Abstract Particle filters avoid parametric estimates for Bayesian posterior densities, which alleviates Gaussian assumptions in nonlinear regimes. These methods, however, are more sensitive to sampling errors than Gaussian-based techniques such as ensemble Kalman filters. A recent study by the authors introduced an iterative strategy for particle filters that match posterior moments—where iterations improve the filter’s ability to draw samples from non-Gaussian posterior densities. The iterations follow from a factorization of particle weights, providing a natural framework for combining particle filters with alternative filters to mitigate the impact of sampling errors. The current study introduces a novel approach to forming an adaptive hybrid data assimilation methodology, exploiting the theoretical strengths of nonparametric and parametric filters. At each data assimilation cycle, the iterative particle filter performs a sequence of updates while the prior sample distribution is non-Gaussian, then an ensemble Kalman filter provides the final adjustment when Gaussian distributions for marginal quantities are detected. The method employs the Shapiro–Wilk test to determine when to make the transition between filter algorithms, which has outstanding power for detecting departures from normality. Experiments using low-dimensional models demonstrate that the approach has a significant value, especially for nonhomogeneous observation networks and unknown model process errors. Moreover, hybrid factors are extended to consider marginals of more than one collocated variables using a test for multivariate normality. Findings from this study motivate the use of the proposed method for geophysical problems characterized by diverse observation networks and various dynamic instabilities, such as numerical weather prediction models. Significance Statement Data assimilation statistically processes observation errors and model forecast errors to provide optimal initial conditions for the forecast, playing a critical role in numerical weather forecasting. The ensemble Kalman filter, which has been widely adopted and developed in many operational centers, assumes Gaussianity of the prior distribution and solves a linear system of equations, leading to bias in strong nonlinear regimes. On the other hand, particle filters avoid many of those assumptions but are sensitive to sampling errors and are computationally expensive. We propose an adaptive hybrid strategy that combines their advantages and minimizes the disadvantages of the two methods. The hybrid particle filter–ensemble Kalman filter is achieved with the Shapiro–Wilk test to detect the Gaussianity of the ensemble members and determine the timing of the transition between these filter updates. Demonstrations in this study show that the proposed method is advantageous when observations are heterogeneous and when the model has an unknown bias. Furthermore, by extending the statistical hypothesis test to the test for multivariate normality, we consider marginals of more than one collocated variable. These results encourage further testing for real geophysical problems characterized by various dynamic instabilities, such as real numerical weather prediction models.
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Detection of Gaussian Attacks in Power Systems under a Scalable Kalman Consensus Filter Framework
The dynamic non-linear state-space model of a power-system consisting of synchronous generators, buses, and static loads has been linearized and a linear measurement function has been considered. A distributed dynamic framework for estimating the state vector of the power system has been designed here. This framework employs a type of distributed Kalman filter (DKF) known as a Kalman consensus filter (KCF) which
is located at distributed control centers (DCCs) that fuse locally available noise ridden measurements, state vector estimates of neighboring control centers, and a prediction obtained by the linearized model to obtain a filtered state vector estimate. Further, the local residual at each control center is checked by a median chi-squared detector designed here for bad data/Gaussian attack detection. Simulation results show the working of the KCF for an 8 bus 5 generator system, and the efficacy of the median chi-squared detector in detecting the DCC affected by Gaussian attacks.
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- Award ID(s):
- 1837472
- NSF-PAR ID:
- 10299541
- Date Published:
- Journal Name:
- 2021 IEEE PES General Meeting
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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