Widely-Linear MMSE Estimation of Complex-Valued Graph Signals

Amar, Alon; Routtenberg, Tirza

doi:10.1109/tsp.2023.3256536

Cited by 5 publications

(2 citation statements)

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“…These models are functions of the network topology (G and B), the available measurements or given data (X), and may also incorporate additional noise and errors. The specific log-likelihood of the measurement model, −ψ(X, G, B), serves as the objective function in our optimization problem, as presented in (5). Notably, the constraints are identical across all models.…”

Section: Cmlementioning

confidence: 99%

“…Complex-valued graph signals arise in several real-world applications [5], such as multi-agent systems [6], wireless communication systems [7], voltage and power phasors in electrical networks [8]- [10], and probabilistic graphical models with complex-valued multivariate Gaussian vectors [11]. Despite the widespread use of complex-valued graph signals, the recovery of complex-valued Laplacians is a crucial problem that has not been well explored.…”

Section: Introductionmentioning

confidence: 99%

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Estimation of the Admittance Matrix in Power Systems Under Laplacian and Physical Constraints

Halihal

Routtenberg

2022

ICASSP 2022 - 2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In this paper, we investigate the problem of estimating a complex-valued Laplacian matrix from a linear Gaussian model, with a focus on its application in the estimation of admittance matrices in power systems. The proposed approach is based on a constrained maximum likelihood estimator (CMLE) of the complex-valued Laplacian, which is formulated as an optimization problem with Laplacian and sparsity constraints. The complex-valued Laplacian is a symmetric, non-Hermitian matrix that exhibits a joint sparsity pattern between its real and imaginary parts. Leveraging the ℓ1 relaxation and the joint sparsity, we develop two estimation algorithms for the implementation of the CMLE. The first algorithm is based on casting the optimization problem as a semi-definite programming (SDP) problem, while the second algorithm is based on developing an efficient augmented Lagrangian method (ALM) solution. Next, we apply the proposed SDP and ALM algorithms for the problem of estimating the admittance matrix under three commonly-used measurement models, that stem from Kirchhoff's and Ohm's laws, each with different assumptions and simplifications: 1) the nonlinear alternating current (AC) model; 2) the decoupled linear power flow (DLPF) model; and 3) the direct current (DC) model. The performance of the SDP and the ALM algorithms is evaluated using data from the IEEE 33-bus power system data under different settings. The numerical experiments demonstrate that the proposed algorithms outperform existing methods in terms of mean-squared-error (MSE) and F-score, thus, providing a more accurate recovery of the admittance matrix.

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Section: Cmlementioning

confidence: 99%