This paper presents a novel algorithm for recovering missing data of phasor measurement units (PMUs). Due to the low-rank property of PMU data, missing measurement recovery can be formulated as a low-rank matrix-completion problem. Based on maximum-margin matrix factorization, we propose an efficient algorithm based on alternating direction method of multipliers (ADMM) for solving the matrix co...

where each θj is supported only on Ω ⊂ {1, 2, . . . , N}, with |Ω| = K. The matrix Ψ is orthonormal, with dimension N × N (we consider only signals sparse in an orthonormal basis). We denote by Φj the measurement matrix for signal j, where Φj is of dimension M ×N , where M < N . We let yj = Φjxj = ΦjΨθj be the observations of signal j. We assume that the measurement matrix Φj is random with i.i...

We consider the problem of testing for the presence (or detection) of an unknown sparse signal in additive white noise. Given a fixed measurement budget, much smaller than the dimension of the signal, we consider the general problem of designing compressive measurements to maximize the measurement signal-to-noise ratio (SNR), as increasing SNR improves the detection performance in a large class...

Compressive sensing is a method for recording a k-sparse signal x ∈ R with (possibly noisy) linear measurements of the form y = Ax, where A ∈ Rm×n describes the measurement process. Seminal results in compressive sensing show that it is possible to recover the signal x from m = O(k log n k ) measurements and that this is tight. The model-based compressive sensing framework overcomes this lower ...

Nomenclature F = state transition matrix H = matrix giving the ideal/noiseless connection between measurements and states I = identity matrix k = time index L = noise sensitivity matrix in nonlinear systems N = lag time constant integer P = estimation-error covariance matrix s = arbitrary time step used in inductive proof xk = state at time index k x̂ = state estimate x̂k = a priori state estimat...

Recently, it has been proved in [1] that in noisy compressed sensing, a joint typical estimator can asymptotically achieve the CramérRao lower bound of the problem. To prove this result, [1] used a lemma, which is provided in [2], that comprises the main building block of the proof. This lemma is based on the assumption of Gaussianity of the measurement matrix and its randomness in the domain o...

In the past few lectures we have been studying the problem of sparse signal reconstruction from a small number of noiseless linear measurements. The objective is to recover an unknown, k-sparse, n-dimensional vector x from a measurement vector y = Ax ∈ R, which is a linear transformation of x by a known m× n matrix A, where m < n. We have presented various heuristics for sparse signal recovery,...

The accuracy of leak detection and calibration of pipe networks by means of the inverse transient analysis (ITA) is highly affected by the number and location of the measurement sites. This study introduces a conceptual decision-making model, the Decision Table Method (DTM), for the measurement site design of pipe networks with the aim of inverse transient analysis. Through the Decision Table M...

In this paper, the innovative intelligent fuzzy weighted input estimation method (FWIEM) can be applied to the inverse heat transfer conduction problem (IHCP) to estimate the unknown time-varying heat flux efficiently as presented. The feasibility of this method can be verified by adopting the temperature measurement experiment. We would like to focus attention on the heat flux estimation to th...