Andrea Simonetto

Distributed Maximum Likelihood Sensor Network Localization

We propose a class of convex relaxations to solve the sensor network localization problem, based on a maximum likelihood (ML) formulation. This class, as well as the tightness of the relaxations, depends on the noise probability density function (PDF) of the collected measurements. We derive a computational efficient edge-based version of this ML convex relaxation class and we design a distributed algorithm that enables the sensor nodes to solve these edge-based convex programs locally by communicating only with their close neighbors. This algorithm relies on the alternating direction method of multipliers (ADMM), it converges to the centralized solution, it can run asynchronously, and it is computation error-resilient. Finally, we compare our proposed distributed scheme with other available methods, both analytically and numerically, and we argue the added value of ADMM, especially for large-scale networks.

Sparsity-Aware Sensor Selection: Centralized and Distributed Algorithms

The selection of the minimum number of sensors within a network to satisfy a certain estimation performance metric is an interesting problem with a plethora of applications. We explore the sparsity embedded within the problem and propose a relaxed sparsity-aware sensor selection approach which is equivalent to the unrelaxed problem under certain conditions. We also present a reasonably low-complexity and elegant distributed version of the centralized problem with convergence guarantees such that each sensor can decide itself whether it should contribute to the estimation or not. Our simulation results corroborate our claims and illustrate a promising performance for the proposed centralized and distributed algorithms.

Distributed Computation Particle Filters on GPU Architectures for Real-Time Control Applications

We present the design, analysis, and real-time implementation of a distributed computation particle filter on a graphic processing unit (GPU) architecture that is especially suited for fast real-time control applications. The proposed filter architecture is composed of a number of local subfilters that can share limited information among each other via an arbitrarily chosen abstract connected communication topology. We develop a detailed implementation procedure for GPU architectures focusing on distributed resampling as a crucial step in our approach, and describe alternative methods in the literature. We analyze the role of the most important parameters such as the number of exchanged particles and the effect of the particle exchange topology. The significant speedup and increase in performance obtained with our framework with respect to both available GPU solutions and standard sequential CPU methods enable particle filter implementations in fast real-time feedback control systems. This is illustrated via experimental and simulation results using a real-time visual servoing problem of a robotic arm capable of running in closed loop with an update rate of 100 Hz, while performing particle filter calculations that involve over one million particles.

Distributed nonlinear estimation for robot localization using weighted consensus

Distributed linear estimation theory has received increased attention in recent years due to several promising industrial applications. Distributed nonlinear estimation, however is still a relatively unexplored field despite the need in numerous practical situations for techniques that can handle nonlinearities. This paper presents a unified way of describing distributed implementations of three commonly used nonlinear estimators: the Extended Kalman Filter, the Unscented Kalman Filter and the Particle Filter. Leveraging on the presented framework, we propose new distributed versions of these methods, in which the nonlinearities are locally managed by the various sensors whereas the different estimates are merged based on a weighted average consensus process. The proposed versions are shown to outperform the few published ones in two robot localization test cases.

A Class of Prediction-Correction Methods for Time-Varying Convex Optimization

This paper considers unconstrained convex optimization problems with time-varying objective functions. We propose algorithms with a discrete time-sampling scheme to find and track the solution trajectory based on prediction and correction steps, while sampling the problem data at a constant rate of 1/h, where h is the sampling period. The prediction step is derived by analyzing the iso-residual dynamics of the optimality conditions. The correction step adjusts for the distance between the current prediction and the optimizer at each time step, and consists either of one or multiple gradient steps or Newton steps, which respectively correspond to the gradient trajectory tracking (GTT) or Newton trajectory tracking (NTT) algorithms. Under suitable conditions, we establish that the asymptotic error incurred by both proposed methods behaves as O(h2), and in some cases as O(h4), which outperforms the state-of-the-art error bound of O(h) for correction-only methods in the gradient-correction step. Moreover, when the characteristics of the objective function variation are not available, we propose approximate gradient and Newton tracking algorithms (AGT and ANT, respectively) that still attain these asymptotical error bounds. Numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude.

Distributed Autoregressive Moving Average Graph Filters

We introduce the concept of autoregressive moving average (ARMA) filters on a graph and show how they can be implemented in a distributed fashion. Our graph filter design philosophy is independent of the particular graph, meaning that the filter coefficients are derived irrespective of the graph. In contrast to finite-impulse response (FIR) graph filters, ARMA graph filters are robust against changes in the signal and/or graph. In addition, when time-varying signals are considered, we prove that the proposed graph filters behave as ARMA filters in the graph domain and, depending on the implementation, as first or higher order ARMA filters in the time domain.

On distributed maximization of algebraic connectivity in robotic networks

We consider the problem of maximizing the algebraic connectivity of the communication graph in a network of mobile robots by moving them into appropriate positions. We describe the Laplacian of the graph as dependent on the pairwise distance between the robots and formulate an approximate problem as a Semi-Definite Program (SDP). We propose a consistent, non-iterative distributed solution by solving local SDPs which use information only from nearby neighboring robots. Numerical simulations show the performance of the algorithm with respect to the centralized solution.

Autoregressive Moving Average Graph Filtering

One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogs of classical filters, but intended for signals defined on graphs. This paper brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions, which are able to approximate any desired graph frequency response, and give exact solutions for specific graph signal denoising and interpolation problems. The philosophy to design the ARMA coefficients independently from the underlying graph renders the ARMA graph filters suitable in static and, particularly, time-varying settings. The latter occur when the graph signal and/or graph topology are changing over time. We show that in case of a time-varying graph signal, our approach extends naturally to a two-dimensional filter, operating concurrently in the graph and regular time domain. We also derive the graph filter behavior, as well as sufficient conditions for filter stability when the graph and signal are time varying. The analytical and numerical results presented in this paper illustrate that ARMA graph filters are practically appealing for static and time-varying settings, as predicted by theoretical derivations.

Primal Recovery from Consensus-Based Dual Decomposition for Distributed Convex Optimization

Dual decomposition has been successfully employed in a variety of distributed convex optimization problems solved by a network of computing and communicating nodes. Often, when the cost function is separable but the constraints are coupled, the dual decomposition scheme involves local parallel subgradient calculations and a global subgradient update performed by a master node. In this paper, we propose a consensus-based dual decomposition to remove the need for such a master node and still enable the computing nodes to generate an approximate dual solution for the underlying convex optimization problem. In addition, we provide a primal recovery mechanism to allow the nodes to have access to approximate near-optimal primal solutions. Our scheme is based on a constant stepsize choice, and the dual and primal objective convergence are achieved up to a bounded error floor dependent on the stepsize and on the number of consensus steps among the nodes.

Optimal Power Flow Pursuit

This paper considers distribution networks featuring inverter-interfaced distributed energy resources, and develops distributed feedback controllers that continuously drive the inverter output powers to solutions of ac optimal power flow (OPF) problems. Particularly, the controllers update the power setpoints based on voltage measurements as well as given (time-varying) OPF targets, and entail elementary operations implementable onto low-cost microcontrollers that accompany power-electronics interfaces of gateways and inverters. The design of the control framework is based on suitable linear approximations of the ac power-flow equations as well as Lagrangian regularization methods. Convergence and OPF-target tracking capabilities of the controllers are analytically established. Overall, the proposed method allows to bypass traditional hierarchical setups where feedback control and optimization operate at distinct time scales, and to enable real-time optimization of distribution systems.