Abstract-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 Cramér-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.Index Terms-Node localization, range measurements, semi-definite programming, sensor networks.

Abstract-For a positioning system with sensors, a maximum of ( 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 ( 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 Cramér-Rao lower bound for TDOA-based positioning is produced in closed-form, which will be useful for optimum sensor array design.

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Abstract-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 Cramér-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.

Abstract-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 Cramér-Rao lower bound for different frequencies, observation lengths, and signal-to-noise ratios.

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A common technique for source localization is to utilize the time-of-arrival (TOA) measurements between the source and several spatially separated sensors. The TOA information defines a set of circular equations from which the source position can be calculated with the knowledge of the sensor positions. Apart from nonlinear optimization, least squares calibration (LSC) and linear least squares (LLS) are two computationally simple positioning alternatives which reorganize the circular equations into a unique and non-unique set of linear equations, respectively. As the LSC and LLS algorithms employ standard least squares (LS), an obvious improvement is to utilize weighted LS estimation. In this paper, it is proved that the best linear unbiased estimator (BLUE) version of the LLS algorithm will give identical estimation performance as long as the linear equations correspond to the independent set. The equivalence of the BLUE-LLS approach and the BLUE variant of the LSC method is analyzed. Simulation results are also included to show the comparative performance of the BLUE-LSC, BLUE-LLS, LSC, LLS and constrained weighted LSC methods with Cramér-Rao lower bound.

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