arXiv subjects

Tirza Routtenberg

Publications and source records attributed to Tirza Routtenberg.

43 records · Page 3Linked to original sources

arXiv2020

Low-Complexity Methods for Estimation After Parameter Selection

Statistical inference of multiple parameters often involves a preliminary parameter selection stage. The selection stage has an impact on subsequent estimation, for example by introducing a selection bias. The post-selection maximum likelihood (PSML) estimator is shown to reduce the selection bias and the post-selection mean-squared-error (PSMSE) compared with conventional estimators, such as the maximum likelihood (ML) estimator. However, the computational complexity of the PSML is usually high due to the multi-dimensional exhaustive search for a global maximum of the post-selection log-likelihood (PSLL) function. Moreover, the PSLL involves the probability of selection that, in general, does not have an analytical form. In this paper, we develop new low-complexity post-selection estimation methods for a two-stage estimation after parameter selection architecture. The methods are based on implementing the iterative maximization by parts (MBP) approach, which is based on the decomposition of the PSLL function into "easily-optimized" and complicated parts. The proposed second-best PSML method applies the MBP-PSML algorithm with a pairwise probability of selection between the two highest-ranked parameters w.r.t. the selection rule. The proposed SA-PSML method is based on using stochastic approximation (SA) and Monte Carlo integrations to obtain a non-parametric estimation of the gradient of the probability of selection and then applying the MBP-PSML algorithm on this approximation. For low-complexity performance analysis, we develop the empirical post-selection Cramer-Rao-type lower bound. Simulations demonstrate that the proposed post-selection estimation methods are tractable and reduce both the bias and the PSMSE, compared with the ML estimator, while only requiring moderate computational complexity.

eess.SP↗

arXiv2019

Detection of false data injection attacks in smart grids based on graph signal processing

The smart grid combines the classical power system with information technology, leading to a cyber-physical system. In such an environment the malicious injection of data has the potential to cause severe consequences. Classical residual-based methods for bad data detection are unable to detect well designed false data injection (FDI) attacks. Moreover, most work on FDI attack detection is based on the linearized DC model of the power system and fails to detect attacks based on the AC model. The aim of this paper is to address these problems by using the graph structure of the grid and the AC power flow model. We derive an attack detection method that is able to detect previously undetectable FDI attacks. This method is based on concepts originating from graph signal processing (GSP). The proposed detection scheme calculates the graph Fourier transform of an estimated grid state and filters the graph's high-frequency components. By comparing the maximum norm of this outcome with a threshold we can detect the presence of FDI attacks. Case studies on the IEEE 14-bus system demonstrate that the proposed method is able to detect a wide range of previously undetectable attacks, both on angles and on magnitudes of the voltages.

eess.SP↗

arXiv2018

Cramer-Rao Bound for Constrained Parameter Estimation Using Lehmann-Unbiasedness

The constrained Cramer-Rao bound (CCRB) is a lower bound on the mean-squared-error (MSE) of estimators that satisfy some unbiasedness conditions. Although the CCRB unbiasedness conditions are satisfied asymptotically by the constrained maximum likelihood (CML) estimator, in the non-asymptotic region these conditions are usually too strict and the commonly-used estimators, such as the CML estimator, do not satisfy them. Therefore, the CCRB may not be a lower bound on the MSE matrix of such estimators. In this paper, we propose a new definition for unbiasedness under constraints, denoted by C-unbiasedness, which is based on using Lehmann-unbiasedness with a weighted MSE (WMSE) risk and taking into account the parametric constraints. In addition to C-unbiasedness, a Cramer-Rao-type bound on the WMSE of C-unbiased estimators, denoted as Lehmann-unbiased CCRB (LU-CCRB), is derived. This bound is a scalar bound that depends on the chosen weighted combination of estimation errors. It is shown that C-unbiasedness is less restrictive than the CCRB unbiasedness conditions. Thus, the set of estimators that satisfy the CCRB unbiasedness conditions is a subset of the set of C-unbiased estimators and the proposed LU-CCRB may be an informative lower bound in cases where the corresponding CCRB is not. In the simulations, we examine linear and nonlinear estimation problems under nonlinear constraints in which the CML estimator is shown to be C-unbiased and the LU-CCRB is an informative lower bound on the WMSE, while the corresponding CCRB on the WMSE is not a lower bound and is not informative in the non-asymptotic region.

cs.IT↗

arXiv2018

Power Systems Topology and State Estimation by Graph Blind Source Separation

In this paper, we consider the problem of blind estimation of states and topology (BEST) in power systems. We use the linearized DC model of real power measurements with unknown voltage phases (i.e. states) and an unknown admittance matrix (i.e. topology) and show that the BEST problem can be formulated as a blind source separation (BSS) problem with a weighted Laplacian mixing matrix. We develop the constrained maximum likelihood (ML) estimator of the Laplacian matrix for this graph BSS (GBSS) problem with Gaussian-distributed states. The ML-BEST is shown to be only a function of the states second-order statistics. Since the topology recovery stage of the ML-BEST approach results in a high-complexity optimization problem, we propose two low-complexity methods to implement it 1) Two- phase topology recovery, which is based on solving the relaxed convex optimization and then finding the closest Laplacian matrix, and 2) Augmented Lagrangian topology recovery. We derive a closed-form expression for the associated Cramer-Rao bound (CRB) on the topology matrix estimation. The performance of the proposed methods is evaluated for the IEEE-14 bus test-case system and for a random network. It is shown that, asymptotically, the state estimation performance of the proposed ML-BEST methods coincides with the oracles minimum mean-squared-error (MSE) state estimator, and the MSE of the topology estimation achieves the proposed CRB.

cs.IT↗

arXiv2015

Estimation after Parameter Selection: Performance Analysis and Estimation Methods

In many practical parameter estimation problems, prescreening and parameter selection are performed prior to estimation. In this paper, we consider the problem of estimating a preselected unknown deterministic parameter chosen from a parameter set based on observations according to a predetermined selection rule, $Ψ$. The data-based parameter selection process may impact the subsequent estimation by introducing a selection bias and creating coupling between decoupled parameters. This paper introduces a post-selection mean squared error (PSMSE) criterion as a performance measure. A corresponding Cramér-Rao-type bound on the PSMSE of any $Ψ$-unbiased estimator is derived, where the $Ψ$-unbiasedness is in the Lehmann-unbiasedness sense. The post-selection maximum-likelihood (PSML) estimator is presented .It is proved that if there exists an $Ψ$-unbiased estimator that achieves the $Ψ$-Cramér-Rao bound (CRB), i.e. an $Ψ$-efficient estimator, then it is produced by the PSML estimator. In addition, iterative methods are developed for the practical implementation of the PSML estimator. Finally, the proposed $Ψ$-CRB and PSML estimator are examined in estimation after parameter selection with different distributions.

cs.IT↗

arXiv2014

PMU based Detection of Imbalance in Three-Phase Power Systems

The problem of imbalance detection in a three-phase power system using a phasor measurement unit (PMU) is considered. A general model for the zero, positive, and negative sequences from a PMU measurement at off-nominal frequencies is presented and a hypothesis testing framework is formulated. The new formulation takes into account the fact that minor degree of imbalance in the system is acceptable and does not indicate subsequent interruptions, failures, or degradation of physical components. A generalized likelihood ratio test (GLRT) is developed and shown to be a function of the negative-sequence phasor estimator and the acceptable level of imbalances for nominal system operations. As a by-product to the proposed detection method, a constrained estimation of the positive and negative phasors and the frequency deviation is obtained for both balanced and unbalanced situations. The theoretical and numerical performance analyses show improved performance over benchmark techniques and robustness to the presence of additional harmonics.

stat.AP↗

arXiv2010

General Classes of Lower Bounds on the Probability of Error in Multiple Hypothesis Testing

In this paper, two new classes of lower bounds on the probability of error for $m$-ary hypothesis testing are proposed. Computation of the minimum probability of error which is attained by the maximum a-posteriori probability (MAP) criterion is usually not tractable. The new classes are derived using Holder's inequality and reverse Holder's inequality. The bounds in these classes provide good prediction of the minimum probability of error in multiple hypothesis testing. The new classes generalize and extend existing bounds and their relation to some existing upper bounds is presented. It is shown that the tightest bounds in these classes asymptotically coincide with the optimum probability of error provided by the MAP criterion for binary or multiple hypothesis testing problem. These bounds are compared with other existing lower bounds in several typical detection and classification problems in terms of tightness and computational complexity.

cs.IT↗