Terms Of Localization Error Research Articles

Swarm Intelligence Based Location Estimation for Wireless Sensor Network

Object tracking is a noteworthy application in the field of wireless sensor networks that has attracted major Research attention recently. Most object tracking schemes uses prediction scheme to minimize the energy consumption and to maintain low missing rate in a sensor network. However objects need to be localize, when object was found missing during tracking process. In this article, we proposed a swarm intelligence mechanism, such as particle swarm optimization (PSO) to accurately estimate the location of the missing object, using updated object position and velocity and the extensive simulations are also shown to demonstrate the effectiveness of the proposed algorithm against the centroid and weighted centroid methods to evaluate its performance in terms of localization error.

Binary Particle Swarm Optimization (BPSO) Algorithm for Distributed Node Localization

In this paper, we propose a binary particle swarm optimization (BPSO) algorithm for distributed node localization in wireless sensor networks (WSNs). Each unknown node performs localization under the distance measurement from three or more neighboring anchors. The node that gets localized will be used as a reference for remaining nodes. A comparison of the performances of PSO and BPSO in terms of localization error and computation time is presented using simulations in Matlab.

Reduction of the Regularization Error of the Method of Regularized Stokeslets for a Rigid Object Immersed in a Three-Dimensional Stokes Flow

AbstractWe focus on the problem of evaluating the velocity field outside a solid object moving in an incompressible Stokes flow using the boundary integral formulation. For points near the boundary, the integral is nearly singular, and accurate computation of the velocity is not routine. One way to overcome this problem is to regularize the integral kernel. The method of regularized Stokeslet (MRS) is a systematic way to regularize the kernel in this situation. For a specific blob function which is widely used, the error of the MRS is only of first order with respect to the blob parameter. We prove that this is the case for radial blob functions with decay propertyϕ(r)=O(r−3−α) whenr→∞ for some constantα>1. We then find a class of blob functions for which the leading local error term can be removed to get second and third order errors with respect to blob parameter. Since the addition of these terms might give a flow field that is not divergence free, we introduce a modification of these terms to make the divergence of the corrected flow field close to zero while keeping the desired accuracy. Furthermore, these dominant terms are explicitly expressed in terms of blob function and so the computation time is negligible.

Efficient and accurate sensor network localization

Wireless sensor networks (WSN) have great potential in ubiquitous computing. However, the severe resource constraints of WSN rule out the use of many existing networking protocols and require careful design of systems that prioritizes energy conservation over performance optimization. A key infrastructural problem in WSN is localization--the problem of determining the geographical locations of nodes. WSN typically have some nodes called seeds that know their locations using global positioning systems or other means. Non-seed nodes compute their locations by exchanging messages with nodes within their radio range. Several algorithms have been proposed for localization in different scenarios. Algorithms have been designed for networks in which each node has ranging capabilities, i.e., can estimate distances to its neighbours. Other algorithms have been proposed for networks in which no node has such capabilities. Some algorithms only work when nodes are static. Some other algorithms are designed specifically for networks in which all nodes are mobile. We propose a very general, fully distributed localization algorithm called range-based Monte Carlo boxed (RMCB) for WSN. RMCB allows nodes to be static or mobile and that can work with nodes that can perform ranging as well as with nodes that lack ranging capabilities. RMCB uses a small fraction of seeds. It makes use of the received signal strength measurements that are available from the sensor hardware. We use RMCB to investigate the question: "When does range-based localization work better than range-free localization?" We demonstrate using empirical signal strength data from sensor hardware (Texas Instruments EZ430-RF2500) and simulations that RMCB outperforms a very good range-free algorithm called weighted Monte Carlo localization (WMCL) in terms of localization error in a number of scenarios and has a similar computational complexity to WMCL. We also implement WMCL and RMCB on sensor hardware and demonstrate that it outperforms WMCL. The performance of RMCB depends critically on the quality of range estimation. We describe the limitations of our range estimation approach and provide guidelines on when range-based localization is preferable.

A modified sectoral sweeper-based localization estimation and its implementation in a multi-hop wireless sensor networking environment by using OPNET

In wireless sensor networks, location awareness along with the sensed data is important for most of the applications. Although there are many localization techniques in the literature, some of these techniques involve tiny sensor nodes, which need to be computationally powerful and complex in hardware to estimate their locations. This paper proposes a modified sectoral sweeper-based localization estimation (M-SSLE) method, which is the improved version of our previously studied SSLE method, to achieve position information of sensor nodes. This technique requires only a central node having a smart antenna capability to estimate locations of sensor nodes and simplified message formats. Using the SSLE technique, the computational burden for location estimation is carried out by a central node and no hardware or software modification to tiny sensor devices is required. The M-SSLE is implemented using an OPNET modeler for realistic fading channel conditions. The detailed implementation methodology in OPNET is presented in terms of node and process models. The performance of the M-SSLE method is evaluated through different network scenarios and channel parameters in terms of localization error, average throughput, and node energy consumption. Furthermore, its localization performance is compared with the SSLE and Cramér Rao Bound methods in the two different scenarios for the deployment of the sensor nodes. The M-SSLE average localization errors of 4.3 and 8.9 m are demonstrated under the log-distance and the log-normal shadowing channel conditions in a 250 m × 250 m area, respectively.

Time-Reversal UWB Positioning Beacon for Railway Application

This paper studies a new positioning beacon for railway transport using Ultra Wideband (UWB) radio and Time Reversal (TR) techniques. UWB radio has the potential to offer a good level of performance in terms of localization accuracy. Time Reversal channel pre-filtering facilitates signal detection and also helps increasing the received energy in the targeted area. In this paper, we evaluate the characteristics of TR technique in terms of temporal focusing. The theoretical and simulation results for Power Delay Profile, equivalent channel model and focusing gain of TR-UWB are given. We analyze the contribution of Time Reversal associated with UWB technology to enhance the localization resolution. The IEEE 802.15.3achannel models are used to evaluate the performance of this system. In terms of localization error, the theoretical and simulation results show that TR-UWB technique delivers improved performance over the UWB localization approach.

An efficient family of strongly A-stable Runge–Kutta collocation methods for stiff systems and DAEs. Part II: Convergence results

The convergence properties of a newly defined uniparametric family of collocation Runge–Kutta methods on non-stiff systems, stiff semi-linear problems and Differential-Algebraic Equations are analysed. For each s⩾3, the so-called family of SAFERK methods is based on interpolatory quadrature rules of order 2s−3, and they have the same number of implicit stages as the s-stage LobattoIIIA and (s−1)-stage RadauIIA methods. Since s-stage SAFERK methods possess the same algebraic order as the (s−1)-stage RadauIIA method, the corresponding principal terms of local error are compared, and it is shown that those SAFERK methods with positive weights and nodes located in the integration interval possess, in the l2-norm, a smaller principal term of local error. Moreover, it is proved that SAFERK methods are convergent when integrating relevant classes of stiff problems and Differential-Algebraic Equations. In particular, they possess a higher stiff order than the RadauIIA method of the same algebraic order, due to a higher stage order of the new methods. On the other hand, because of the strong A-stability, SAFERK methods can be competitive with LobattoIIIA methods, particularly for stiff problems on large time intervals.

Effcient and Accurate Range-based Sensor Network Localization

Localization is defined as the problem of determining the geographical locations of nodes in a wireless ad hoc or sensor network. Networks typically have some nodes (called seeds) that know their locations (using GPS or other means). Other (non-seed) nodes compute their locations by exchanging messages with nodes within their radio range.Several algorithms have been proposed for localization in different scenarios. Algorithms have been designed for networks in which each node has ranging capabilities (i.e., can estimate distances to its neighbors). Other algorithms have been proposed for networks in which no node has such capabilities. Some algorithms only work when nodes are static. Some other algorithms are designed specifically for networks in which all nodes are mobile. In this paper we propose a range-based localization algorithm RMCB for wireless sensor networks. Our algorithm uses a small fraction of seeds. It also makes use of the received signal strength measurements that are available from the sensor hardware. Our algorithm works well when nodes are static or mobile. We demonstrate using empirical data from sensor hardware (Texas Instruments EZ 430-RF2500) and simulations that RMCB outperforms a very good range-free algorithm WMCL in terms of localization error and has a similar computational complexity to WMCL.

Three-dimensional neuronal brain activity estimation using shrinking smooth weighted-minimum-norm focal underdetermined-system solver methods

A new nonparametric method, based on the smooth weighted-minimum-norm (WMN) focal underdetermined-system solver (FOCUSS), for electrical cerebral activity localization using electroencephalography measurements is proposed. This method iteratively adjusts the spatial sources by reducing the size of the lead-field and the weighting matrix. Thus, an enhancement of source localization is obtained, as well as a reduction of the computational complexity. The performance of the proposed method, in terms of localization errors, robustness, and computation time, is compared with the WMN-FOCUSS and nonshrinking smooth WMN-FOCUSS methods as well as with standard generalized inverse methods (unweighted minimum norm, WMN, and FOCUSS). Simulation results for single-source localization confirm the effectiveness and robustness of the proposed method with respect to the reconstruction accuracy of a simulated single dipole.

Scalable location estimation using smart antennas in wireless sensor networks

For Wireless Sensor Networks (WSNs), although many localization techniques have been proposed, development of effective localization techniques for sensor nodes, which do not require any hardware or computational burdens on them, continues to be a challenging task. Motivated by this need, this paper proposes a new location discovery scheme in WSNs so called Sectoral Sweeper based Location Estimation (SSLE). Sectoral Sweeper (SS) relies on integration of smart antenna processing capability only at a central node. By expanding the SS scheme, the key idea in the SSLE is to perform two dimensional (azimuth and range) sweeping process over a given sensor field with beamforming capable central node followed by range estimation and direction estimation algorithms. It does not require any hardware or computational load at tiny sensor nodes. Performance evaluation of the SSLE is given in terms of localization error, response message statistics, and complexity analysis for grid and randomly deployed sensor node scenarios under various sweeping conditions. The SSLE performance is also compared with the Centroid method. The advantage of the SSLE is that it is applicable to environments with hard-to-access sensor deployment scenarios and that desired localization accuracy can be obtained by properly adjusting sweeping parameters.

An range-free localization scheme for large scale underwater wireless sensor networks

In this paper, we study an area localization problem in large scale underwater wireless sensor networks (UWSNs). The limited bandwidth, the severely impaired channel and the cost of underwater equipment all make the underwater localization problem very challenging. Exact localization is very difficult for UWSNs in deep underwater environment. We propose a range free method based on mobile detachable elevator transceiver (DET) and 3D multi-power area localization scheme (3D-MALS) to address the challenging problem. In the proposed scheme, the ideas of 2D multi-power area localization scheme (2D-ALS) and utilizing DET are used to achieve the simplicity, location accuracy, scalability and low cost performances. The DET can rise and get down to broadcast its position. And it is assumed that all the underwater nodes underwater have pressure sensors and know their z coordinates. We evaluate the performances of 2D-ALS and our proposed 3D-MALS schemes under both ideal and non-ideal channel propagation conditions, in terms of localization error and localization ratio. The simulation results show that our proposed scheme is much more efficient than the 2D-ALS.

An electrode addressing protocol for imaging brain function with electrical impedance tomography using a 16-channel semi-parallel system

Electrical impedance tomography of brain function poses special problems because applied current is diverted by the resistive skull. In the past, image resolution was maximized with the use of an electrode addressing protocol with widely spaced drive electrode pairs and use of a multiplexer so that many electrode pairs could be flexibly addressed. The purpose of this study was to develop and test an electrode protocol for a 16-channel semi-parallel system which uses parallel recording channels with fixed wiring, the Kyung Hee University (KHU) Mk1. Ten protocols were tested, all addressing pairs of electrodes for recording or current drive, based on recording with a spiral, spiral with suboccipital electrodes (spiral s-o) and zig-zag configurations, and combinations of current injection from electrode pairs at 180°, 120° and 60°. These were compared by assessing the image reconstruction quality of five simulated perturbations in a homogenous model of the human head and of four epileptic foci in an anatomically realistic model in the presence of realistic noise, in terms of localization error, resolution, image distortion and sensitivity in the region of interest. The spiral s-o with current injection at 180°+ 120°+ 60° gave the best image quality and permitted reconstruction with a localization error of less than 10% of the head diameter. This encourages the view that it might be possible to obtain satisfactory images of focal abnormalities in the human brain with 16 scalp electrodes and improved instrumentation avoiding multiplexers on recording circuits.

Localization of Active Pathways in Peripheral Nerves: A Simulation Study

A methodology is investigated for determining the location of active pathways in a peripheral nerve using measurements from a multicontact cuff electrode. The problem is treated as an inverse problem of source localization and solved using the sLORETA algorithm, developed for the electroencephalogram/magnetoencephalogram source localization problem. Simulated measurements are generated corresponding to action potentials traveling along either one or three pathways in a rat sciatic nerve. The performance of the proposed methodology using these measurements is evaluated in terms of localization error, missed pathways, and spurious pathways. The source localization performance when assuming an idealized nerve anatomy is compared to that when the correct anatomy is known. The effect of a spatio-temporal constraint based on the nerve anatomy and electrophysiology is also investigated. The approach in its present form was not found to be sufficiently reliable for subfascicular localization in practice, due to mean localization errors in the 140-180 mum range, high numbers of spurious pathways, and low resolution. Nonetheless, the constraints were shown to produce a marked reduction in the number of spurious pathways. Conditions under which the source localization approach may be useful for peripheral nerves are discussed.

On the error in computing Lyapunov exponents by QR Methods

We consider the error introduced using QR methods to approximate Lyapunov exponents. We give a backward error statement for linear non-autonomous systems, and further discuss nonlinear autonomous problems. In particular, for linear systems we show that one approximates a ``nearby'' discontinuous problem where how nearby is measured in terms of local errors and a measure of non-normality. For nonlinear problems we use a type of shadowing result.

Slip locking in finite elements for composite beams with deformable shear connection

In this paper, the authors discuss problems that may occur in the finite element analysis of composite beams with deformable shear connection, where slip arises between beam components while contact is preserved. Effects of locking problems, comparable to the membrane and shear locking that may develop in finite elements for common beams, are illustrated. These locking problems mostly affect the description of the curvature and interface slip. A strategy to avoid locking by means of a calibrated choice of the displacement shape functions is then proposed and a comparison between different displacement-based elements, in terms of local error, global error and convergence rate, is presented. The authors also illustrate the effects of slip locking on mixed finite elements and comparisons between displacement-based and mixed elements are shown.

Focused local learning with wavelet neural networks

A novel objective function is presented that incorporates both local and global errors as well as model parsimony in the construction of wavelet neural networks. Two methods are presented to assist in the minimization of this objective function, especially the local error term. First, during network initialization, a locally adaptive grid is utilized to include candidate wavelet basis functions whose local support addresses the local error of the local feature set. This set can be either user-defined or determined using information derived from the wavelet transform modulus maxima representation. Next, during the network construction, a new selection procedure based on a subspace projection operator is presented to help focus the selection of wavelet basis functions to reduce the local error. Simulation results demonstrate the effectiveness of these methodologies in minimizing local and global error while maintaining model parsimony and incurring a minimal increase on computational complexity.

On the error and its control in a two-parameter generalised Newton-Cotes rule

A quadrature formula containing two free (phase) parameters k, k′, and recently written by Van Daele et al. [13], is rederived using an extension of Lagrange's identity. By using this method, a closed-form expression is determined for the local error term E[ f] and the relevant Peano kernel is given explicitly. Sufficient conditions are established, under which this kernel remains definite, thus allowing a particularly simple expression to be deduced for E[ f] which reduces to the classical result for Boole's rule in the limit k, k′ → 0. Recent work on optimisation of global error is extended to include the new rule. It is shown that this error can be reduced by a factor O( h 2) on a certain curve in the phase space. A further reduction by a factor O( h 2) is sometimes possible by choosing the phase parameters on the intersection of this curve and another such. When these curves intersect only at complex values, the reduction is still achieved. A closed-form expression for the global error is also derived under these circumstances and this is seen to be asymptotically O( h 10) as h → 0. A second limiting form of the five-point formula is found to reduce to the generalised Boole's rule written by Vanden Berghe et al. [14] and a third limiting form is also written. This third rule, which is a special case of a one-parameter family of generalised Boole's rules, is seen to perform better than the other two in the two examples studied. Several numerical examples are given, with extensive diagrams, to illustrate all uses of the techniques proposed.

Numerical Integration of the Differential Riccati Equation and Some Related Issues

Abstract. In this paper the problem of direct numerical integration of differential Riccati equations (DREs) and some related issues are considered. The DRE is an expression of a particular change of variables for a linear system of ordinary differential equations. The error that an approximate solution of the DRE induces on the original variables of the system is considered, and it is related to geometrical properties of the system itself. Sharp bounds on the global error for the computed solution are also given in terms of local errors and geometrical properties of the original system. Nonstiff and stiff DREs of unsymmetric and symmetric type are considered. A useful matrix interpretation is given for many integration schemes (such as the backward differentiation formulas, BDF), when applied to the DRE. This allows the matrix structure of the problem to be exploited. In particular, for stiff DREs, the resulting strategy allows for a saving of three orders of magnitude with respect to the standard reform...

Accurate computation of higher Sturm-Liouville eigenvalues

The computation of eigenvalues of regular Sturm-Liouville problems is considered. It is shown that a simple step-dependent linear multistep method can be used to reduce the error of the orderk 4 h 2 of the centered finite difference estimate of thek-th eigenvalue with uniform step lengthh, to an error of orderkh 2. By an appropriate minimization of the local error term of the method one can obtain even more accurate results. A comparison of the simple correction techniques of Paine, de Hoog and Anderssen and of Andrew and Paine is given. Numerical examples demonstrate the usefulness of this correction even for low values ofk.

A modified numerov method for higher sturm-liouville eigenvalues

The computation of eigenvalues of regular Sturm-Liouville problems is considered. It is shown that a modified Numerov method can be used to reduce the error of the order k 6 h 4 of the classical Numerov method of the kth eigenvalue with uniform step length h, to an error of order k 3 h 4 . By an appropriate minimization of the local error term of the method one can obtain even more accurate results. A comparison of the simple correction techniques of Andrew and Paine to Numerov's method is given. Numerical examples demonstrate the usefulness of the present approach even for low values of k.