### Distributed Localization from Relative Noisy Measurements: a Gradient Based Approach

"... Abstract — In this work we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard least-squares problem, the main challenge is to devise scalable algorithms that allo ..."

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Abstract — In this work we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard least-squares problem, the main challenge is to devise scalable algorithms that allow each agent to estimate its own position by means of only local communication and bounded complexity, independently of the network size and topology. We propose a gradient based algorithm that is guaranteed to have exponentially convergence rate to the optimal centralized least-square solution. Moreover we show the effectiveness also in presence of delays. We finally provide numerical results to support our work. I.

### 1State

"... estimation in power distribution networks with poorly synchronized measurements ..."

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estimation in power distribution networks with poorly synchronized measurements

### Asynchronous Newton-Raphson Consensus for Distributed Convex Optimization ⋆

"... Abstract: We consider the distributed unconstrained minimization of separable convex cost functions, where the global cost is given by the sum of several local and private costs, each associated to a specific agent of a given communication network. We specifically address an asynchronous distributed ..."

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Abstract: We consider the distributed unconstrained minimization of separable convex cost functions, where the global cost is given by the sum of several local and private costs, each associated to a specific agent of a given communication network. We specifically address an asynchronous distributed optimization technique called Newton-Raphson Consensus. Beside having low computational complexity, low communication requirements and being interpretable as a distributed Newton-Raphson algorithm, the technique has also the beneficial properties of requiring very little coordination and naturally supporting time-varying topologies. In this work we analytically prove that under some assumptions it shows either local or global convergence properties, and corroborate this result by the means of numerical simulations.

### An

"... exponential-rate consensus-based algorithms for estimation from relative measurements: implementation and performance analysis ..."

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exponential-rate consensus-based algorithms for estimation from relative measurements: implementation and performance analysis

### An

"... exponential-rate consensus-based algorithms for estimation from relative measurements: implementation and performance analysis ..."

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exponential-rate consensus-based algorithms for estimation from relative measurements: implementation and performance analysis

### Distributed Localization from Relative Noisy Measurements: a Robust Gradient Based Approach

"... Abstract — In this work we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard least-squares problem, the main challenge is to devise scalable algorithms that allo ..."

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Abstract — In this work we address the problem of optimal estimating the position of each agent in a network from relative noisy vectorial distances with its neighbors. Although the problem can be cast as a standard least-squares problem, the main challenge is to devise scalable algorithms that allow each agent to estimate its own position by means of only local communication and bounded complexity, independently of the network size and topology. We propose a gradient based algorithm that is guaranteed to have exponentially convergence rate to the optimal centralized least-square solution. Moreover we show the convergence also in presence of bounded delays and packet losses. We finally provide numerical results to support our work. I.