Hing Cheung So

Least squares algorithms for time-of-arrival-based mobile location

Localization of mobile phones is of considerable interest in wireless communications. In this correspondence, two algorithms are developed for accurate mobile location using the time-of-arrival measurements of the signal from the mobile station received at three or more base stations. The first algorithm is an unconstrained least squares (LS) estimator that has implementation simplicity. The second algorithm solves a nonconvex constrained weighted least squares (CWLS) problem for improving estimation accuracy. It is shown that the CWLS estimator yields better performance than the LS method and achieves both the Crame/spl acute/r-Rao lower bound and the optimal circular error probability at sufficiently high signal-to-noise ratio conditions.

Time-of-arrival based localization under NLOS conditions

Three or more base stations (BS) making time-of-arrival measurements of a signal from a mobile station (MS) can locate the MS. However, when some of the measurements are from non-line-of-sight (NLOS) paths, the location errors can be very large. This paper proposes a residual test (RT) that can simultaneously determine the number of line-of-sight (LOS) BS and identify them. Then, localization can proceed with only those LOS BS. The RT works on the principle that when all measurements are LOS, the normalized residuals have a central Chi-Square distribution, versus a noncentral distribution when there is NLOS. The residuals are the squared differences between the estimates and the true position. Normalization by their variances gives a unity variance to the resultant random variables. In simulation studies, for the chosen geometry and NLOS and measurement noise errors, the RT can determine the correct number of LOS-BS over 90% of the time. For four or more BS, where there are at least three LOS-BS, the estimator has variances that are near the Cramer--Rao lower bound.

A constrained least squares approach to mobile positioning: algorithms and optimality

The problem of locating a mobile terminal has received significant attention in the field of wireless communications. Time-of-arrival (TOA), received signal strength (RSS), time-difference-of-arrival (TDOA), and angle-of-arrival (AOA) are commonly used measurements for estimating the position of the mobile station. In this paper, we present a constrained weighted least squares (CWLS) mobile positioning approach that encompasses all the above described measurement cases. The advantages of CWLS include performance optimality and capability of extension to hybrid measurement cases (e.g., mobile positioning using TDOA and AOA measurements jointly). Assuming zero-mean uncorrelated measurement errors, we show by mean and variance analysis that all the developed CWLS location estimators achieve zero bias and the Cramér-Rao lower bound approximately when measurement error variances are small. The asymptotic optimum performance is also confirmed by simulation results.

A multidimensional scaling framework for mobile location using time-of-arrival measurements

Localization of mobile phones is now a very popular research topic. A simple algorithm is devised for mobile location estimation using time-of-arrival measurements of the signal from the mobile station received at three or more base stations, via modifying the classical multidimensional scaling technique, which has been developed for analyzing data obtained from physical, biological, and behavioral science. The bias and variance of the proposed algorithm are also derived. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with several conventional approaches as well as the Crame/spl acute/r-Rao lower bound.

Fast communication: a fast algorithm for 2-D direction-of-arrival estimation

A computationally efficient method for two-dimensional direction-of-arrival estimation of multiple narrowband sources impinging on the far field of a planar array is presented. The key idea is to apply the propagator method which only requires linear operations but does not involve any eigendecomposition or singular value decomposition as in common subspace techniques such as MUSIC and ESPRIT. Comparing with a fast ESPRIT-based algorithm, it has a lower computational complexity particularly when the ratio of array size to the number of sources is large, at the expense of negligible performance loss. Simulation results are included to demonstrate the performance of the proposed technique.

Linear Least Squares Approach for Accurate Received Signal Strength Based Source Localization

A conventional approach for passive source localization is to utilize signal strength measurements of the emitted source received at an array of spatially separated sensors. The received signal strength (RSS) information can be converted to distance estimates for constructing a set of circular equations, from which the target position is determined. Nevertheless, a major challenge in this approach lies in the shadow fading effect which corresponds to multiplicative measurement errors. By utilizing the mean and variance of the squared distance estimates, we devise two linear least squares (LLS) estimators for RSS-based positioning in this paper. The first one is a best linear unbiased estimator while the second is its improved version by exploiting the known relation between the parameter estimates. The variances of the position estimates are derived and confirmed by computer simulations. In particular, it is proved that the performance of the improved LLS estimator achieves Cramer-Rao lower bound at sufficiently small noise conditions.

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.

Non-Line-of-Sight Node Localization Based on Semi-Definite Programming in Wireless Sensor Networks

An unknown-position sensor can be localized if there are three or more anchors making time-of-arrival (TOA) measurements of a signal from it. However, the location errors can be very large due to the fact that some of the measurements are from non-line-of-sight (NLOS) paths. In this paper, a semi-definite programming (SDP) based node localization algorithm in NLOS environments is proposed for ultra-wideband (UWB) wireless sensor networks. The positions of sensors can be estimated using the distance estimates from location-aware anchors as well as other sensors. However, in the absence of line-of-sight (LOS) paths, e.g., in indoor networks, the NLOS range estimates can be significantly biased. As a result, the NLOS error can remarkably decrease the location accuracy, and it is not easy to accurately distinguish LOS from NLOS measurements. According to the information known about the prior probabilities and distributions of the NLOS errors, three different cases are introduced and the respective localization problems are addressed. Simulation results demonstrate that this algorithm achieves high location accuracy even for the case in which NLOS and LOS measurements are not identifiable.

Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses

Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Crame/spl acute/r-Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions.

Accurate approximation algorithm for TOA-based maximum likelihood mobile location using semidefinite programming

The techniques of using wireless cellular networks to locate mobile stations have recently received considerable interest. The paper addresses the problem of maximum likelihood (ML) location estimation using (uplink) time-of-arrival (TOA) measurements. Under the standard assumption of Gaussian TOA measurement errors, ML location estimation is a nonconvex optimization problem in which the presence of local minima makes the search of the globally optimal solution hard. To circumvent this difficulty, we propose to approximate the ML problem by relaxing it to a convex optimization problem, namely semidefinite programming. Simulation results indicate that this semidefinite relaxation location estimator provides mean square position error performance close to the Cramer-Rao lower bound for a wide range of TOA measurement error levels.