MagLoc-AR: Magnetic-Based Localization for Visual-Free Augmented Reality in Large-Scale Indoor Environments

Accurate localization of a display device is essential for AR in large-scale environments. Visual-based localization is the most commonly used solution, but poses privacy risks, suffers from robustness issues and consumes high power. Wireless signal-based localization is a potential visual-free solution, but its accuracy is not enough for AR. In this paper, we present MagLoc-AR, a novel visual-free localization solution that achieves sufficient accuracy for some AR applications (e.g. AR navigation) in large-scale indoor environments. We exploit the location-dependent magnetic field interference that is ubiquitous indoors as a localization signal. Our method requires only a consumer-grade 9-axis IMU, with the gyroscope and acceleration measurements used to recover the motion trajectory, and the magnetic measurements used to register the trajectory to the global map. To meet the accuracy requirement of AR, we propose a mapping method to reconstruct a globally consistent magnetic field of the environment, and a localization method fusing the biased magnetic measurements with the network-predicted motion to improve localization accuracy. In addition, we provide the first dataset for both visual-based and geomagnetic-based localization in large-scale indoor environments. Evaluations on the dataset demonstrate that our proposed method is sufficiently accurate for AR navigation and has advantages over the visual-based methods in terms of power consumption and robustness. Project page: https://github.com/zju3dv/MagLoc-AR/.

A minimum assumption approach to MEG sensor array design

Objective.Our objective is to formulate the problem of the magnetoencephalographic (MEG) sensor array design as a well-posed engineering problem of accurately measuring the neuronal magnetic fields. This is in contrast to the traditional approach that formulates the sensor array design problem in terms of neurobiological interpretability the sensor array measurements.Approach.We use the vector spherical harmonics (VSH) formalism to define a figure-of-merit for an MEG sensor array. We start with an observation that, under certain reasonable assumptions, any array ofmperfectly noiseless sensors will attain exactly the same performance, regardless of the sensors' locations and orientations (with the exception of a negligible set of singularly bad sensor configurations). We proceed to the conclusion that under the aforementioned assumptions, the only difference between different array configurations is the effect of (sensor) noise on their performance. We then propose a figure-of-merit that quantifies, with a single number, how much the sensor array in question amplifies the sensor noise.Main results.We derive a formula for intuitively meaningful, yet mathematically rigorous figure-of-merit that summarizes how desirable a particular sensor array design is. We demonstrate that this figure-of-merit is well-behaved enough to be used as a cost function for a general-purpose nonlinear optimization methods such as simulated annealing. We also show that sensor array configurations obtained by such optimizations exhibit properties that are typically expected of 'high-quality' MEG sensor arrays, e.g. high channel information capacity.Significance.Our work paves the way toward designing better MEG sensor arrays by isolating the engineering problem of measuring the neuromagnetic fields out of the bigger problem of studying brain function through neuromagnetic measurements.

Fast and Noise-Resilient Magnetic Field Mapping on a Low-Cost UAV Using Gaussian Process Regression

This study presents a comprehensive approach to mapping local magnetic field anomalies with robustness to magnetic noise from an unmanned aerial vehicle (UAV). The UAV collects magnetic field measurements, which are used to generate a local magnetic field map through Gaussian process regression (GPR). The research identifies two categories of magnetic noise originating from the UAV's electronics, adversely affecting map precision. First, this paper delineates a zero-mean noise arising from high-frequency motor commands issued by the UAV's flight controller. To mitigate this noise, the study proposes adjusting a specific gain in the vehicle's PID controller. Next, our research reveals that the UAV generates a time-varying magnetic bias that fluctuates throughout experimental trials. To address this issue, a novel compromise mapping technique is introduced, enabling the map to learn these time-varying biases with data collected from multiple flights. The compromise map circumvents excessive computational demands without sacrificing mapping accuracy by constraining the number of prediction points used for regression. A comparative analysis of the magnetic field maps' accuracy and the spatial density of observations employed in map construction is then conducted. This examination serves as a guideline for best practices when designing trajectories for local magnetic field mapping. Furthermore, the study presents a novel consistency metric intended to determine whether predictions from a GPR magnetic field map should be retained or discarded during state estimation. Empirical evidence from over 120 flight tests substantiates the efficacy of the proposed methodologies. The data are made publicly accessible to facilitate future research endeavors.

Minimization of measuring points for the electric field exposure map generation in indoor environments by means of Kriging interpolation and selective sampling

In a world with increasing systems accessing to radio spectrum, the concern for exposure to electromagnetic fields is growing and therefore it is necessary to check limits in those areas where electromagnetic sources are working. Therefore, radio and exposure maps are continuously being generated, mainly in outdoor areas, by using many interpolation techniques. In this work, Surfer software and Kriging interpolation have been used for the first time to generate an indoor exposure map. A regular measuring mesh has been generated. Elimination of Less Significant Points (ELSP) and Geometrical Elimination of Neighbors (GEN) strategies to reduce the measuring points have been presented and evaluated. Both strategies have been compared to the map generated with all the measurements by calculating the root mean square and mean absolute errors. Results indicate that ELSP method can reduce up to 70% of the mesh measuring points while producing similar exposure maps to the one generated with all the measuring points. GEN, however, produces distorted maps and much higher error indicators even for 50% of eliminated measuring points. As a conclusion, a procedure for reducing the measuring points to generate radio and exposure maps is proposed based on the ELSP method and the Kriging interpolation.

Magnetic field mapping of inaccessible regions using physics-informed neural networks

A difficult problem concerns the determination of magnetic field components within an experimentally inaccessible region when direct field measurements are not feasible. In this paper, we propose a new method of accessing magnetic field components using non-disruptive magnetic field measurements on a surface enclosing the experimental region. Magnetic field components in the experimental region are predicted by solving a set of partial differential equations (Ampere’s law and Gauss’ law for magnetism) numerically with the aid of physics-informed neural networks (PINNs). Prediction errors due to noisy magnetic field measurements and small number of magnetic field measurements are regularized by the physics information term in the loss function. We benchmark our model by comparing it with an older method. The new method we present will be of broad interest to experiments requiring precise determination of magnetic field components, such as searches for the neutron electric dipole moment.

Analysis of Magnetic Field Measurements for Indoor Positioning

Infrastructure-free magnetic fields are ubiquitous and have attracted tremendous interest in magnetic field-based indoor positioning. However, magnetic field-based indoor positioning applications face challenges such as low discernibility, heterogeneous devices, and interference from ferromagnetic materials. This paper first analyzes the statistical characteristics of magnetic field (MF) measurements from heterogeneous smartphones. It demonstrates that, in the absence of disturbances, the MF measurements in indoor environments follow a Gaussian distribution with temporal stability and spatial discernibility. It shows the fluctuations in magnetic field intensity caused by the rotation of a smartphone around the Z-axis. Secondly, it suggests that the RLOWESS method can be used to eliminate magnetic field anomalies, using magnetometer calibration to ensure consistent MF measurements in heterogeneous smartphones. Thirdly, it tests the magnetic field positioning performance of homogeneous and heterogeneous devices using different machine learning methods. Finally, it summarizes the feasibility/limitations of using only MF measurement for indoor positioning.

An Extended Kalman Filter for Magnetic Field SLAM Using Gaussian Process Regression

We present a computationally efficient algorithm for using variations in the ambient magnetic field to compensate for position drift in integrated odometry measurements (dead-reckoning estimates) through simultaneous localization and mapping (SLAM). When the magnetic field map is represented with a reduced-rank Gaussian process (GP) using Laplace basis functions defined in a cubical domain, analytic expressions of the gradient of the learned magnetic field become available. An existing approach for magnetic field SLAM with reduced-rank GP regression uses a Rao-Blackwellized particle filter (RBPF). For each incoming measurement, training of the magnetic field map using an RBPF has a computational complexity per time step of O(NpNm2), where Np is the number of particles, and Nm is the number of basis functions used to approximate the Gaussian process. Contrary to the existing particle filter-based approach, we propose applying an extended Kalman filter based on the gradients of our learned magnetic field map for simultaneous localization and mapping. Our proposed algorithm only requires training a single map. It, therefore, has a computational complexity at each time step of O(Nm2). We demonstrate the workings of the extended Kalman filter for magnetic field SLAM on an open-source data set from a foot-mounted sensor and magnetic field measurements collected onboard a model ship in an indoor pool. We observe that the drift compensating abilities of our algorithm are comparable to what has previously been demonstrated for magnetic field SLAM with an RBPF.

A Survey of Magnetic-Field-Based Indoor Localization

Magnetic fields have attracted considerable attention in indoor localization due to their ubiquitous and infrastructure-free characteristics. This survey provides a comprehensive review of magnetic-field-based indoor localization methods. We first introduce characteristics of the magnetic field, its advantages, and its challenges. We then describe the magnetometer model and the effect of ferromagnetic interference. We also present coordinate systems commonly used for magnetic field localization and describe their transformation relationships. We then compare the existing publicly available magnetic field benchmark datasets, present magnetometer calibration algorithms, and show how efficiently magnetic field maps can be built. We also summarize state-of-the-art magnetic field localization methods (e.g., magnetic landmarks, dynamic time warping, magnetic fingerprinting, filters, simultaneous localization and mapping, and neural network). The smartphone-based pedestrian dead reckoning approach is also reviewed.

Self-Localization of IoT Devices Using Noisy Anchor Positions and RSSI Measurements

Location-enabled Internet of things (IoT) has attracted much attention from the scientific and industrial communities given its high relevance in application domains such as agriculture, wildlife management, and infectious disease control. The frequency and accuracy of location information plays an important role in the success of these applications. However, frequent and accurate self-localization of IoT devices is challenging due to their resource-constrained nature. In this paper, we propose a new algorithm for self-localization of IoT devices using noisy received signal strength indicator (RSSI) measurements and perturbed anchor node position estimates. In the proposed algorithm, we minimize a weighted sum-square-distance-error cost function in an iterative fashion utilizing the gradient-descent method. We calculate the weights using the statistical properties of the perturbations in the measurements. We assume log-normal distribution for the RSSI-induced distance estimates due to considering the log-distance path-loss model with normally-distributed perturbations for the RSSI measurements in the logarithmic scale. We also assume normally-distributed perturbation in the anchor position estimates. We compare the performance of the proposed algorithm with that of an existing algorithm that takes a similar approach but only accounts for the perturbations in the RSSI measurements. Our simulation results show that by taking into account the error in the anchor positions, a significant improvement in the localization accuracy can be achieved. The proposed algorithm uses only a single measurement of RSSI and one estimate of each anchor position. This makes the proposed algorithm suitable for frequent and accurate localization of IoT devices.

Improving Attitude Estimation Using Gaussian-Process-Regression-Based Magnetic Field Maps

Magnetometers measure the local magnetic field and are present in most modern inertial measurement units (IMUs). Readings from magnetometers are used to identify Earth’s Magnetic North outdoors, but are often ignored during indoor experiments since the magnetic field does not behave how most expect. This paper presents methods to create, validate, and visualize three-dimensional magnetic field maps to expand the use of magnetic fields as a sensing modality for navigation. The utility of these maps is measured in their ability to accurately represent the magnetic field and to enable dynamic attitude estimation. In experiments with motion capture truth data, a small multicopter with three-axis inertial measurements, including magnetometer, traversed five flight profiles distinctly exciting roll, pitch, and yaw motion to provide interesting trajectories for attitude estimation. Indoor experimental results were compared to those outdoors to emphasize how spatial variation in the magnetic field drives the need for our mapping techniques. Our work presents a new way of visualizing 3D magnetic fields, which allows users to better reason about the magnetic field in their workspace. Next, we show that magnetic field maps generated from coverage patterns are generally more accurate, but training such maps using observations from desired flight paths is sufficient in the vicinity of these paths. All training sets were interpolated using Gaussian process regression (GPR), which yielded maps with <1 μT of error when interpolating between and extrapolating outside of observed locations. Finally, we validated the utility of our GPR-based maps in enabling attitude estimates in regions of high magnetic field spatial variation with experimental data.

OutFin, a multi-device and multi-modal dataset for outdoor localization based on the fingerprinting approach

In recent years, fingerprint-based positioning has gained researchers' attention since it is a promising alternative to the Global Navigation Satellite System and cellular network-based localization in urban areas. Despite this, the lack of publicly available datasets that researchers can use to develop, evaluate, and compare fingerprint-based positioning solutions constitutes a high entry barrier for studies. As an effort to overcome this barrier and foster new research efforts, this paper presents OutFin, a novel dataset of outdoor location fingerprints that were collected using two different smartphones. OutFin is comprised of diverse data types such as WiFi, Bluetooth, and cellular signal strengths, in addition to measurements from various sensors including the magnetometer, accelerometer, gyroscope, barometer, and ambient light sensor. The collection area spanned four dispersed sites with a total of 122 reference points. Each site is different in terms of its visibility to the Global Navigation Satellite System and reference points' number, arrangement, and spacing. Before OutFin was made available to the public, several experiments were conducted to validate its technical quality.

Smartphone Sensor Based Indoor Positioning: Current Status, Opportunities, and Future Challenges

The last two decades have witnessed a rich variety of indoor positioning and localization research. Starting with Microsoft Research pioneering the fingerprint approach based RADAR, MIT’s Cricket, and then moving towards beacon-based localization are few among many others. In parallel, researchers looked into other appealing and promising technologies like radio frequency identification, ultra-wideband, infrared, and visible light-based systems. However, the proliferation of smartphones over the past few years revolutionized and reshaped indoor localization towards new horizons. The deployment of MEMS sensors in modern smartphones have initiated new opportunities and challenges for the industry and academia alike. Additionally, the demands and potential of location-based services compelled the researchers to look into more robust, accurate, smartphone deployable, and context-aware location sensing. This study presents a comprehensive review of the approaches that make use of data from one or more sensors to estimate the user’s indoor location. By analyzing the approaches leveraged on smartphone sensors, it discusses the associated challenges of such approaches and points out the areas that need considerable research to overcome their limitations.

Magnetometer Calibration and Field Mapping through Thin Plate Splines

While the undisturbed Earth’s magnetic field represents a fundamental information source for orientation purposes, magnetic distortions have been mostly considered as a source of error. However, when distortions are temporally stable and spatially distinctive, they could provide a unique magnetic landscape that can be used in different applications, from indoor localization to sensor fusion algorithms for attitude estimation. The main purpose of this work, therefore, is to present a method to characterize the 3D magnetic vector in every point of the measurement volume. The possibility of describing the 3D magnetic field map through Thin Plate Splines (TPS) interpolation is investigated and demonstrated. An algorithm for the simultaneous estimation of the parameters related to magnetometer calibration and those describing the magnetic map, is proposed and tested on both simulated and real data. Results demonstrate that an accurate description of the local magnetic field using TPS interpolation is possible. The proposed procedure leads to errors in the estimation of the local magnetic direction with a standard deviation lower than 1 degree. Magnetometer calibration and magnetic field mapping could be integrated into different algorithms, for example to improve attitude estimation in highly distorted environments or as an aid to indoor localization.