On weighted structured total least squares

In this contribution we extend the result of (Markovsky et. al, SIAM J. of Matrix Anal. and Appl., 2005) to the case of weighted cost function. It is shown that the computational complexity of the proposed algorithm is preserved linear in the sample size when the weight matrix is banded with bandwidth that is independent of the sample size

Approximate low-rank factorization with structured factors

An approximate rank revealing factorization problem with structure constraints on the normalized factors is considered. Examples of structure, motivated by an application in microarray data analysis, are sparsity, nonnegativity, periodicity, and smoothness. In general, the approximate rank revealing factorization problem is nonconvex. An alternating projections algorithm is developed, which is globally convergent to a locally optimal solution. Although the algorithm is developed for a specific application in microarray data analysis, the approach is applicable to other types of structure

RSSI-Based Self-Localization with Perturbed Anchor Positions

We consider the problem of self-localization by a resource-constrained mobile node given perturbed anchor position information and distance estimates from the anchor nodes. We consider normally-distributed noise in anchor position information. The distance estimates are based on the log-normal shadowing path-loss model for the RSSI measurements. The available solutions to this problem are based on complex and iterative optimization techniques such as semidefinite programming or second-order cone programming, which are not suitable for resource-constrained environments. In this paper, we propose a closed-form weighted least-squares solution. We calculate the weights by taking into account the statistical properties of the perturbations in both RSSI and anchor position information. We also estimate the bias of the proposed solution and subtract it from the proposed solution. We evaluate the performance of the proposed algorithm considering a set of arbitrary network topologies in comparison to an existing algorithm that is based on a similar approach but only accounts for perturbations in the RSSI measurements. We also compare the results with the corresponding Cramer-Rao lower bound. Our experimental evaluation shows that the proposed algorithm can substantially improve the localization performance in terms of both root mean square error and bias.Comment: Accepted for publication in 28th Annual IEEE International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE PIMRC 2017

An adapted version of the element-wise weighted total least squares method for applications in chemometrics

The Maximum Likelihood PCA (MLPCA) method has been devised in chemometrics as a generalization of the well-known PCA method in order to derive consistent estimators in the presence of errors with known error distribution. For similar reasons, the Total Least Squares (TLS) method has been generalized in the field of computational mathematics and engineering to maintain consistency of the parameter estimates in linear models with measurement errors of known distribution. In a previous paper [M. Schuermans, I. Markovsky, P.D. Wentzell, S. Van Huffel, On the equivalance between total least squares and maximum likelihood PCA, Anal. Chim. Acta, 544 (2005), 254–267], the tight equivalences between MLPCA and Element-wise Weighted TLS (EW-TLS) have been explored. The purpose of this paper is to adapt the EW-TLS method in order to make it useful for problems in chemometrics. We will present a computationally efficient algorithm and compare this algorithm with the standard EW-TLS algorithm and the MLPCA algorithm in computation time and convergence behaviour on chemical data

Approximating the Row-Wise Total Least Squares Linear Regression Solution

Motivated by applications as a kernel of nonlinear regression algorithms, the row-wise weighted total least squares regression problem is examined to find a consistent and accurate estimator. Specifically, the estimator will have a time complexity linear in the number of observations and a space complexity constant in the same value, as the number of observations can be quite large in many modern applications, often many orders of magnitude larger than the number of input and output features. Further, to accommodate large data sets, an algorithm is sought to update an intermediate representation from each observation, allowing for parallelization of the necessary computation. The proposed method is based on approximating the noncentral second moment of the underlying data by a precision-weighted mean, requiring only linear time in the number of observations. Initial findings show the proposed algorithm to be less accurate than existing methods intended to solve other variants of the Total Least Squares problem. Directions for continued iteration and further investigation are proposed as next steps in developing a better algorithm

RSS-based sensor localization with unknown transmit power

Received signal strength (RSS)-based single source localization when there is not a prior knowledge about the transmit power of the source is investigated. Because of nonconvex behavior of maximum likelihood (ML) estimator, convoluted computations are required to achieve its global minimum. Therefore, we propose a novel semidefinite programming (SDP) approach by approximating ML problem to a convex optimization problem which can be solved very efficiently. Computer simulations show that our proposed SDP has a remarkable performance very close to ML estimator. Linearizing RSS model, we also derive the partly novel least squares (LS) and weighted total least squares (WTLS) algorithms for this problem. Simulations illustrate that WTLS improves the performance of LS considerably

Bearing-only target localization with uncertainties in observer position

In this paper, the bearing-only target localization problem when the observer positions are subject to error is investigated. In this problem, the angle of arrival of the transmitted signal between target and observer are used to estimate the target position. It is assumed that not only the bearing measurements are corrupted by noise but also the exact position of observer is not available to the estimator. The accuracy of estimated location of target depends on the reliability of information from the observer position. Therefore, the previously published algorithms considering only the bearing measurement noise do not meet the expected performance when the observer positions are subject to error. The maximum likelihood, the least squares and total least square algorithms and a new method of localization based on weighted total least squares approach are developed for this problem. The corresponding Cram´er-Rao lower bound (CRLB) is derived for this problem. Computer simulations are performed to evaluate the performance of the proposed algorithms. Simulation results show that the new method can attain the CRLB for sufficiently high SNR