Bayesian Cramér-Rao Lower Bound for Magnetic Field-Based Localization

In this paper, we show how to analyze the achievable position accuracy of magnetic localization based on Bayesian Cramér-Rao lower bounds and how to account for deterministic inputs in the bound. The derivation of the bound requires an analytical model, e.g., a map or database, that links the position that is to be estimated to the corresponding magnetic field value. Unfortunately, finding an analytical model from the laws of physics is not feasible due to the complexity of the involved differential equations and the required knowledge about the environment. In this paper, we therefore use a Gaussian process (GP) that approximates the true analytical model based on training data. The GP ensures a smooth, differentiable likelihood and allows a strict Bayesian treatment of the estimation problem. Based on a novel set of measurements recorded in an indoor environment, the bound is evaluated for different sensor heights and is compared to the mean squared error of a particle filter. Furthermore, the bound is calculated for the case when only the magnetic magnitude is used for positioning and the case when the whole vector field is considered. For both cases, the resulting position bound is below 10cm indicating an high potential accuracy of magnetic localization

Cramér–Rao Lower Bound for Magnetic Field Localization around Elementary Structures

The determination of a mobile terminal’s position with high accuracy and ubiquitous coverage is still challenging. Global satellite navigation systems (GNSSs) provide sufficient accuracy in areas with a clear view to the sky. For GNSS-denied environments like indoors, complementary positioning technologies are required. A promising approach is to use the Earth’s magnetic field for positioning. In open areas, the Earth’s magnetic field is almost homogeneous, which makes it possible to determine the orientation of a mobile device using a compass. In more complex environments like indoors, ferromagnetic materials cause distortions of the Earth’s magnetic field. A compass usually fails in such areas. However, these magnetic distortions are location dependent and therefore can be used for positioning. In this paper, we investigate the influence of elementary structures, in particular a sphere and a cylinder, on the achievable accuracy of magnetic positioning methods. In a first step, we analytically calculate the magnetic field around a sphere and a cylinder in an outer homogeneous magnetic field. Assuming a noisy magnetic field sensor, we investigate the achievable positioning accuracy when observing these resulting fields. For our analysis, we calculate the Cramér–Rao lower bound, which is a fundamental lower bound on the variance of an unbiased estimator. The results of our investigations show the dependency of the positioning error variance on the magnetic sensor properties, in particular the sensor noise variance and the material properties, i.e., the relative permeability of the sphere with respect to the cylinder and the location of the sensor relative to the sphere with respect to the cylinder. The insights provided in this work make it possible to evaluate experimental results from a theoretical perspective

Bayesian Cramér-Rao Lower Bound for Magnetic Field-based Localization

In this paper, we show how to analyze the achievable position accuracy of magnetic localization based on Bayesian Cramér-Rao lower bounds and how to account for deterministic inputs in the bound. The derivation of the bound requires an analytical model, e.g., a map or database, that links the position that is to be estimated to the corresponding magnetic field value. Unfortunately, finding an analytical model from the laws of physics is not feasible due to the complexity of the involved differential equations and the required knowledge about the environment. In this paper, we therefore use a Gaussian process (GP) that approximates the true analytical model based on training data. The GP ensures a smooth, differentiable likelihood and allows a strict Bayesian treatment of the estimation problem. Based on a novel set of measurements recorded in an indoor environment, the bound is evaluated for different sensor heights and is compared to the mean squared error of a particle filter. Furthermore, the bound is calculated for the case when only the magnetic magnitude is used for positioning and the case when the whole vector field is considered. For both cases, the resulting position bound is below 10 cm indicating an high potential accuracy of magnetic localization

Wide Band Propagation in Train-to-Train Scenarios - Measurement Campaign and First Results

Within the next decades the railway systems will change to fully autonomous high speed trains (HSTs). An increase in efficiency and safety and a reduction of costs would go hand in hand. Today’s centralized railway management system and established regulations can not cope with trains driving within the absolute braking distance as it would be necessary for electronic coupling or platooning maneuvers. Hence, to ensure safety and reliability, new applications and changes in the train control and management are necessary. Such changes demand new reliable control communication links between train-to-train (T2T) and future developments on train-to-ground (T2G). T2G will be covered by long term evolution-railway (LTE-R) which shall replace today’s global system for mobile communications-railway (GSM-R). The decentralized T2T communication is hardly investigated and no technology has been selected. This publication focuses on the wide band propagation for T2T scenarios and describes a extensive channel sounding measurement campaign with two HSTs. First results of T2T communication at high speed conditions in different environments are presented

Magnetic Train Localization: High-Speed and Tunnel, Experiment and Evaluation

Magnetic train localization uses the characteristic distortions of the Earth magnetic field from the railway tracks. The magnetic train localization is able to identify the correct track and can solve an along-track location on the tracks. In contrast to GNSS, the magnetic train localization works in tunnels. In order to prove the practicality of the magnetic train localization method, a comprehensive train experiment has been conducted. Therefore, a high-speed train has been equipped with 28 magnetic and reference sensors such as wheel odometer, GNSS and inertial sensors. Measurements have been recorded in urban, high-speed and tunnel scenarios over 2200 km in eight measurement days. This paper describes briefly the measurement setup, the research questions, the experiment scenarios, the evaluation method and first results and findings

Measurement Methods for Train Localization with Onboard Sensors

Real-time train localization with onboard mounted sensors is a basis for future railway applications. In contrast to infrastructure based train localization with way-side sensors, the onboard train localization uses only train-side sensors and a digital map of the railway tracks. Therefore, the trains are equipped with sensors, e.g. near the train-front and near the train-end. The train-front location and the train-end location are determined on the tracks in track coordinates with absolute train localization methods. A distance on tracks between two locations is determined with relative localization methods. This distance on the tracks can be used to monitor the train length and also to observe the distance between trains. This paper contains an overview of different measurement methods for speed measurement, absolute train localization and relative train localization based on GNSS (Global Navigation Satellite System), IMU (Inertial Measurement Unit), magnetometers and RF (radio frequency) ranging

Bayesian multipath-enhanced device-free localization: Simulation- and measurement-based evaluation

Device-free localisation (DFL) systems infer presence and location of moving users by measuring to which extent they change the received signal power in wireless links. Consequently, users not only induce perturbations to the power of the line of sight but also to the power of reflected and scattered signals which are observed in the received signal as multipath components (MPCs). Since the propagation paths of MPCs differ inherently from the line-of-sight path, these propagation paths can be considered as additional network links. This extended network determines the multipath-enhanced device-free localisation (MDFL) system. Based on empirical models that relate perturbations in the received power of MPCs to the user location, the localisation problem can be solved by non-linear Bayesian filtering. In this work, we investigate the point mass filter and the particle filter as possible solutions. We demonstrate the applicability of these solutions using ultra-wideband measurements and develop and verify a numerical simulation framework that flexibly enables a sound evaluation of MDFL. Based on both measurements and simulations, we show a significant improvement of the localisation performance of MDFL compared to DFL. The overall localisation performance is thereby comparable for both filters. Eventually, we show that complexity and divergence probability, rather than localisation performance, are the decisive factors for the choice of the filter solution