106 research outputs found
TW-TOA based positioning in the presence of clock imperfections
This manuscript studies the positioning problem based on two-way time-of-arrival (TW-TOA) measurements in semi-asynchronous wireless sensor networks in which the clock of a target node is unsynchronized with the reference time. Since the optimal estimator for this problem involves difficult nonconvex optimization, two suboptimal estimators are proposed based on the squared-range least squares and the least absolute mean of residual errors. We formulated the former approach as an extended general trust region subproblem (EGTR) and propose a simple technique to solve it approximately. The latter approach is formulated as a difference of convex functions programming (DCP), which can be solved using a concaveâconvex procedure. Simulation results illustrate the high performance of the proposed techniques, especially for the DCP approach
TDOA based positioning in the presence of unknown clock skew
Cataloged from PDF version of article.This paper studies the positioning problem of a
single target node based on time-difference-of-arrival (TDOA)
measurements in the presence of clock imperfections. Employing
an affine model for the behaviour of a local clock, it is observed
that TDOA based approaches suffer from a parameter of the
model, called the clock skew. Modeling the clock skew as a
nuisance parameter, this paper investigates joint clock skew and
position estimation. The maximum likelihood estimator (MLE)
is derived for this problem, which is highly nonconvex and
difficult to solve. To avoid the difficulty in solving the MLE, we
employ suitable approximations and relaxations and propose two
suboptimal estimators based on semidefinite programming and
linear estimation. To further improve the estimation accuracy,
we also propose a refining step. In addition, the Cramer-Rao ÂŽ
lower bound (CRLB) is derived for this problem as a benchmark.
Simulation results show that the proposed suboptimal estimators
can attain the CRLB for sufficiently high signal-to-noise ratios
TDOA Based Positioning in the Presence of Unknown Clock Skew
This paper studies the positioning problem of a single target node based on time-difference-of-arrival (TDOA) measurements in the presence of clock imperfections. Employing an affine model for the behaviour of a local clock, it is observed that TDOA based approaches suffer from a parameter of the model, called the clock skew. Modeling the clock skew as a nuisance parameter, this paper investigates joint clock skew and position estimation. The maximum likelihood estimator (MLE) is derived for this problem, which is highly nonconvex and difficult to solve. To avoid the difficulty in solving the MLE, we employ suitable approximations and relaxations and propose two suboptimal estimators based on semidefinite programming and linear estimation. To further improve the estimation accuracy, we also propose a refining step. In addition, the CrameÌr-Rao lower bound (CRLB) is derived for this problem as a benchmark. Simulation results show that the proposed suboptimal estimators can attain the CRLB for sufficiently high signal-to-noise ratios
Analysis and Accuracy Improvement of UWB-TDoA-Based Indoor Positioning System
Positioning systems are used in a wide range of applications which require determining the position of an object in space, such as locating and tracking assets, people and goods; assisting navigation systems; and mapping. Indoor Positioning Systems (IPSs) are used where satellite and other outdoor positioning technologies lack precision or fail. Ultra-WideBand (UWB) technology is especially suitable for an IPS, as it operates under high data transfer rates over short distances and at low power densities, although signals tend to be disrupted by various objects. This paper presents a comprehensive study of the precision, failure, and accuracy of 2D IPSs based on UWB technology and a pseudo-range multilateration algorithm using Time Difference of Arrival (TDoA) signals. As a case study, the positioning of a 4Ă4m2 area, four anchors (transceivers), and one tag (receiver) are considered using bitcrazeâs Loco Positioning System. A CramĂ©râRao Lower Bound analysis identifies the convex hull of the anchors as the region with highest precision, taking into account the anisotropic radiation pattern of the anchorsâ antennas as opposed to ideal signal distributions, while bifurcation envelopes containing the anchors are defined to bound the regions in which the IPS is predicted to fail. This allows the formulation of a so-called flyable area, defined as the intersection between the convex hull and the region outside the bifurcation envelopes. Finally, the static bias is measured after applying a built-in Extended Kalman Filter (EKF) and mapped using a Radial Basis Function Network (RBFN). A debiasing filter is then developed to improve the accuracy. Findings and developments are experimentally validated, with the IPS observed to fail near the anchors, precision around ±3cm, and accuracy improved by about 15cm for static and 5cm for dynamic measurements, on average
Majorization-Minimization based Hybrid Localization Method for High Precision Localization in Wireless Sensor Networks
This paper investigates the hybrid source localization problem using the four
radio measurements - time of arrival (TOA), time difference of arrival (TDOA),
received signal strength (RSS) and angle of arrival (AOA). First, after
invoking tractable approximations in the RSS and AOA models, the maximum
likelihood estimation (MLE) problem for the hybrid TOA-TDOA-RSS-AOA data model
is derived. Then, in the MLE, which has the least-squares objective, weights
determined using the range-based characteristics of the four heterogeneous
measurements, are introduced. The resultant weighted least-squares problem
obtained, which is non-smooth and non-convex, is solved using the principle of
the majorization-minimization (MM), leading to an iterative algorithm that has
a guaranteed convergence. The key feature of the proposed method is that it
provides a unified framework where localization using any possible merger out
of these four measurements can be implemented as per the
requirement/application. Extensive numerical simulations are conducted to study
the estimation efficiency of the proposed method. The proposed method employing
all four measurements is compared against a conventionally used method and also
against the proposed method employing only limited combinations of the four
measurements. The results obtained indicate that the hybrid localization model
improves the localization accuracy compared to the heterogeneous measurements.
The integration of different measurements also yields good accuracy in the
presence of non-line of sight (NLOS) errors
Optimization methods for active and passive localization
Active and passive localization employing widely distributed sensors is a problem of interest in various fields. In active localization, such as in MIMO radar, transmitters emit signals that are reflected by the targets and collected by the receive sensors, whereas, in passive localization the sensors collect the signals emitted by the sources themselves. This dissertation studies optimization methods for high precision active and passive localization.
In the case of active localization, multiple transmit elements illuminate the targets from different directions. The signals emitted by the transmitters may differ in power and bandwidth. Such resources are often limited and distributed uniformly among the transmitters. However, previous studies based on the well known Cramer-Rao lower bound have shown that the localization accuracy depends on the locations of the transmitters as well as the individual channel gains between different transmitters, targets and receivers. Thus, it is natural to ask whether localization accuracy may be improved by judiciously allocating such limited resources among the transmitters. Using the CrÂŽamer-Rao lower bound for target localization of multiple targets as a figure of merit, approximate solutions are proposed to the problems of optimal power, optimal bandwidth and optimal joint power and bandwidth allocation. These solutions are computed by minimizing a sequence of convex problems. The quality of these solutions is assessed through extensive numerical simulations and with the help of a lower-bound that certifies their optimality. Simulation results reveal that bandwidth allocation policies have a stronger impact on performance than power.
Passive localization of radio frequency sources over multipath channels is a difficult problem arising in applications such as outdoor or indoor geolocation. Common approaches that combine ad-hoc methods for multipath mitigation with indirect localization relying on intermediary parameters such as time-of-arrivals, time difference of arrivals or received signal strengths, are unsatisfactory. This dissertation models the localization of known waveforms over unknown multipath channels in a sparse framework, and develops a direct approach in which multiple sources are localized jointly, directly from observations obtained at distributed sources. The proposed approach exploits channel properties that enable to distinguish line-of-sight (LOS) from non-LOS signal paths. Theoretical guarantees are established for correct recovery of the sourcesâ locations by atomic norm minimization. A second-order-cone-based algorithm is developed to produce the optimal atomic decomposition, and it is shown to produce high accuracy location estimates over complex scenes, in which sources are subject to diverse multipath conditions, including lack of LOS
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