules is one-way, allowing the system to scale to multiple robots. Furthermore, the system's high position update rate makes it suitable to be used in a feedback control system, and enables the robot to track and perform high-speed, dynamic motions. This paper describes the algorithmic underpinnings of the system, discusses design decisions and their impact on the performance of the resulting localization, and highlights challenges faced during implementation. Performance of the localization system is experimentally verified through comparison with data from a motion-capture system. Finally, the system's application to robot self-localization is demonstrated through integration with a quadrocopter.

title: Smartphone Inertial Sensor-Based Indoor Localization and Tracking With iBeacon Corrections
abstract: The Global Positioning System (GPS) can be readily used for outdoor localization, but GPS signals are degraded in indoor environments. How to develop a robust and accurate indoor localization system is an emergent task. In this paper, we propose a smartphone inertial sensor-based indoor localization and tracking system with occasional iBeacon corrections. Some important issues in a smartphone-based pedestrian dead reckoning (PDR) approach, i.e., step detection, walking direction estimation, and initial point estimation, are studied. One problem of the PDR approach is the drift with walking distance. We apply a recent technology, iBeacon, to occasionally calibrate the drift of the PDR approach. By analyzing iBeacon measurements, we define an efficient calibration range where an extended Kalman filter is utilized. The proposed localization and tracking system can be implemented in resource-limited smartphones. To evaluate the performance of the proposed approach, real experiments under two different environments have been conducted. The experimental results demonstrated the effectiveness of the proposed approach. We also tested the localization accuracy with respect to the number of iBeacons.

title: Kervolutional Neural Networks
abstract: Convolutional neural networks (CNNs) have enabled the state-of-the-art performance in many computer vision tasks. However, little effort has been devoted to establishing convolution in non-linear space. Existing works mainly leverage on the activation layers, which can only provide point-wise non-linearity. To solve this problem, a new operation, kervolution (kernel convolution), is introduced to approximate complex behaviors of human perception systems leveraging on the kernel trick. It generalizes convolution, enhances the model capacity, and captures higher order interactions of features, via patch-wise kernel functions, but without introducing additional parameters. Extensive experiments show that kervolutional neural networks (KNN) achieve higher accuracy and faster convergence than baseline CNN.

title: Ultra-Wideband-Based Localization for Quadcopter Navigation
abstract: Micro unmanned aerial vehicles (UAVs) are promising to play more and more important roles in both civilian and military activities. Currently, the navigation of UAVs is critically dependent on the localization service provided by the Global Positioning System (GPS), which suffers from the multipath effect and blockage of line-of-sight, and fails to work in an indoor, forest or urban environment. In this paper, we establish a localization system for quadcopters based on ultra-wideband (UWB) range measurements. To achieve the localization, a UWB module is installed on the quadcopter to actively send ranging requests to some fixed UWB modules at known positions (anchors). Once a distance is obtained, it is calibrated first and then goes through outlier detection before being fed to a localization algorithm. The localization algorithm is initialized by trilateration and sustained by the extended Kalman filter (EKF). The position and velocity estimates produced by the algorithm will be further fed to the control loop to aid the navigation of the quadcopter. Various flight tests in different environments have been conducted to validate the performance of UWB ranging and localization algorithm.

title: An Ultra-Wideband-based Multi-UAV Localization System in GPS-denied environments
abstract: This paper presents a technique for multiUAV localization using ranging measurements from Two-Way Time-Of-Flight Ultra-Wideband (UWB) transceivers. In continuation with our previous work, the use of the Extended Kalman Filter (EKF) estimate is extended by fusing with other sensors to achieve a usable altitude estimate. Besides EKF, another method based on Non-linear Regression (NLR) is also developed to serve as an auxiliary localization to supplement the EKF. Experiments of autonomous flights are carried out to study the performance of these localization methods. Our success in supporting 4 UAVs demonstrates the capability of UWB for multi-UAV localization as a substitute for GPS in GPS-denied conditions. It can also serve as a cost-competitive alternative for very accurate yet expensive, highly centralized motion capture systems for indoor localization.

title: Received Signal Strength Based Indoor Positioning Using a Random Vector Functional Link Network
abstract: Fingerprinting based indoor positioning system is gaining more research interest under the umbrella of location-based services. However, existing works have certain limitations in addressing issues such as noisy measurements, high computational complexity, and poor generalization ability. In this work, a random vector functional link network based approach is introduced to address these issues. In the proposed system, a subset of informative features from many randomized noisy features is selected to both reduce the computational complexity and boost the generalization ability. Moreover, the feature selector and predictor are jointly learned iteratively in a single framework based on an augmented Lagrangian method. The proposed system is appealing as it can be naturally fit into parallel or distributed computing environment. Extensive real-world indoor localization experiments are conducted on users with smartphone devices and results demonstrate the superiority of the proposed method over the existing approaches.

title: G2o: A general framework for graph optimization
abstract: Many popular problems in robotics and computer vision including various types of simultaneous localization and mapping (SLAM) or bundle adjustment (BA) can be phrased as least squares optimization of an error function that can be represented by a graph. This paper describes the general structure of such problems and presents g2o, an open-source C++ framework for optimizing graph-based nonlinear error functions. Our system has been designed to be easily extensible to a wide range of problems and a new problem typically can be specified in a few lines of code. The current implementation provides solutions to several variants of SLAM and BA. We provide evaluations on a wide range of real-world and simulated datasets. The results demonstrate that while being general g2o offers a performance comparable to implementations of state-of-the-art approaches for the specific problems.

title: Distributed Self Localization for Relative Position Sensing Networks in 2D Space
abstract: This paper studies the 2D localization problem of a sensor network given anchor node positions in a common global coordinate frame and relative position measurements in local coordinate frames between node pairs. It is assumed that the local coordinate frames of different sensors have different orientations and the orientation difference with respect to the global coordinate frame are not known. In terms of graph connectivity, a necessary and sufficient condition is obtained for self-localizability that leads to a fully distributed localization algorithm. Moreover, a distributed verification algorithm is developed to check the graph connectivity condition, which can terminate successfully when the sensor network is self-localizable. Finally, a fully distributed, linear, and iterative algorithm based on the complex-valued Laplacian associated with the sensor network is proposed, which converges globally and gives the correct localization result.

title: Globally Convergent Distributed Network Localization Using Locally Measured Bearings
abstract: This paper studies the problem of bearing-based network localization, which aims to estimate the absolute positions of the nodes in a network by using the inter-node bearings measured in each node's local reference frame and the absolute positions of a small number of nodes called anchors. In the first part of the paper, we propose a continuous-time localization algorithm, which consists of coupled orientation and position estimation procedures. Compared to the existing works, the proposed algorithm has a concise form and guarantees global estimation convergence. In the second part of the paper, we study the discrete-time case which is still an open problem till now. We fill this gap by proposing a discrete-time localization algorithm to globally localize three-dimensional networks using locally measured bearings. The discrete-time algorithm does not require designing sufficiently small step sizes to ensure convergence. Numerical simulation is presented to verify the proposed algorithms.

title: Ultra-wideband aided fast localization and mapping system
abstract: This paper proposes an ultra-wideband (UWB) aided localization and mapping system that leverages on inertial sensor and depth camera. Inspired by the fact that visual odometry (VO) system, regardless of its accuracy in the short term, still faces challenges with accumulated errors in the long run or under unfavourable environments, the UWB ranging measurements are fused to remove the visual drift and improve the robustness. A general framework is developed which consists of three parallel threads, two of which carry out the visualinertial odometry (VIO) and UWB localization respectively. The other mapping thread integrates visual tracking constraints into a pose graph with the proposed smooth and virtual range constraints, such that a bundle adjustment is performed to provide robust trajectory estimation. Experiments show that the proposed system is able to create dense drift-free maps in real-time even running on an ultra-low power processor in featureless environments.

title: Model-free Approach for Sensor Network Localization with Noisy Distance Measurement
abstract: A model-free localization method with noisy distance measurement is proposed for estimating a moving robot in 3D space. Considering that the traditional filter-based sensor network localization algorithms can not provide acceptable estimation accuracy in altitude in 3D space, the proposed method utilizes not only current measurements but also previous measurements to localize a robot. This character adds more constraints to localization to avoid local minimum. In addition, different from the traditional filter-based localization methods which need kinetic model for localization, our proposed method is model-free and converts the localization problem to graph optimization problem. The advantage is that we avoid the possible estimation error caused by inaccurate or simplified kinetic model. Considering that the communication limitation in application makes many graph optimization theories such as distributed localization theory and trilateration difficult to be realized, our method proposes to add constrained equation between adjacent positions to solve this problem. Experiments under a variety of scenarios verify the stability of this method and show that the algorithm achieves better localization accuracy than filter-based methods.

title: Lie Groups, Lie Algebras, and Representations
abstract: An important concept in physics is that of symmetry, whether it be rotational symmetry for many physical systems or Lorentz symmetry in relativistic systems. In many cases, the group of symmetries of a system is a continuous group, that is, a group that is parameterized by one or more real parameters. More precisely, the symmetry group is often a Lie group, that is, a smooth manifold endowed with a group structure in such a way that operations of inversion and group multiplication are smooth. The tangent space at the identity in a Lie group has a natural “bracket” operation that makes the tangent space into a Lie algebra. The Lie algebra of a Lie group encodes many of the properties of the Lie group, and yet the Lie algebra is easier to work with because it is a linear space.

title: Fusing ultra-wideband range measurements with accelerometers and rate gyroscopes for quadrocopter state estimation
abstract: A state estimator for a quadrocopter is presented, using measurements from an accelerometer, angular rate gyroscope, and a set of ultra-wideband ranging radios. The estimator uses an extended aerodynamic model for the quadrocopter, where the full 3D airspeed is observable through accelerometer measurements. The remaining quadrocopter states, including the yaw orientation, are rendered observable by fusing ultra-wideband range measurements, under the assumption of no wind. The estimator is implemented on a standard microcontroller using readily-available, low-cost sensors. Performance is experimentally investigated in a variety of scenarios, where the quadrocopter is flown under feedback control using the estimator output.

title: An IMU/UWB/Vision-based Extended Kalman Filter for Mini-UAV Localization in Indoor Environment using 802.15.4a Wireless Sensor Network
abstract: Indoor localization of mobile agents using wireless technologies is becoming very important in military and civil applications. This paper introduces an approach for the indoor localization of a mini UAV based on Ultra-WideBand technology, low cost IMU and vision based sensors. In this work an Extended Kalman Filter (EKF) is introduced as a possible technique to improve the localization. The proposed approach allows to use a low-cost Inertial Measurement Unit (IMU) in the prediction step and the integration of vision-odometry for the detection of markers nearness the touchdown area. The ranging measurements allow to reduce the errors of inertial sensors due to the limited performance of accelerometers and gyros. The obtained results show that an accuracy of 10 cm can be achieved.

title: The unconstrained and inequality constrained moving horizon approach to robot localization
abstract: We present a moving horizon approach for estimating the state of a nonlinear dynamic system that may be subject to inequality constraints. The method takes advantage of a recent smoothing algorithm proposed in the literature based on interior point techniques. The approach exploits the same decomposition used for unconstrained Kalman-Bucy smoothers. Hence, the number of operations required by the algorithm scales linearly with the length of the horizon, making it suitable for online applications. We apply this method to the robot localization problem, showing that it is able to produce much more accurate results than the iterated Kalman filter with little additional computational effort.

title: Vehicle localization by sensor fusion of LRS measurement and odometry information based on moving horizon estimation
abstract: In this study, we propose a localization method based on the fusion of the laser range sensor (LRS) measurements and the odometry information of a vehicle using moving horizon estimation (MHE). LRS measurement includes outliers and suffers from the intermittent observation; alleviation of their effect is required in order to localize a vehicle position with high accuracy. Proposed localization method merges multi-sampling data by exploiting MHE, which greatly reduces the effect of outliers and intermittent observation on localization using the data of other sampling. We show the efficacy of proposed localization by numerical simulations and experiments.

title: A Distributed Moving Horizon Estimator for Mobile Robot Localization Problems
abstract: We propose a distributed moving horizon estimator (MHE) for a mobile robot localization problem using sensor networks. The application scenario represents a constrained nonlinear system, where the process is locally unobservable by each sensor alone. The proposed distributed MHE algorithm is based on a weighted average consensus process. Crucial aspects such as stability, unbiased estimates, and the approximation of the arrival cost are discussed. Simulation results show the performance of the algorithm in comparison to the centralized approach.

title: An optimization based Moving Horizon Estimation with application to localization of Autonomous Underwater Vehicles
abstract: Localizing small Autonomous Underwater Vehicles (AUVs) that have limited payload and perception capability is of importance to promote popularization of underwater applications. Two different methodologies, filter and optimization based methods, can both be used to address the localization problem. But they are seldom rigorously compared and their relative advantages are rarely established. This paper presents a rigorous investigation on the relationship between these two methods. Based on this examination, a novel cooperative localization algorithm for the scenario where AUVs are localized by using range measurements from a single surface mobile beacon is proposed. The main contribution of this paper is threefold. First, major difference and close connection between filter based method and optimization based Maximum a Posteriori method are explicitly clarified by analytically solving optimization problems. Second, a novel localization algorithm combining a filter based extended Kalman filter and an optimization based Moving Horizon Estimation is developed for three-dimensional underwater localization in real-time and long-term applications. The algorithm allows data fusion of multiple sensors, imposes physical constraints on states and noises, bounds computational complexity, and achieves a compromise between better accuracy and lower computational requirement. Third, observability analysis of single beacon based localization algorithm is conducted in the context of nonlinear discrete time systems and a sufficient condition is derived. The observability and improved localization accuracy of the proposed localization algorithm are verified in a customized underwater simulator by extensive numerical simulations.

title: Optimization-Based Sensor Fusion of GNSS and IMU Using a Moving Horizon Approach
abstract: The rise of autonomous systems operating close to humans imposes new challenges in terms of robustness and precision on the estimation and control algorithms. Approaches based on nonlinear optimization, such as moving horizon estimation, have been shown to improve the accuracy of the estimated solution compared to traditional filter techniques. This paper introduces an optimization-based framework for multi-sensor fusion following a moving horizon scheme. The framework is applied to the often occurring estimation problem of motion tracking by fusing measurements of a global navigation satellite system receiver and an inertial measurement unit. The resulting algorithm is used to estimate position, velocity, and orientation of a maneuvering airplane and is evaluated against an accurate reference trajectory. A detailed study of the influence of the horizon length on the quality of the solution is presented and evaluated against filter-like and batch solutions of the problem. The versatile configuration possibilities of the framework are finally used to analyze the estimated solutions at different evaluation times exposing a nearly linear behavior of the sensor fusion problem.

title: IMU Preintegration on Manifold for Efficient Visual-Inertial Maximum-a-Posteriori Estimation
abstract: Recent results in monocular visual-inertial navigation (VIN) have shown that optimization-based approaches outperform filtering methods in terms of accuracy due to their capability to relinearize past states. However, the improvement comes at the cost of increased computational complexity. In this paper, we address this issue by preintegrating inertial measurements between selected keyframes. The preintegration allows us to accurately summarize hundreds of inertial measurements into a single relative motion constraint. Our first contribution is a preintegration theory that properly addresses the manifold structure of the rotation group and carefully deals with uncertainty propagation. The measurements are integrated in a local frame, which eliminates the need to repeat the integration when the linearization point changes while leaving the opportunity for belated bias corrections. The second contribution is to show that the preintegrated IMU model can be seamlessly integrated in a visual-inertial pipeline under the unifying framework of factor graphs. This enables the use of a structureless model for visual measurements, further accelerating the computation. The third contribution is an extensive evaluation of our monocular VIN pipeline: experimental results confirm that our system is very fast and demonstrates superior accuracy with respect to competitive state-of-the-art filtering and optimization algorithms, including off-the-shelf systems such as Google Tango

title: Machine Learning in Wireless Sensor Networks: Algorithms, Strategies, and Applications
abstract: Wireless sensor networks (WSNs) monitor dynamic environments that change rapidly over time. This dynamic behavior is either caused by external factors or initiated by the system designers themselves. To adapt to such conditions, sensor networks often adopt machine learning techniques to eliminate the need for unnecessary redesign. Machine learning also inspires many practical solutions that maximize resource utilization and prolong the lifespan of the network. In this paper, we present an extensive literature review over the period 2002-2013 of machine learning methods that were used to address common issues in WSNs. The advantages and disadvantages of each proposed algorithm are evaluated against the corresponding problem. We also provide a comparative guide to aid WSN designers in developing suitable machine learning solutions for their specific application challenges.

title: Steerable, Progressive Multidimensional Scaling
abstract: Current implementations of multidimensional scaling (MDS), an approach that attempts to best represent data point similarity in a low-dimensional representation, are not suited for many of today's large-scale datasets. We propose an extension to the spring model approach that allows the user to interactively explore datasets that are far beyond the scale of previous implementations of MDS. We present MDSteer, a steerable MDS computation engine and visualization tool that progressively computes an MDS layout and handles datasets of over one million points. Our technique employs hierarchical data structures and progressive layouts to allow the user to steer the computation of the algorithm to the interesting areas of the dataset. The algorithm iteratively alternates between a layout stage in which a subselection of points are added to the set of active points affected by the MDS iteration, and a binning stage which increases the depth of the bin hierarchy and organizes the currently unplaced points into separate spatial regions. This binning strategy allows the user to select onscreen regions of the layout to focus the MDS computation into the areas of the dataset that are assigned to the selected bins. We show both real and common synthetic benchmark datasets with dimensionalities ranging from 3 to 300 and cardinalities of over one million points

title: Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
abstract: CHOLMOD is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AAT, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level-3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. CHOLMOD is written in ANSI/ISO C, with both C and MATLABTM interfaces. It appears in MATLAB 7.2 as x = A\b when A is sparse symmetric positive definite, as well as in several other sparse matrix functions.

title: Accurate indoor localization with ultra-wideband using spatial models and collaboration
abstract: Ultra-wideband (UWB) localization is a recent technology that performs competitively with many indoor localization methods currently available. Despite its desirable traits, such as potential high accuracy and high material penetrability, the resolution of non-line-of-sight signals remains a very hard problem and has a significant impact on the localization performance. In this work, we address the peculiarities of UWB error behavior by building models that capture the spatiality as well as the multimodal statistics of the error behavior. Our framework utilizes tessellated maps that associate probabilistic error models to localities in space. In addition to our UWB localization strategy (which provides absolute position estimates), we investigate the effects of collaboration in the form of relative positioning. To this end, we develop a relative range and bearing model and, together with the UWB model, present a unified localization technique based on a particle filter framework. We test our approach experimentally on a group of 10 mobile robots equipped with UWB emitters and extension modules providing inter-robot relative range and bearing measurements. Our experimental insights highlight the benefits of collaboration, which are consistent over numerous experimental scenarios. Also, we show the relevance, in terms of positioning accuracy, of our multimodal UWB measurement model by performing systematic comparisons with two alternative measurement models. Our final results show median localization errors below 10 cm in cluttered environments, using a modest set of 50 particles in our filter.

title: GROF: Indoor Localization Using a Multiple-Bandwidth General Regression Neural Network and Outlier Filter
abstract: In recent years, a variety of methods have been developed for indoor localization utilizing fingerprints of received signal strength (RSS) that are location dependent. Nevertheless, the RSS is sensitive to environmental variations, in that the resulting fluctuation severely degrades the localization accuracy. Furthermore, the fingerprints survey course is time-consuming and labor-intensive. Therefore, the lightweight fingerprint-based indoor positioning approach is preferred for practical applications. In this paper, a novel multiple-bandwidth generalized regression neural network (GRNN) with the outlier filter indoor positioning approach (GROF) is proposed. The GROF method is based on the GRNN, for which we adopt a new kind of multiple-bandwidth kernel architecture to achieve a more flexible regression performance than that of the traditional GRNN. In addition, an outlier filtering scheme adopting the k-nearest neighbor (KNN) method is embedded into the localization module so as to improve the localization robustness against environmental changes. We discuss the multiple-bandwidth spread value training process and the outlier filtering algorithm, and demonstrate the feasibility and performance of GROF through experiment data, using a Universal Software Radio Peripheral (USRP) platform. The experimental results indicate that the GROF method outperforms the positioning methods, based on the standard GRNN, KNN, or backpropagation neural network (BPNN), both in localization accuracy and robustness, without the extra training sample requirement.