Distributed Estimation and Detection under Local Information

This work considers the problem of obtaining optimal estimates via distributed computation in a large scale system. The electric power system, the transportation system, and generally any computer or network system, are examples of large scale systems: a decentralized estimation of signals based on observations acquired by spatially distributed sensors is the basis for a wide range of important applications. In this work, we focus on the problem of reconstructing the initial state of a linear network in the presence of process and measurement noise. We consider a local model information setup, in which the entire dynamical and measurement model is nowhere available and cannot be reconstructed for the computation. Our estimation procedure relies upon a novel technique to solve a consistent system of linear equations, for which we prove correctness and convergence. In the second part of the paper we consider the problem of detecting anomalies in a large scale network driven by noise. Despite the theoretical advances in this field of research, the currently available procedures to enforce security in large scale systems are computationally inefficient and numerically unreliable. Using our optimal estimation scheme, we describe a distributed procedure with performance guarantees that only requires local knowledge of the system model.