Space-Time Sampling For Network Observability

Abstract

We will investigate under what conditions taking coarse samples from a network will contain the same information as a finer set of samples. Our goal is to estimate the initial state of a linear network of subsystems, which are distributed in a spatial domain, from noisy measurements. We develop a framework to produce feasible sets of spatio-temporal samples for the estimation problem, which essentially have a non-uniform space-time sampling pattern. If the number of sampling locations is comparable to the size of the network, the sampling pattern will have a high degree of redundancy. For these cases, using an efficient algorithm, we present a method for finding a feasible subset of samples that have a sparser space-time sampling pattern. It is shown that spatial samples can be traded for time samples: choosing to sample from a smaller set of subsystems must be compensated by taking more frequent time samples from those subsystems. Furthermore, we apply the Kadison-Singer paving solution to sparsify a feasible redundant sampling strategy with guaranteed estimation bounds. We support our theoretical findings via several numerical examples.

Publication Date

1-1-2018

Publication Title

IFAC-PapersOnLine

Volume

51

Issue

23

Number of Pages

408-413

Document Type

Article; Proceedings Paper

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.ifacol.2018.12.070

Socpus ID

85058496860 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85058496860

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