Frankie K. W. Chan

Semi-Definite Programming Algorithms for Sensor Network Node Localization With Uncertainties in Anchor Positions and/or Propagation Speed

Finding the positions of nodes in an ad hoc wireless sensor network (WSN) with the use of the incomplete and noisy distance measurements between nodes as well as anchor position information is currently an important and challenging research topic. However, most WSN localization studies have considered that the anchor positions and the signal propagation speed are perfectly known which is not a valid assumption in the underwater and underground scenarios. In this paper, semi-definite programming (SDP) algorithms are devised for node localization in the presence of these uncertainties. The corresponding Cramer-Rao lower bound (CRLB) is also produced. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional SDP method and CRLB.

Efficient Weighted Multidimensional Scaling for Wireless Sensor Network Localization

Localization of sensor nodes is a fundamental and important problem in wireless sensor networks. Although classical multidimensional scaling (MDS) is a computationally attractive positioning method, it is statistically inefficient and cannot be applied in partially-connected sensor networks. In this correspondence, a weighted MDS algorithm is devised to circumvent these limitations. It is proved that the estimation performance of the proposed algorithm can attain Cramer-Rao lower bound (CRLB) for sufficiently small noise conditions. Computer simulations are included to contrast the performance of the proposed algorithm with the classical MDS and distributed weighted MDS algorithms as well as CRLB.

A Generalized Subspace Approach for Mobile Positioning With Time-of-Arrival Measurements

The problem of locating mobile terminals has received considerable attention particularly in the field of wireless communications. In this correspondence, a simple subspace-based algorithm for mobile positioning with the use of time-of-arrival measurements deduced from signals received at three or more reference base stations is derived and analyzed. It is shown that the proposed approach is a generalization of the mobile localization method based on multidimensional similarity analysis. Computer simulations are included to contrast the estimator performance with Cramer-Rao lower bound.

Closed-Form Formulae for Time-Difference-of-Arrival Estimation

For a positioning system with L sensors, a maximum of L(L-1)/2 distinct time-difference-of-arrival (TDOA) measurements, which are referred to as the full TDOA set, can be obtained. In this paper, closed-form expressions regarding optimum conversion of the full TDOA set to the nonredundant TDOA set, which corresponds to (L-1) TDOA measurements with respect to a common reference receiver, in the case of white signal source and noise, are derived. The most interesting finding is that optimum conversion can be achieved via the standard least squares estimation procedure. Furthermore, the Cramer-Rao lower bound for TDOA-based positioning is produced in closed-form, which will be useful for optimum sensor array design.

A generalized weighted linear predictor frequency estimation approach for a complex sinusoid

Based on linear prediction and weighted least squares, three simple iterative algorithms for frequency estimation of a complex sinusoid in additive white noise are devised. The proposed approach, which utilizes the first-order as well as higher order linear prediction terms simultaneously but does not require phase unwrapping, can be considered as a generalized version of the weighted linear predictor frequency estimator. In particular, convergence as well as mean and variance analysis of the most computationally efficient frequency estimator, namely, GWLP 2, are provided. Computer simulations are included to contrast the performance of the proposed algorithms with several conventional computationally attractive frequency estimators and Crame/spl acute/r-Rao lower bound for different frequencies, observation lengths, and signal-to-noise ratios.

Accurate Distributed Range-Based Positioning Algorithm for Wireless Sensor Networks

Localization of sensor nodes is a fundamental and important problem in wireless sensor networks. In this correspondence, a recursive distributed positioning algorithm is devised with the use of range measurements. Computer simulations are included to contrast the performance of the proposed approach with the conventional semi-definite relaxation positioning method as well as Crameacuter-Rao lower bound.

Semidefinite Programming Approach for Range-Difference Based Source Localization

A common technique for passive source localization is to utilize the range-difference (RD) measurements between the source and several spatially separated sensors. The RD information defines a set of hyperbolic equations from which the source position can be calculated with the knowledge of the sensor positions. Under the standard assumption of Gaussian distributed RD measurement errors, it is well known that the maximum-likelihood (ML) position estimation is achieved by minimizing a multimodal cost function which corresponds to a difficult task. In this correspondence, we propose to approximate the nonconvex ML optimization by relaxing it to a convex optimization problem using semidefinite programming. A semidefinite relaxation RD-based positioning algorithm, which makes use of the admissible source position information, is proposed and its estimation performance is contrasted with the two-step weighted least squares method and nonlinear least squares estimator as well as Cramer-Rao lower bound.

A new constrained weighted least squares algorithm for TDOA-based localization

The linear least squares (LLS) technique is widely used in time-difference-of-arrival based positioning because of its computational efficiency. Two-step weighted least squares (2WLS) and constrained weighted least squares (CWLS) algorithms are two common LLS schemes where an additional variable is introduced to obtain linear equations. However, they both have the same measurement matrix that becomes ill-conditioned when the sensor geometry is a uniform circular array and the source is close to the array center. In this paper, a new CWLS estimator is proposed to circumvent this problem. The main strategy is to separate the source coordinates and the additional variable to different sides of the linear equations where the latter is first solved via a quadratic equation. In doing so, the matrix to be inverted has a smaller condition number than that of the conventional LLS approach. The performance of the proposed method is analyzed in the presence of zero-mean white Gaussian disturbances. Numerical examples are also included to evaluate its localization accuracy by comparing with the existing 2WLS and CWLS algorithms as well as the Cramer-Rao lower bound.

An Efficient Approach for Two-Dimensional Parameter Estimation of a Single-Tone

In this paper, parameter estimation of a two-dimensional (2-D) single damped real/complex tone in the presence of additive white Gaussian noise is addressed. By utilizing the rank-one property of the 2-D noise-free data matrix, the damping factor and frequency for each dimension are estimated in a separable manner from the principal left and right singular vectors according to an iterative weighted least squares procedure. The remaining parameters are then obtained straightforwardly using standard least squares. The biases as well as variances of the damping factor and frequency estimates are also derived, which show that they are approximately unbiased and their performance achieves Crame¿r-Rao lower bound (CRLB) at sufficiently large signal-to-noise ratio (SNR) and/or data size conditions. We refer the proposed approach to as principal-singular-vector utilization for modal analysis (PUMA) which performs estimation in a fast and accurate manner. The development and analysis can easily be adapted for a tone which is undamped in at least one dimension. Furthermore, comparative simulation results with several conventional 2-D estimators and CRLB are included to corroborate the theoretical development of the PUMA approach as well as to demonstrate its superiority.

A Novel Subspace Approach for Cooperative Localization in Wireless Sensor Networks Using Range Measurements

Estimating the positions of sensor nodes is a fundamental and crucial problem in wireless sensor networks. In this paper, three novel subspace methods for node localization in a fully connected network are devised with the use of range measurements. Biases and mean square errors of the sensor node position estimates are also derived. Computer simulations are included to contrast the performance of the proposed algorithms with the conventional subspace positioning method, namely, classical multidimensional scaling, as well as Cramer-Rao lower bound.