Sum of Squares Method for Sensor Network Localization
英文摘要:
This paper has been withdrawn by the author due to its publication
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
Jiawang Nie
This paper has been withdrawn by the author due to its publication
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。
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We propose to solve large instances of the non-convex optimization problems reformulated with canonical duality theory. To this aim we propose an interior point potential reduction algorithm based on the solution of the primal-dual total complementarity (Lagrange) function. We establish the global convergence result for the algorithm under mild assumptions and demonstrate the method on instances of the Sensor Network Localization problem. Our numerical results are promising and show the possibility of devising efficient interior points methods for non-convex duality.
This manuscript is a preliminary pre-print version of a journal submission by the authors, revisiting the problem of range measurement based localization of a signal source or a sensor. The major geometric difficulty of the problem comes from the non-convex structure of optimization tasks associated with range measurements, noting that the set of source locations corresponding to a certain distance measurement by a fixed point sensor is non-convex both in two and three dimensions. Differently from various recent approaches to this localization problem, all starting with a non-convex geometric …
There are variety of methods to solve the localization problem and among them semi-definite programming based methods have shown great performance in both complexity and accuracy aspects. In this paper, we introduce a class of less noise-sensitive relaxation to reduce the complexity of SDP-based methods. We apply our relaxation to Edge-based Semi-Definite Programming (ESDP) method and the resulted model is called PESDP. Simulation results confirm that our proposed PESDP method is less noise-sensitive and faster compared to the original ESDP.
Many of the distributed localization algorithms are based on relaxed optimization formulations of the localization problem. These algorithms commonly rely on first-order optimization methods, and hence may require many iterations or communications among computational agents. Furthermore, some of these distributed algorithms put a considerable computational demand on the agents. In this paper, we show that for tree-structured scattered sensor networks, which are networks that their inter-sensor range measurement graphs have few edges (few range measurements among sensors) and can be represented…
We address the sensor network localization problem given noisy range measurements between pairs of nodes. We approach the non-convex maximum-likelihood formulation via a known simple convex relaxation. We exploit its favorable optimization properties to the full to obtain an approach that: is completely distributed, has a simple implementation at each node, and capitalizes on an optimal gradient method to attain fast convergence. We offer a parallel but also an asynchronous flavor, both with theoretical convergence guarantees and iteration complexity analysis. Experimental results establish le…
The problem of sensor network localization (SNL) can be formulated as a semidefinite programming problem with a rank constraint. We propose a new method for solving such SNL problems. We factorize a semidefinite matrix with the rank constraint into a product of two matrices via the Burer--Monteiro factorization. Then, we add the difference of the two matrices, with a penalty parameter, to the objective function, thereby reformulating SNL as an unconstrained multiconvex optimization problem, to which we apply the block coordinate descent method. In this paper, we also provide theoretical analys…
We consider a state estimation problem where observations are made by multiple sensors. These observations are communicated over a lossy wireless network to a central base station that computes estimates via a Kalman filter. The goal is to determine the optimal location of the base station under a certain class of packet loss probability models. It is shown in the two sensor case that the base station is optimally located at one of the sensor locations. Empirical evidence suggests that the result holds in some generality.
Stealthy Optimal Range-Sensor Placement for Target Localization
针对需平衡目标定位能力与传感器隐蔽性的开放挑战问题,研究了隐蔽距离传感器部署,提供了二维场景下任意数量传感器定位两个目标的解析解。
We present DCOOL-NET, a scalable distributed in-network algorithm for sensor network localization based on noisy range measurements. DCOOL-NET operates by parallel, collaborative message passing between single-hop neighbor sensors, and involves simple computations at each node. It stems from an application of the majorization-minimization (MM) framework to the nonconvex optimization problem at hand, and capitalizes on a novel convex majorizer. The proposed majorizer is endowed with several desirable properties and represents a key contribution of this work. It is a more accurate match to the u…
The sensor network localization (SNL) problem is to reconstruct the positions of all the sensors in a network with the given distance between pairs of sensors and within the radio range between them. It is proved that the computational complexity of the SNL problem is NP-hard, and semi-definite programming or second-order cone programming relaxation methods are only able to solve some special problems of this kind. In this study, a stochastic global optimization method called the state transition algorithm is introduced to solve the SNL problem without additional assumptions and conditions of …
A Semidefinite Programming (SDP) relaxation is an effective computational method to solve a Sensor Network Localization problem, which attempts to determine the locations of a group of sensors given the distances between some of them [11]. In this paper, we analyze and determine new sufficient conditions and formulations that guarantee that the SDP relaxation is exact, i.e., gives the correct solution. These conditions can be useful for designing sensor networks and managing connectivities in practice. Our main contribution is twofold: We present the first non-asymptotic bound on the connectiv…
Optimal Sensor Placement for Target Localization and Tracking in 2D and 3D
本文通过统一框架和框架理论,分析了二维和三维中仅方位、仅距离和接收信号强度三种传感器的最优布置问题,给出了最优布置的充要条件及其解析性质,并提出了梯度控制律以数值构造最优布置。
Almost sure convergence of a randomized algorithm for relative localization in sensor networks
针对传感器网络相对定位问题,提出一种基于输入驱动共识动力学和成对gossip通信更新的随机化算法,证明状态时间平均几乎必然收敛到最小二乘解,且无需公共时钟,实现完全分布式异步计算。
We propose an algorithm for the Wireless Sensor Network localization problem, which is based on the well-known algorithmic framework of Alternating Minimization. We start with a non-smooth and non-convex minimization, and transform it into an equivalent smooth and non-convex problem, which stands at the heart of our study. This paves the way to a new method which is globally convergent: not only does the sequence of objective function values converge, but the sequence of the location estimates also converges to a unique location that is a critical point of the corresponding (original) objectiv…
Decentralized Sensor Network Localization using Matrix-Parametrized Proximal Splittings
针对去中心化传感器网络定位,本文提出矩阵参数化近端分裂方法,并用去中心化Sinkhorn-Knopp构造参数,在收敛、内存、热启动和估计精度上优于ADMM及节点SDP松弛。
The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast theoretical and algorithmic literature on the latter to tackle the former. Leveraging this connection, we develop a two-stage algorithm for phase retrieval that can provably recover the desired signal. In both sparse and dense settings, our proposed algorithm improves upon prior approaches simultaneously in the number of required measurements for recovery an…
This paper studies angle-based sensor network localization (ASNL) in a plane, which is to determine locations of all sensors in a sensor network, given locations of partial sensors (called anchors) and angle measurements obtained in the local coordinate frame of each sensor. Firstly it is shown that a framework with a non-degenerate bilateration ordering must be angle fixable, implying that it can be uniquely determined by angles between edges up to translations, rotations, reflections and uniform scaling. Then ASNL is proved to have a unique solution if and only if the grounded framework is a…
Distributed Maximum Likelihood for Simultaneous Self-localization and Tracking in Sensor Networks
将传感器自定位问题转化为隐马尔可夫模型的静态参数估计问题,并实现递归最大似然和在线期望最大化算法的全分布式版本,以同时进行传感器网络定位与目标跟踪。
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