Local strong convexity of maximum-likelihood TDOA-Based source localization and its algorithmic implications

Liu, Huikang; Pun, Yuen-Man; So, Anthony Man–Cho

doi:10.1109/camsap.2017.8313119

Cited by 11 publications

(4 citation statements)

References 9 publications

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“…Moreover, we give an explicit estimate of the size of the strong convexity region. We remark that similar results have previously been established for a time-difference-of-arrival (TDOA)-based least-squares loss function [32]. However, to the best of our knowledge, our results for the TOA-based least-squares loss function are new and can be of independent interest.…”

Section: Introductionsupporting

confidence: 86%

“…A possible future direction is to design and analyze online methods for TDOA-based tracking, which corresponds to a sequential version of the TDOA-based source localization problem (see, e.g., [38] and the references therein). One possible approach is to combine the results in [32] with the techniques developed in this paper. Another future direction is to study the performance of different online methods for solving the TOA-based tracking problem.…”

Section: Discussionmentioning

confidence: 99%

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Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements

Pun,

2021

Preprint

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In this paper, we consider a time-varying optimization approach to the problem of tracking a moving target using noisy time-of-arrival (TOA) measurements. Specifically, we formulate the problem as that of sequential TOA-based source localization and apply online gradient descent (OGD) to it to generate the position estimates of the target. To analyze the tracking performance of OGD, we first revisit the classic leastsquares formulation of the (static) TOA-based source localization problem and elucidate its estimation and geometric properties. In particular, under standard assumptions on the TOA measurement model, we establish a bound on the distance between an optimal solution to the least-squares formulation and the true target position. Using this bound, we show that the loss function in the formulation, albeit non-convex in general, is locally strongly convex at its global minima. To the best of our knowledge, these results are new and can be of independent interest. By combining them with existing techniques from online strongly convex optimization, we then establish the first non-trivial bound on the cumulative target tracking error of OGD. Our numerical results corroborate the theoretical findings and show that OGD can effectively track the target at different noise levels.

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Section: Introductionsupporting

confidence: 86%

Section: Discussionmentioning

confidence: 99%

Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements

Pun,

2021

Preprint

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“…In recent years, there has been a growing body of literature exploring the design and analysis of fast methods for tackling non-convex formulations that arise in applications. These include deep neural networks [32,33], low-rank matrix recovery [12,23], phase retrieval [27,35], source localization [24,31], and synchronization [25,39]. As these works show, the non-convex formulations in question often possess structures that can be exploited by simple and scalable methods, thereby allowing optimal solutions of those formulations to be found efficiently.…”

Section: Our Contributionsmentioning

confidence: 99%

Non-convex exact community recovery in stochastic block model

Wang

Zhou

2021

Math. Program.

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Community detection in graphs that are generated according to stochastic block models (SBMs) has received much attention lately. In this paper, we focus on the binary symmetric SBM-in which a graph of n vertices is randomly generated by first partitioning the vertices into two equal-sized communities and then connecting each pair of vertices with probability that depends on their community memberships-and study the associated exact community recovery problem. Although the maximum-likelihood formulation of the problem is non-convex and discrete, we propose to tackle it using a popular iterative method called projected power iterations. To ensure fast convergence of the method, we initialize it using a point that is generated by another iterative method called orthogonal iterations, which is a classic method for computing invariant subspaces of a symmetric matrix. We show that in the logarithmic sparsity regime of the problem, with high probability the proposed two-stage method can exactly recover the two communities down to the information-theoretic limit in O(n log 2 n/ log log n) time, which is competitive with a host of existing state-of-the-art methods that have the same recovery performance. We also conduct numerical experiments on both synthetic

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“…To reduce the computation cost of the grid searching methods, Huang et al [13] proposed to utilize the Levenberg-Marquardt (L-M) algorithm to solve the localization problem after the phase unwrapping. Even though this localization problem is non-convex, it locally exhibits a strong convexity at an optimal solution [14]. So the performance of the L-M algorithm highly depends on the initialization.…”

Section: Introductionmentioning

confidence: 99%

ReLoc 2.0: UHF-RFID Relative Localization for Drone-Based Inventory Management

Tanghe

Suanet³

et al. 2021

IEEE Trans. Instrum. Meas.

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Radio frequency identification (RFID) technology attracts extensive attention for industrial applications, especially supply chain businesses and inventory management. In this paper, a passive RFID localization scheme based on unmanned aerial vehicle (UAV) or drones is established for inventory management in warehouses. In case of the major challenge of the on-board antenna tracking errors in practical scenarios, the state-of-the-art numerical methods rely on accurate antenna positions, such as synthetic aperture radar-based algorithms, which will introduce large positioning errors and become unreliable. To this end, we propose a new relative RFID localization method based on phase, received signal strength indicator (RSSI), and readability, which is little affected by antenna tracking errors. In the proposed method, the tagged items on the racks are located laterally through pinpointing the minimum of the unwrapped phases, which have been unwrapped based on the hybrid random forest model. RSSI differences and the read count of each patch antenna's beam are utilized to distinguish the rack level of tagged assets via a boosting tree classifier. The experimental results in a real warehouse show that the proposed method achieves 27.1-cm mean lateral positioning accuracy, and orders the tagged items horizontally and vertically with more than 96.7% and 98.0% accuracy, respectively.

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Local strong convexity of maximum-likelihood TDOA-Based source localization and its algorithmic implications

Cited by 11 publications

References 9 publications

Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements

Local Strong Convexity of Source Localization and Error Bound for Target Tracking under Time-of-Arrival Measurements

Non-convex exact community recovery in stochastic block model

ReLoc 2.0: UHF-RFID Relative Localization for Drone-Based Inventory Management

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