Space–Time Sampling for Network Observability

Designing sparse sampling strategies is crucial in having resilient estimation and control in networked systems as they make sampling less expensive and networks more resilient w.r.t where and when samples are collected. It is shown under what conditions taking coarse samples from a network will contain the same amount of information as a finer set of samples. Our goal is to estimate the initial condition of linear time-invariant networks using a set of noisy measurements. The observability condition is reformulated as the frame condition, where one can easily trace the location and time stamps of each sample. We compare the estimation quality of various sampling strategies using estimation measures, which depend on the spectrum of the corresponding frame operators. Using properties of the minimal polynomial of the state matrix, deterministic and randomized methods are suggested to construct observability frames. Intrinsic tradeoffs assert that collecting samples from fewer subsystems dictates taking more samples (in average) per subsystem. Three scalable algorithms are developed to generate sparse space–time sampling strategies with explicit error bounds.