Browsing by Subject "Cramér-Rao lower bound"
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Item Open Access Comparative theoretical analysis of distance estimation in visible light positioning systems(Institute of Electrical and Electronics Engineers Inc., 2016) Keskin, M. F.; Gezici, SinanIn this paper, theoretical limits and estimators are studied for synchronous and asynchronous visible light positioning (VLP) systems. Specifically, the Cramér-Rao lower bounds (CRLBs) and maximum likelihood estimators are investigated for distance estimation based on time-of-arrival (TOA) and/or received signal strength (RSS) parameters. Hybrid TOA/RSS-based distance estimation is proposed for VLP systems, and its CRLB is compared analytically against the CRLBs of TOA-based and RSS-based distance estimation. In addition, to investigate the effects of sampling, asymptotic performance results are obtained under sampling rate limitations as the noise variance converges to zero. A modified hybrid TOA/RSS-based distance estimator is proposed to provide performance improvements in the presence of sampling rate limitations. Numerical examples are presented to illustrate the theoretical results. © 2015 IEEE.Item Open Access Direct and two-step positioning in visible light systems(IEEE, 2018) Keskin, Musa Furkan; Gezici, Sinan; Arıkan, OrhanVisible light positioning (VLP) systems based on light emitting diodes can facilitate high accuracy localization services for indoor scenarios. In this paper, direct and two-step positioning approaches are investigated for both synchronous and asynchronous VLP systems. First, the Cramér-Rao lower bound (CRLB) and the direct positioning-based maximum likelihood estimator are derived for 3-D localization of a visible light communication receiver in a synchronous scenario by utilizing information from both time delay parameters and channel attenuation factors. Then, a two-step position estimator is designed for synchronous VLP systems by exploiting the asymptotic properties of time-of-arrival and received signal strength estimates. The proposed two-step estimator is shown to be asymptotically optimal, i.e., converges to the direct estimator at high signal-to-noise ratios. In addition, the CRLB and the direct and two-step estimators are obtained for positioning in asynchronous VLP systems. It is proved that the two-step position estimation is optimal in asynchronous VLP systems for practical pulse shapes. Various numerical examples are provided to illustrate the improved performance of the proposed estimators with respect to the current state-of-the-art and to investigate their robustness against model uncertainties in VLP systems.Item Open Access Direct positioning in synchronous and asynchronous visible light systems(IEEE, 2018) Keskin, Musa Furkan; Gezici, Sinan; Arıkan, OrhanIn this paper, direct positioning approaches are investigated for both synchronous and asynchronous visible light systems. First, the maximum likelihood estimator (MLE) and the Cramér-Rao lower bound (CRLB) are derived for the synchronous scenario by considering the information from both channel attenuation factors and time delay parameters. Then, asynchronous visible light positioning (VLP) systems are investigated and the corresponding CRLBs and MLEs are obtained based on received signal strength (RSS) information. It is shown that the direct and two-step position estimators are equivalent in the asynchronous scenario under mild conditions. Numerical examples are provided to illustrate the theoretical results.Item Open Access Distance and position estimation in visible light systems with RGB LEDs(Elsevier, 2022-01-17) Demirel, I.; Gezici, SinanIn this paper, distance and position estimation problems are investigated for visible light positioning (VLP) systems with red-green-blue (RGB) light emitting diodes (LEDs). The accuracy limits on distance and position estimation are calculated in terms of the Cramér-Rao lower bound (CRLB) for three different scenarios. Scenario 1 and Scenario 2 correspond to synchronous and asynchronous systems, respectively, with known channel attenuation formulas at the receiver. In Scenario 3, a synchronous system is considered but channel attenuation formulas are not known at the receiver. The derived CRLB expressions reveal the relations among distance/position estimation accuracies in the considered scenarios and lead to intuitive explanations for the benefits of using RGB LEDs. In addition, maximum likelihood (ML) estimators are derived in all scenarios, and it is shown that they can achieve close performance to the CRLBs in some cases for sufficiently high source optical powers. © 2022 Elsevier Inc.Item Open Access Enhancements to threshold based range estimation for ultra-wideband systems(IEEE, 2014-09) Soğancı, Hamza; Gezici, Sinan; Güldoğan, M. B.Ultra-wideband (UWB) signals have very high time resolution, which makes them a very good candidate for range estimation based wireless positioning. Although the accuracy is the major concern for range estimation, it is also important to have low-complexity algorithms that can be employed in real time. In this study, two low-complexity range estimation algorithms are proposed for UWB signals, which achieve improved performance compared to the state-of-the-art low-complexity ranging algorithms. The proposed algorithms are inspired from two well-known algorithms; 'serial backward search' (SBS) and 'jump back and search forward' (JBSF). Performances of the proposed algorithms are compared with those of the SBS and JBSF algorithms based on real measurements. In addition, theoretical bounds are calculated in order to quantify the statistical performance of the algorithms. © 2014 IEEE.Item Open Access Fundamental limits on localization in single input multiple output visible light systems(Bilkent University, 2017-09) Kökdoğan, FurkanVisible light systems have recently been considered as an e ective and promising solution for indoor positioning. In this thesis, a theoretical accuracy analysis is conducted for position estimation in visible light systems based on received signal strength (RSS) measurements. Considering a single light emitting diode (LED) at the transmitter and multiple photo-detectors (PDs) at the receiver, the Cram er-Rao lower bound (CRLB) is derived for both a generic three-dimensional scenario and speci c con gurations of the PDs at the receiver. For the special case in which the height of the receiver is known, a compact expression is derived for the CRLB, considering a uniform circular layout and the same elevation angle for all the PDs. Asymptotic analysis and accuracy of derived compact expression is investigated for this con guration of the system. In addition, the optimal placement of the PDs at the receiver is investigated by taking the e ects of the elevation angle parameter of the PDs into consideration. The optimal values are obtained theoretically and also veri ed by simulations. Numerical examples are presented to illustrate the impacts of system parameters on localization accuracy, namely radius of the uniform circular layout, elevation angle and number of PDs. Finally, theoretical limits are compared against the maximum likelihood estimator (MLE) as a benchmark to evaluate the performance of receiver position estimation.Item Open Access Jamming of Wireless Localization Systems(Institute of Electrical and Electronics Engineers Inc., 2016) Gezici, Sinan; Gholami, M. R.; Bayram, S.; Jansson M.In this paper, the optimal jamming of wireless localization systems is investigated. Two optimal power allocation schemes are proposed for jammer nodes in the presence of total and peak power constraints. In the first scheme, power is allocated to jammer nodes in order to maximize the average Cramér-Rao lower bound (CRLB) of target nodes, whereas in the second scheme, the power allocation is performed for the aim of maximizing the minimum CRLB of target nodes. Both the schemes are formulated as linear programs, and a closed-form solution is obtained for the first scheme. For the second scheme, under certain conditions, the property of full total power utilization is specified, and a closed-form solution is obtained when the total power is lower than a specific threshold. In addition, it is shown that non-zero power is allocated to at most NT jammer nodes according to the second scheme in the absence of peak power constraints, where NT is the number of target nodes. In the presence of parameter uncertainty, robust versions of the power allocation schemes are proposed. Simulation results are presented to investigate the performance of the proposed schemes and to illustrate the theoretical results. © 2016 IEEE.Item Open Access Optimal jammer placement in wireless localization networks(IEEE, 2015-06-07) Gezici, Sinan; Bayram, S.; Gholami, M. R.; Jansson, M.The optimal jammer placement problem is proposed for a wireless localization network, where the aim is to degrade the accuracy of locating target nodes as much as possible. In particular, the optimal location of a jammer node is obtained in order to maximize the minimum of the Cramér-Rao lower bounds for a number of target nodes under location related constraints for the jammer node. Theoretical results are derived to specify scenarios in which the jammer node should be located as close to a certain target node as possible, or the optimal location of the jammer node is determined by two or three of the target nodes. In addition, explicit expressions for the optimal location of the jammer node are derived in the presence of two target nodes. Numerical examples are presented to illustrate the theoretical results. © 2015 IEEE.Item Open Access Optimal jamming of wireless localization systems(IEEE, 2015-06) Gezici, Sinan; Gholami, M.R.; Bayram, S.; Jansson, M.In this study, optimal jamming of wireless localization systems is investigated. Two optimal power allocation schemes are proposed for jammer nodes in the presence of total and peak power constraints. In the first scheme, power is allocated to jammer nodes in order to maximize the average Cramér-Rao lower bound (CRLB) of target nodes whereas in the second scheme the power allocation is performed for the aim of maximizing the minimum CRLB of target nodes. Both schemes are formulated as linear programs, and a closed-form expression is obtained for the first scheme. Also, the full total power utilization property is specified for the second scheme. Simulation results are presented to investigate performance of the proposed schemes. © 2015 IEEE.Item Open Access Optimal power allocation for jammer nodes in wireless localization systems(Institute of Electrical and Electronics Engineers Inc., 2017) Bayram, S.; Keskin, M. F.; Gezici, Sinan; Arıkan, OrhanIn this paper, optimal power allocation strategies are investigated for jammer nodes in a wireless localization system. Building upon the concept of the restricted Bayesian approach, a generalized optimization strategy, called the restricted scheme, is proposed for power allocation of jammer nodes, and its theoretical properties are characterized. In the restricted scheme, the aim is to maximize the average Cramér-Rao lower bound (CRLB) of target nodes while keeping their minimum CRLB above a predefined level in the presence of average (total) and peak power constraints. It is proved that the average CRLB achieved by the restricted scheme is a strictly decreasing and concave function of the constraint on the minimum CRLB level. A closed-form solution is obtained for the restricted scheme when the tradeoff parameter and the total power limit are below certain thresholds. In addition, it is shown that the optimal solution of the restricted scheme corresponds to the use of at most NT jammer nodes, where NT is the number of target nodes, and that the optimal solution of the minimum CRLB maximization scheme is determined by at most NJ target nodes, where NJ is the number of jammer nodes. Extensions of the restricted scheme and an alternative scheme that aims to maximize the number of disabled target nodes (whose CRLBs are above a preset level) are considered, and the corresponding optimal strategies for jammer power allocation are identified. Numerical examples are provided to verify the theoretical derivations for various network configurations.Item Open Access Power adaptation for vector parameter estimation according to Fisher information based optimality criteria(Elsevier BV, 2022-03) Gürgünoğlu, Doğa; Dülek, Berkan; Gezici, SinanThe optimal power adaptation problem is investigated for vector parameter estimation according to various Fisher information based optimality criteria. By considering an observation model that involves a linear transformation of the parameter vector and an additive noise component with an arbitrary probability distribution, six different optimal power allocation problems are formulated based on Fisher information based objective functions. Via optimization theoretic approaches, various closed-form solutions are derived for the proposed problems. Also, the results are extended to cases in which nuisance parameters exist in the system model or certain types of nonlinear transformations are applied on the parameter vector. Numerical examples are presented to investigate performance of the proposed power allocation strategies.Item Open Access Theoretical limits on localization in single input multiple output (SIMO) visible light systems(Elsevier, 2018) Kökdoğan,Furkan; Erdem, Osman; Gezici, SinanIn this work, a theoretical accuracy analysis is conducted for position estimation in visible light systems based on received signal strength (RSS) measurements. Considering a single light emitting diode (LED) at the transmitter and multiple photo-detectors (PDs) at the receiver, the Cramér-Rao lower bound (CRLB) is derived for both a generic three-dimensional scenario and specific configurations of the PDs at the receiver. For the special case in which the height of the receiver is known, a compact expression is derived for the CRLB, considering a uniform circular layout and the same elevation angle for all the PDs. In addition, the optimal placement of the PDs at the receiver is investigated by taking the effects of the elevation angle parameter of the PDs into consideration. The optimal values are obtained theoretically and also verified by simulations. Numerical examples are provided to illustrate the impacts of various system parameters on localization accuracy and to compare the theoretical limits against the maximum likelihood estimator (MLE) for the receiver position.