292 research outputs found
A comprehensive analysis of the geometry of TDOA maps in localisation problems
In this manuscript we consider the well-established problem of TDOA-based
source localization and propose a comprehensive analysis of its solutions for
arbitrary sensor measurements and placements. More specifically, we define the
TDOA map from the physical space of source locations to the space of range
measurements (TDOAs), in the specific case of three receivers in 2D space. We
then study the identifiability of the model, giving a complete analytical
characterization of the image of this map and its invertibility. This analysis
has been conducted in a completely mathematical fashion, using many different
tools which make it valid for every sensor configuration. These results are the
first step towards the solution of more general problems involving, for
example, a larger number of sensors, uncertainty in their placement, or lack of
synchronization.Comment: 51 pages (3 appendices of 12 pages), 12 figure
Source localization and denoising: a perspective from the TDOA space
In this manuscript, we formulate the problem of denoising Time Differences of
Arrival (TDOAs) in the TDOA space, i.e. the Euclidean space spanned by TDOA
measurements. The method consists of pre-processing the TDOAs with the purpose
of reducing the measurement noise. The complete set of TDOAs (i.e., TDOAs
computed at all microphone pairs) is known to form a redundant set, which lies
on a linear subspace in the TDOA space. Noise, however, prevents TDOAs from
lying exactly on this subspace. We therefore show that TDOA denoising can be
seen as a projection operation that suppresses the component of the noise that
is orthogonal to that linear subspace. We then generalize the projection
operator also to the cases where the set of TDOAs is incomplete. We
analytically show that this operator improves the localization accuracy, and we
further confirm that via simulation.Comment: 25 pages, 9 figure
Emitter Location Finding using Particle Swarm Optimization
Using several spatially separated receivers, nowadays positioning techniques, which are implemented to determine the location of the transmitter, are often required for several important disciplines such as military, security, medical, and commercial applications. In this study, localization is carried out by particle swarm optimization using time difference of arrival. In order to increase the positioning accuracy, time difference of arrival averaging based two new methods are proposed. Results are compared with classical algorithms and Cramer-Rao lower bound which is the theoretical limit of the estimation error
RSSI-Based Self-Localization with Perturbed Anchor Positions
We consider the problem of self-localization by a resource-constrained mobile
node given perturbed anchor position information and distance estimates from
the anchor nodes. We consider normally-distributed noise in anchor position
information. The distance estimates are based on the log-normal shadowing
path-loss model for the RSSI measurements. The available solutions to this
problem are based on complex and iterative optimization techniques such as
semidefinite programming or second-order cone programming, which are not
suitable for resource-constrained environments. In this paper, we propose a
closed-form weighted least-squares solution. We calculate the weights by taking
into account the statistical properties of the perturbations in both RSSI and
anchor position information. We also estimate the bias of the proposed solution
and subtract it from the proposed solution. We evaluate the performance of the
proposed algorithm considering a set of arbitrary network topologies in
comparison to an existing algorithm that is based on a similar approach but
only accounts for perturbations in the RSSI measurements. We also compare the
results with the corresponding Cramer-Rao lower bound. Our experimental
evaluation shows that the proposed algorithm can substantially improve the
localization performance in terms of both root mean square error and bias.Comment: Accepted for publication in 28th Annual IEEE International Symposium
on Personal, Indoor and Mobile Radio Communications (IEEE PIMRC 2017
Geolocation of a Known Altitude Target Using TDOA and GROA in the Presence of Receiver Location Uncertainty
This paper considers the problem of geolocating a target on the Earth surface using the target signal time difference of arrival (TDOA) and gain ratio of arrival (GROA) measurements when the receiver positions are subject to random errors. The geolocation Cramer-Rao lower bound (CRLB) is derived and the performance improvement due to the use of target altitude information is quantified. An algebraic geolocation solution is developed and its approximate efficiency under small Gaussian noise is established analytically. Its sensitivity to the target altitude error is also studied. Simulations justify the validity of the theoretical developments and illustrate the good performance of the proposed geolocation method
Distributed localization of a RF target in NLOS environments
We propose a novel distributed expectation maximization (EM) method for
non-cooperative RF device localization using a wireless sensor network. We
consider the scenario where few or no sensors receive line-of-sight signals
from the target. In the case of non-line-of-sight signals, the signal path
consists of a single reflection between the transmitter and receiver. Each
sensor is able to measure the time difference of arrival of the target's signal
with respect to a reference sensor, as well as the angle of arrival of the
target's signal. We derive a distributed EM algorithm where each node makes use
of its local information to compute summary statistics, and then shares these
statistics with its neighbors to improve its estimate of the target
localization. Since all the measurements need not be centralized at a single
location, the spectrum usage can be significantly reduced. The distributed
algorithm also allows for increased robustness of the sensor network in the
case of node failures. We show that our distributed algorithm converges, and
simulation results suggest that our method achieves an accuracy close to the
centralized EM algorithm. We apply the distributed EM algorithm to a set of
experimental measurements with a network of four nodes, which confirm that the
algorithm is able to localize a RF target in a realistic non-line-of-sight
scenario.Comment: 30 pages, 11 figure
Localization using Distance Geometry : Minimal Solvers and Robust Methods for Sensor Network Self-Calibration
In this thesis, we focus on the problem of estimating receiver and sender node positions given some form of distance measurements between them. This kind of localization problem has several applications, e.g., global and indoor positioning, sensor network calibration, molecular conformations, data visualization, graph embedding, and robot kinematics. More concretely, this thesis makes contributions in three different areas.First, we present a method for simultaneously registering and merging maps. The merging problem occurs when multiple maps of an area have been constructed and need to be combined into a single representation. If there are no absolute references and the maps are in different coordinate systems, they also need to be registered. In the second part, we construct robust methods for sensor network self-calibration using both Time of Arrival (TOA) and Time Difference of Arrival (TDOA) measurements. One of the difficulties is that corrupt measurements, so-called outliers, are present and should be excluded from the model fitting. To achieve this, we use hypothesis-and-test frameworks together with minimal solvers, resulting in methods that are robust to noise, outliers, and missing data. Several new minimal solvers are introduced to accommodate a range of receiver and sender configurations in 2D and 3D space. These solvers are formulated as polynomial equation systems which are solvedusing methods from algebraic geometry.In the third part, we focus specifically on the problems of trilateration and multilateration, and we present a method that approximates the Maximum Likelihood (ML) estimator for different noise distributions. The proposed approach reduces to an eigendecomposition problem for which there are good solvers. This results in a method that is faster and more numerically stable than the state-of-the-art, while still being easy to implement. Furthermore, we present a robust trilateration method that incorporates a motion model. This enables the removal of outliers in the distance measurements at the same time as drift in the motion model is canceled
- …