Robust Localization Using Range Measurements With Unknown and Bounded Errors

Cooperative geolocation has attracted significant research interests in recent years. A large number of localization algorithms rely on the availability of statistical knowledge of measurement errors, which is often difficult to obtain in practice. Compared with the statistical knowledge of measurement errors, it can often be easier to obtain the measurement error bound. This paper investigates a localization problem assuming unknown measurement error distribution except for a bound on the error. We first formulate this localization problem as an optimization problem to minimize the worst case estimation error, which is shown to be a nonconvex optimization problem. Then, relaxation is applied to transform it into a convex one. Furthermore, we propose a distributed algorithm to solve the problem, which will converge in a few iterations. Simulation results show that the proposed algorithms are more robust to large measurement errors than existing algorithms in the literature. Geometrical analysis providing additional insights is also provided.This work was supported in part by 973 Program under Grant 2015CB352503, in part by National Program for Special Support of Top-Notch Young Professionals, in part by NSFC under Grant 61371159, in part by the Fundamental Research Funds for the Central Universities (2017XZZX009-01), in part by scholarship funded by China Scholarship Council, in part by National ICT Australia Ltd., and in part by the Australian Research Council under Grant DP-110100538, Grant DP-130103610 and Grant DP16010450

Robust Localization from Incomplete Local Information

We consider the problem of localizing wireless devices in an ad-hoc network embedded in a d-dimensional Euclidean space. Obtaining a good estimation of where wireless devices are located is crucial in wireless network applications including environment monitoring, geographic routing and topology control. When the positions of the devices are unknown and only local distance information is given, we need to infer the positions from these local distance measurements. This problem is particularly challenging when we only have access to measurements that have limited accuracy and are incomplete. We consider the extreme case of this limitation on the available information, namely only the connectivity information is available, i.e., we only know whether a pair of nodes is within a fixed detection range of each other or not, and no information is known about how far apart they are. Further, to account for detection failures, we assume that even if a pair of devices is within the detection range, it fails to detect the presence of one another with some probability and this probability of failure depends on how far apart those devices are. Given this limited information, we investigate the performance of a centralized positioning algorithm MDS-MAP introduced by Shang et al., and a distributed positioning algorithm, introduced by Savarese et al., called HOP-TERRAIN. In particular, for a network consisting of n devices positioned randomly, we provide a bound on the resulting error for both algorithms. We show that the error is bounded, decreasing at a rate that is proportional to R/Rc, where Rc is the critical detection range when the resulting random network starts to be connected, and R is the detection range of each device.Comment: 40 pages, 13 figure

Power Optimization for Network Localization

Reliable and accurate localization of mobile objects is essential for many applications in wireless networks. In range-based localization, the position of the object can be inferred using the distance measurements from wireless signals exchanged with active objects or reflected by passive ones. Power allocation for ranging signals is important since it affects not only network lifetime and throughput but also localization accuracy. In this paper, we establish a unifying optimization framework for power allocation in both active and passive localization networks. In particular, we first determine the functional properties of the localization accuracy metric, which enable us to transform the power allocation problems into second-order cone programs (SOCPs). We then propose the robust counterparts of the problems in the presence of parameter uncertainty and develop asymptotically optimal and efficient near-optimal SOCP-based algorithms. Our simulation results validate the efficiency and robustness of the proposed algorithms.Comment: 15 pages, 7 figure

A Survey on Multisensor Fusion and Consensus Filtering for Sensor Networks

Multisensor fusion and consensus filtering are two fascinating subjects in the research of sensor networks. In this survey, we will cover both classic results and recent advances developed in these two topics. First, we recall some important results in the development ofmultisensor fusion technology. Particularly, we pay great attention to the fusion with unknown correlations, which ubiquitously exist in most of distributed filtering problems. Next, we give a systematic review on several widely used consensus filtering approaches. Furthermore, some latest progress on multisensor fusion and consensus filtering is also presented. Finally, conclusions are drawn and several potential future research directions are outlined.the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61329301, 61374039, 61304010, 11301118, and 61573246, the Hujiang Foundation of China under Grants C14002 and D15009, the Alexander von Humboldt Foundation of Germany, and the Innovation Fund Project for Graduate Student of Shanghai under Grant JWCXSL140

Distributed estimation from relative measurements of heterogeneous and uncertain quality

This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes connected by an edge. In order to model heterogeneity and uncertainty of the measurements, we assume them to be affected by additive noise distributed according to a Gaussian mixture. In this original setup, we formulate the problem of computing the Maximum-Likelihood (ML) estimates and we design two novel algorithms, based on Least Squares regression and Expectation-Maximization (EM). The first algorithm (LS- EM) is centralized and performs the estimation from relative measurements, the soft classification of the measurements, and the estimation of the noise parameters. The second algorithm (Distributed LS-EM) is distributed and performs estimation and soft classification of the measurements, but requires the knowledge of the noise parameters. We provide rigorous proofs of convergence of both algorithms and we present numerical experiments to evaluate and compare their performance with classical solutions. The experiments show the robustness of the proposed methods against different kinds of noise and, for the Distributed LS-EM, against errors in the knowledge of noise parameters.Comment: Submitted to IEEE transaction

A New Approach to Linear/Nonlinear Distributed Fusion Estimation Problem

Disturbance noises are always bounded in a practical system, while fusion estimation is to best utilize multiple sensor data containing noises for the purpose of estimating a quantity--a parameter or process. However, few results are focused on the information fusion estimation problem under bounded noises. In this paper, we study the distributed fusion estimation problem for linear time-varying systems and nonlinear systems with bounded noises, where the addressed noises do not provide any statistical information, and are unknown but bounded. When considering linear time-varying fusion systems with bounded noises, a new local Kalman-like estimator is designed such that the square error of the estimator is bounded as time goes to $\infty$. A novel constructive method is proposed to find an upper bound of fusion estimation error, then a convex optimization problem on the design of an optimal weighting fusion criterion is established in terms of linear matrix inequalities, which can be solved by standard software packages. Furthermore, according to the design method of linear time-varying fusion systems, each local nonlinear estimator is derived for nonlinear systems with bounded noises by using Taylor series expansion, and a corresponding distributed fusion criterion is obtained by solving a convex optimization problem. Finally, target tracking system and localization of a mobile robot are given to show the advantages and effectiveness of the proposed methods.Comment: 9 pages, 3 figure