arXiv subjects

João Gomes

Publications and source records attributed to João Gomes.

15 recordsLinked to original sources

arXiv2024

Parameter-free Maximum Likelihood Localization of a Network of Moving Agents from Ranges, Bearings and Velocity measurements

Localization is a fundamental enabler technology for many applications, like vehicular networks, IoT, and even medicine. While Global Navigation Satellite Systems solutions offer great performance, they are unavailable in scenarios like indoor or underwater environments, and, for large networks, the instrumentation cost is prohibitive. We develop a localization algorithm from ranges and bearings, suitable for generic mobile networks. Our algorithm is built on a tight convex relaxation of the Maximum Likelihood position estimator. To serve positioning to mobile agents, a horizon-based version is developed accounting for velocity measurements at each agent. To solve the convex problem, a distributed gradient-based method is provided. This constitutes an advantage over centralized approaches, which usually exhibit high latency for large networks and present a single point of failure. Additionally, the algorithm estimates all required parameters and effectively becomes parameter-free. Our solution to the dynamic network localization problem is theoretically well-founded and still easy to understand. We obtain a parameter-free, outlier-robust and trajectory-agnostic algorithm, with nearly constant positioning error regardless of the trajectories of agents and anchors, achieving better or comparable performance to state-of-the-art methods, as our simulations show. Furthermore, the method is distributed, convex and does not require any particular anchor configuration.

math.OC↗

arXiv2023

ISEE.U: Distributed online active target localization with unpredictable targets

This paper addresses target localization with an online active learning algorithm defined by distributed, simple and fast computations at each node, with no parameters to tune and where the estimate of the target position at each agent is asymptotically equal in expectation to the centralized maximum-likelihood estimator. ISEE.U takes noisy distances at each agent and finds a control that maximizes localization accuracy. We do not assume specific target dynamics and, thus, our method is robust when facing unpredictable targets. Each agent computes the control that maximizes overall target position accuracy via a local estimate of the Fisher Information Matrix. We compared the proposed method with a state of the art algorithm outperforming it when the target movements do not follow a prescribed trajectory, with x100 less computation time, even when our method is running in one central CPU.

cs.LG↗

arXiv2021

STRONG: Synchronous and asynchronous RObust Network localization, under Non-Gaussian noise

Real-world network applications must cope with failing nodes, malicious attacks, or nodes facing corrupted data - data classified as outliers. Our work addresses these concerns in the scope of the sensor network localization problem where, despite the abundance of technical literature, prior research seldom considered outlier data. We propose robust, fast, and distributed network localization algorithms, resilient to high-power noise, but also precise under regular Gaussian noise. We use a Huber M-estimator, thus obtaining a robust (but nonconvex) optimization problem. We convexify and change the problem representation, to allow for distributed robust localization algorithms: a synchronous distributed method that has optimal convergence rate and an asynchronous one with proven convergence guarantees. A major highlight of our contribution lies on the fact that we pay no price for provable distributed computation neither in accuracy, nor in communication cost or convergence speed. Simulations showcase the superior performance of our algorithms, both in the presence of outliers and under regular Gaussian noise: our method exceeds the accuracy of alternative approaches, distributed and centralized, even under heavy additive and multiplicative outlier noise.

math.OC↗

arXiv2021

Autonomous orbit determination for satelite formations using relative sensing: observability analysis and optimization

Orbit determination of spacecraft in orbit has been mostly dependent on either GNSS satellite signals or ground station telemetry. Both methods present their limitations, however: GNSS signals can only be used effectively in earth orbit, and ground-based orbit determination presents an inherent latency that increases with the Earth-spacecraft distance. For spacecraft flying formations, an alternative method of orbit determination, independent of external signals, consists in the observation of the spacecraft's position with respect to the central body through the relative positioning history of the spacecraft within the formation. In this paper, the potential of the relative positioning method is demonstrated in the context of the SunRISE mission, and compared with the mission's previously proposed orbit determination methods. An optimization study is then made to find the optimal placement of a new spacecraft in the formation so as to maximize the positioning accuracy of the system. Finally, the possibility of removing part of the system's relative bearing measurements while maintaing its observability is also studied. The resulting system is found to be observable, but ill-conditioned.

eess.SY↗

arXiv2019

On the exact entropy of $\mathcal{N}=2$ black holes

We study the exact entropy of four-dimensional $\mathcal{N}=2$ black holes in M-theory both from the brane and supergravity points of view. On the microscopic side the degeneracy is given by a Fourier coefficient of the elliptic genus of the dual two-dimensional $\mathcal{N}=(0,4)$ SCFT and can be extracted via a Rademacher expansion. We show how this expansion is mapped to a modified OSV formula derived by Denef and Moore. On the macroscopic side the degeneracy is computed by applying localization techniques to Sen's quantum entropy functional reducing it to a finite number of integrals. The measure for this finite dimensional integral is determined using a connection with Chern-Simons theory on AdS$_2 \times$S$^1$. The leading answer is a Bessel function in agreement with the microscopic answer. Other subleading corrections can be explained in terms of instanton contributions.

hep-th↗

arXiv2019

CvxPnPL: A Unified Convex Solution to the Absolute Pose Estimation Problem from Point and Line Correspondences

We present a new convex method to estimate 3D pose from mixed combinations of 2D-3D point and line correspondences, the Perspective-n-Points-and-Lines problem (PnPL). We merge the contributions of each point and line into a unified Quadratic Constrained Quadratic Problem (QCQP) and then relax it into a Semi Definite Program (SDP) through Shor's relaxation. This makes it possible to gracefully handle mixed configurations of points and lines. Furthermore, the proposed relaxation allows us to recover a finite number of solutions under ambiguous configurations. In such cases, the 3D pose candidates are found by further enforcing geometric constraints on the solution space and then retrieving such poses from the intersections of multiple quadrics. Experiments provide results in line with the best performing state of the art methods while providing the flexibility of solving for an arbitrary number of points and lines.

cs.CV↗

arXiv2019

Learning from Demonstration in the Wild

Learning from demonstration (LfD) is useful in settings where hand-coding behaviour or a reward function is impractical. It has succeeded in a wide range of problems but typically relies on manually generated demonstrations or specially deployed sensors and has not generally been able to leverage the copious demonstrations available in the wild: those that capture behaviours that were occurring anyway using sensors that were already deployed for another purpose, e.g., traffic camera footage capturing demonstrations of natural behaviour of vehicles, cyclists, and pedestrians. We propose Video to Behaviour (ViBe), a new approach to learn models of behaviour from unlabelled raw video data of a traffic scene collected from a single, monocular, initially uncalibrated camera with ordinary resolution. Our approach calibrates the camera, detects relevant objects, tracks them through time, and uses the resulting trajectories to perform LfD, yielding models of naturalistic behaviour. We apply ViBe to raw videos of a traffic intersection and show that it can learn purely from videos, without additional expert knowledge.

cs.LG↗

arXiv2018

FLORIS and CLORIS: Hybrid Source and Network Localization Based on Ranges and Video

We propose hybrid methods for localization in wireless sensor networks fusing noisy range measurements with angular information (extracted from video). Compared with conventional methods that rely on a single sensed variable, this may pave the way for improved localization accuracy and robustness. We address both the single-source and network (i.e., cooperative multiple-source) localization paradigms, solving them via optimization of a convex surrogate. The formulations for hybrid localization are unified in the sense that we propose a single nonlinear least-squares cost function, fusing both angular and range measurements. We then relax the problem to obtain an estimate of the optimal positions. This contrasts with other hybrid approaches that alternate the execution of localization algorithms for each type of measurement separately, to progressively refine the position estimates. Single-source localization uses a semidefinite relaxation to obtain a one-shot matrix solution from which the source position is derived via factorization. Network localization uses a different approach where sensor coordinates are retained as optimization variables, and the relaxed cost function is efficiently minimized using fast iterations based on Nesterov's optimal method. Further, an automated calibration procedure is developed to express range and angular information, obtained by different devices, possibly deployed at different locations, in a single consistent coordinate system. This drastically reduces the need for manual calibration that would otherwise negatively impact the practical usability of hybrid range/video localization systems. We develop and test, both in simulation and experimentally, the new hybrid localization algorithms, which not only overcome the limitations of previous fusing approaches but also compare favorably to state-of-the-art methods, outperforming them in some scenarios.

math.OC↗

arXiv2017

DIeSEL: DIstributed SElf-Localization of a network of underwater vehicles

How can teams of artificial agents localize and position themselves in GPS-denied environments? How can each agent determine its position from pairwise ranges, own velocity, and limited interaction with neighbors? This paper addresses this problem from an optimization point of view: we directly optimize the nonconvex maximum-likelihood estimator in the presence of range measurements contaminated with Gaussian noise, and we obtain a provably convergent, accurate and distributed positioning algorithm that outperforms the extended Kalman filter, a standard centralized solution for this problem.

eess.SY↗

arXiv2017

LocDyn: Robust Distributed Localization for Mobile Underwater Networks

How to self-localize large teams of underwater nodes using only noisy range measurements? How to do it in a distributed way, and incorporating dynamics into the problem? How to reject outliers and produce trustworthy position estimates? The stringent acoustic communication channel and the accuracy needs of our geophysical survey application demand faster and more accurate localization methods. We approach dynamic localization as a MAP estimation problem where the prior encodes dynamics, and we devise a convex relaxation method that takes advantage of previous estimates at each measurement acquisition step; The algorithm converges at an optimal rate for first order methods. LocDyn is distributed: there is no fusion center responsible for processing acquired data and the same simple computations are performed for each node. LocDyn is accurate: experiments attest to a smaller positioning error than a comparable Kalman filter. LocDyn is robust: it rejects outlier noise, while the comparing methods succumb in terms of positioning error.

cs.MA↗

arXiv2016

Dealing with bad apples: Robust range-based network localization via distributed relaxation methods

Real-world network applications must cope with failing nodes, malicious attacks, or, somehow, nodes facing corrupted data --- classified as outliers. One enabling application is the geographic localization of the network nodes. However, despite excellent work on the network localization problem, prior research seldom considered outlier data --- even now, when already deployed networks cry out for robust procedures. We propose robust, fast, and distributed network localization algorithms, resilient to high-power noise, but also precise under regular Gaussian noise. We use the Huber M-estimator as a difference measure between the distance of estimated nodes and noisy range measurements, thus obtaining a robust (but nonconvex) optimization problem. We then devise a convex underestimator solvable in polynomial time, and tight in the inter-node terms. We also provide an optimality bound for the convex underestimator. We put forward a new representation of the Huber function composed with a norm, enabling distributed robust localization algorithms to minimize the proposed underestimator. The synchronous distributed method has optimal convergence rate and the asynchronous one converges in finite time, for a given precision. The main highlight of our contribution lies on the fact that we pay no price for distributed computation nor in accuracy, nor in communication cost or convergence speed. Simulations show the advantage of using our proposed algorithms, both in the presence of outliers and under regular Gaussian noise: our method exceeds the accuracy of an alternative robust approach based on L1 norms by at least 100m in an area of 1Km sides.

math.OC↗

arXiv2015

Simple and fast convex relaxation method for cooperative localization in sensor networks using range measurements

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 leading performance. Our algorithms top the accuracy of a comparable state of the art method by one order of magnitude, using one order of magnitude fewer communications.

math.OC↗

arXiv2014

Robust dissimilarity measure for Network Localization

In practice, network applications have to deal with failing nodes, malicious attacks, or, somehow, nodes facing highly corrupted data --- generally classified as outliers. This calls for robust, uncomplicated, and efficient methods. We propose a dissimilarity model for network localization which is robust to high-power noise, but also discriminative in the presence of regular gaussian noise. We capitalize on the known properties of the M-estimator Huber penalty function to obtain a robust, but nonconvex, problem, and devise a convex underestimator, tight in the function terms, that can be minimized in polynomial time. Simulations show the performance advantage of using this dissimilarity model in the presence of outliers and under regular gaussian noise.

math.OC↗

arXiv2011

Approximate Maximum Likelihood Source Localization from Range Measurements Through Convex Relaxation

This work considers the problem of locating a single source from noisy range measurements to a set of nodes in a wireless sensor network. We propose two new techniques that we designate as Source Localization with Nuclear Norm (SLNN) and Source Localization with l1-norm (SL-l1), which extend to arbitrary real dimensions, including 3D, our prior work on 2D source localization formulated in the complex plane. Broadly, our approach is based on formulating a Maximum-Likelihood (ML) estimation problem for the source position, and then using convex relaxation techniques to obtain a semidefinite program (SDP) that can be globally and efficiently solved. SLNN directly approximates the Gaussian ML solution, and the relaxation is shown to be tighter than in other methods in the same class. We present an analysis of the convexity properties of the constraint set for the 2D complex version of SLNN (SLCP) to justify the observed tightness of the relaxation. In terms of global accuracy of localization, SLNN outperforms state-of-the-art optimization-based methods with either iterative or closed-form formulations. We propose the SL-l1 algorithm to address the Laplacian noise case, which models the presence of outliers in range measurements. We overcome the nondifferentiability of the Laplacian likelihood function by rewriting the ML problem as an exact weighted version of the Gaussian case, and compare two solution strategies. One of them is iterative, based on block coordinate descent, and uses SLNN as a subprocessing block. The other, attaining only slightly worse performance, is noniterative and based on an SDP relaxation of the weighted ML problem.

math.OC↗

arXiv2010

Robust Simultaneous Localization of Nodes and Targets in Sensor Networks Using Range-Only Measurements

Simultaneous localization and tracking (SLAT) in sensor networks aims to determine the positions of sensor nodes and a moving target in a network, given incomplete and inaccurate range measurements between the target and each of the sensors. One of the established methods for achieving this is to iteratively maximize a likelihood function (ML), which requires initialization with an approximate solution to avoid convergence towards local extrema. This paper develops methods for handling both Gaussian and Laplacian noise, the latter modeling the presence of outliers in some practical ranging systems that adversely affect the performance of localization algorithms designed for Gaussian noise. A modified Euclidean Distance Matrix (EDM) completion problem is solved for a block of target range measurements to approximately set up initial sensor/target positions, and the likelihood function is then iteratively refined through Majorization-Minimization (MM). To avoid the computational burden of repeatedly solving increasingly large EDM problems in time-recursive operation an incremental scheme is exploited whereby a new target/node position is estimated from previously available node/target locations to set up the iterative ML initial point for the full spatial configuration. The above methods are first derived under Gaussian noise assumptions, and modifications for Laplacian noise are then considered. Analytically, the main challenges to be overcome in the Laplacian case stem from the non-differentiability of $\ell_1$ norms that arise in the various cost functions. Simulation results confirm that the proposed algorithms significantly outperform existing methods for SLAT in the presence of outliers, while offering comparable performance for Gaussian noise.

math.OC↗