Distributed Cooperative Localization in Wireless Sensor Networks without NLOS Identification

In this paper, a 2-stage robust distributed algorithm is proposed for cooperative sensor network localization using time of arrival (TOA) data without identification of non-line of sight (NLOS) links. In the first stage, to overcome the effect of outliers, a convex relaxation of the Huber loss function is applied so that by using iterative optimization techniques, good estimates of the true sensor locations can be obtained. In the second stage, the original (non-relaxed) Huber cost function is further optimized to obtain refined location estimates based on those obtained in the first stage. In both stages, a simple gradient descent technique is used to carry out the optimization. Through simulations and real data analysis, it is shown that the proposed convex relaxation generally achieves a lower root mean squared error (RMSE) compared to other convex relaxation techniques in the literature. Also by doing the second stage, the position estimates are improved and we can achieve an RMSE close to that of the other distributed algorithms which know \textit{a priori} which links are in NLOS.Comment: Accepted in WPNC 201

Bounded perturbation resilience of projected scaled gradient methods

We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, the projected Landweber-type methods and the generalized Expectation-Maximization (EM)-type methods. We prove the convergence of the PSG methods in the presence of bounded perturbations. This resilience to bounded perturbations is relevant to the ability to apply the recently developed superiorization methodology to PSG methods, in particular to the EM algorithm.Comment: Computational Optimization and Applications, accepted for publicatio

Constrained least-squares digital image restoration

The design of a digital image restoration filter must address four concerns: the completeness of the underlying imaging system model, the validity of the restoration metric used to derive the filter, the computational efficiency of the algorithm for computing the filter values and the ability to apply the filter in the spatial domain. Consistent with these four concerns, this dissertation presents a constrained least-squares (CLS) restoration filter for digital image restoration. The CLS restoration filter is based on a comprehensive, continuous-input/discrete- processing/continuous-output (c/d/c) imaging system model that accounts for acquisition blur, spatial sampling, additive noise and imperfect image reconstruction. The c/d/c model-based CLS restoration filter can be applied rigorously and is easier to compute than the corresponding c/d/c model-based Wiener restoration filter. The CLS restoration filter can be efficiently implemented in the spatial domain as a small convolution kernel. Simulated restorations are used to illustrate the CLS filter\u27s performance for a range of imaging conditions. Restoration studies based, in part, on an actual Forward Looking Infrared (FLIR) imaging system, show that the CLS restoration filter can be used for effective range reduction. The CLS restoration filter is also successfully tested on blurred and noisy radiometric images of the earth\u27s outgoing radiation field from a satellite-borne scanning radiometer used by the National Aeronautics and Space Administration (NASA) for atmospheric research