Space-Time Sampling for Network Observability

Abstract

Designing sparse sampling strategies is one of the important components in having resilient estimation and control in networked systems as they make network design problems more cost-effective due to their reduced sampling requirements and less fragile to where and when samples are collected. It is shown that under what conditions taking coarse samples from a network will contain the same amount of information as a more finer set of samples. Our goal is to estimate 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 location and time stamps of each sample. We compare estimation quality of various sampling strategies using estimation measures, which depend on 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.

Space-Fluid Adaptive Sampling by Self-Organisation

“…There are several approaches in the literature that attempt to solve this and similar problems, with heterogeneous techniques, that we collectively refer to under the umbrella term of "adaptive spatial sampling". Amongst these, some [MSM18,Tho90] are restricted to the so-called sampling design problem, that is, their concern is to deliver either design-time decision support about where to deploy sensor devices or analytically devise out the best sampling algorithm given domain expertise or infrastructural requirements (most often, residual energy management). Our approach is not directly comparable to these, as we are concerned with run-time adaptation of the sampling process based on domain-specific properties (e.g.…”

Space-Fluid Adaptive Sampling: A Field-Based, Self-organising Approach

“…There are several approaches in the literature that attempt to solve similar problems, in different research areas and with different techniques. In adaptive sampling [27,17] the goal is to extend or reduce the set of samples drawn depending on temporal dynamics or across space. There, most of the literature is about designing fixed strategies for sensor placement (at design-time), sensor selection (at run-time), or so-called sampling designs, that is, how the sampling process may be adaptive to either network-level measures (energy consumption, communication costs, sensor distance, etc.)…”

Estimation With Fast Feature Selection in Robot Visual Navigation

“…This algorithm is inspired by the graph sparsification using effective resistances [14], [15], where the goal is to construct a sparse weighted graph based on a given weighted graph by ensuring that the Laplacians of the two graphs stay spectrally close to each other. A variation of this method appears in [16] for the case of rank-one selected matrices when the constant termH t,T is zero.…”

“…3. We set parameters R = 7500, ω = 0.08, ω r = 0.0064, σ = 0.1 and Λ t = diag (4,4,16) and initial covariance to be Σ 0 = I.…”

“…, q . Now, we build up our proof based on some of the steps taken in the proof of Theorem 5 in [15] and steps from [16], wherein the authors prove a similar result for the case that selected matrices are rank-one. Using the leverage scores (29), one can verify that becauseH f,i t,T for each (f, i) ∈Φ t is rank-one, then by applying similar steps to the proof of Theorem 5 in [15], with probability at least 1/2 we have…”