Modeling and Recovery of Graph Signals and Difference-Based Signals

Kroizer, Ariel; Eldar, Yonina C.; Routtenberg, Tirza

doi:10.1109/globalsip45357.2019.8969536

Cited by 17 publications

(14 citation statements)

References 29 publications

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“…where e bus contains the elements of the noise vector, e, that are related to the N power measurements at the N buses, and c 1 is an arbitrary constant, which represents the constantinvariant property of the state vector [1], [39] 1 . Without loss of generality, we choose the value of c 1 from (20) to be…”

Section: ) Theoretical Validation -Output Of a Low-pass Graph Filtermentioning

confidence: 99%

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State Estimation in Unobservable Power Systems via Graph Signal Processing Tools

Dabush¹,

Kroizer²,

Routtenberg³

2021

Preprint

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We consider the problem of estimating the states and detecting bad data in an unobservable power system. To this end, we propose novel graph signal processing (GSP) methods. The main assumption behind the proposed GSP approach is that the grid state vector, which includes the phases of the voltages in the system, is a smooth graph signal with respect to the system admittance matrix that represents the underlying graph. Thus, the first step in this paper is to validate the graph-smoothness assumption of the states, both empirically and theoretically. Then, we develop the regularized weighted least squares (WLS) state estimator, which does not require observability of the network. We propose a sensor (meter) placement strategy that aims to optimize the estimation performance of the proposed GSP-WLS estimator. In addition, we develop a joint bad-data and falsedata injected (FDI) attacks detector that integrates the GSP-WLS state estimator into the conventional J(θ)-test with an additional smoothness regularization. Numerical results on the IEEE 118bus test-case system demonstrate that the new GSP methods outperform commonly-used estimation and detection approaches in electric networks and are robust to missing data.

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Section: ) Theoretical Validation -Output Of a Low-pass Graph Filtermentioning

confidence: 99%

“…where e M\S is a zero-mean noise vector with a covariance matrix R M\S . By substituting the GSP-WLS estimator from (32) in (39) and removing the noise term, we obtain the following WLS-type estimator of the missing power measurements:…”

Section: Of Missing Power Measurementsmentioning

confidence: 99%

State Estimation in Unobservable Power Systems via Graph Signal Processing Tools

Dabush¹,

Kroizer²,

Routtenberg³

2021

Preprint

Self Cite

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show abstract

“…) and S3(xi+2, y) Based on the onevariable cubic spline functions built above, after a certain compression, the following view of the following two-variable interpolation bicubic spline function is formed [4][5][6][7][8]: , y) and S3(xi+2, y) are generated by putting the values of the bicubic spline functions of a variable built above (8) [9,10,11,12,13].…”

Section: Astesj Issn: 2415-6698mentioning

confidence: 99%

Lacol Interpolation Bicubic Spline Method in Digital Processing of Geophysical Signals

Zaynidinov¹,

Bahromov²,

Azimov³

et al. 2021

Adv. sci. technol. eng. syst. j.

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The paper a cubic spline built through a local base spline and the local interpolation bicubic spline models we offer have been selected. The construction details of the models are given, the two-dimensional local interpolation bicubic spline models considered in this study provide high accuracy in digital processing of signals, which helps experts to make the right decision as a result of digital processing of signals. As an example, the initial values of the geophysical signal were digitally processed and error results were obtained. The error results obtained by digital processing of the geophysical signal of the considered models were compared on the basis of numerical and graphical comparisons.

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“…Fitting graph-based models for a given data was considered in [31]- [33]. In [34], we proposed a two-stage method for estimation of graph signals from a known nonlinear observation model, which is based on fitting a graph-based model and then implementing a least-squares recovery approach on the approximated model. However, model-fitting approaches aim to minimize the modeling error.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Estimation of Graph Signals

Kroizer,

Routtenberg,

Eldar

2021

Preprint

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We consider the problem of recovering random graph signals from nonlinear measurements. For this case, closed-form Bayesian estimators are usually intractable and even numerical evaluation of these estimators may be hard to compute for large networks. In this paper, we propose a graph signal processing (GSP) framework for random graph signal recovery that utilizes the information of the structure behind the data. First, we develop the GSP-linear minimum mean-squared-error (GSP-LMMSE) estimator, which minimizes the mean-squarederror (MSE) among estimators that are represented as an output of a graph filter. The GSP-LMMSE estimator is based on diagonal covariance matrices in the graph frequency domain, and thus, has reduced complexity compared with the LMMSE estimator. This property is especially important when using the sample-mean versions of these estimators that are based on a training dataset. We then state conditions under which the low-complexity GSP-LMMSE estimator coincides with the optimal LMMSE estimator. Next, we develop the approximated parametrization of the GSP-LMMSE estimator by shift-invariant graph filters by solving a weighted least squared (WLS) problem. We present three implementations of the parametric GSP-LMMSE estimator for typical graph filters. Parametric graph filters are more robust to outliers and to network topology changes. In our simulations, we evaluate the performance of the proposed GSP-LMMSE estimators for the problem of state estimation in power systems, which can be interpreted as a graph signal recovery task. We show that the proposed sample-GSP estimators outperform the sample-LMMSE estimator for a limited training dataset and that the parametric GSP-LMMSE estimators are more robust to topology changes in the form of adding/removing vertices/edges.

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Modeling and Recovery of Graph Signals and Difference-Based Signals

Cited by 17 publications

References 29 publications

State Estimation in Unobservable Power Systems via Graph Signal Processing Tools

State Estimation in Unobservable Power Systems via Graph Signal Processing Tools

Lacol Interpolation Bicubic Spline Method in Digital Processing of Geophysical Signals

Bayesian Estimation of Graph Signals

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