Quantitative Verification of Numerical Stability for Kalman Filters

Evangelidis, Alexandros; Parker, David

doi:10.1007/978-3-030-30942-8_26

Cited by 5 publications

(1 citation statement)

References 17 publications

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“…In this connection, formal verification/model checking of system can be attempted through various ways [16,17]. As far as different applications of Markov chains/formal methods are concerned, the applicability can be seen such as in power systems preventive maintenance of equipment [18], stochastic games [19,20], filter design [21], DNA technology [22], robotics [23] etc.…”

Section: Introductionmentioning

confidence: 99%

Ethernet-Based Fault Diagnosis and Control in Smart Grid: A Stochastic Analysis via Markovian Model Checking

Uddin

Alghamdi

Uddin

et al. 2019

J. Electr. Eng. Technol.

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The fault diagnosis and control through fault detection, isolation and supply restoration (FDIR) technique is the part of a commonly used distribution management system application in smart grid. When the fault occurs, it becomes essential to detect and isolate the faulty section of the distribution network at once and then restore back to its running condition through tie switches. The communication between IEDs is done through different communication mediums such as Ethernet, wireless, power line communication etc. Therefore, formal analysis of the FDIR mechanism is required with communication network (ideally Ethernet), which helps us to predict the behavior of FDIR response upon the occurrence of fault in terms of various important probabilities, reliability study and efficiency (showing the system will work properly). In this regard, for the above said analyses, this article discusses (a) the development of the Markovian model of FDIR for distribution network of smart grid considering Tianjin Electric Power Network as case study with intelligent electronic devices (IEDs) using ideal communication medium (Ethernet); (b) utilized probabilistic model checker (PRISM tool) to predict the probabilities; (c) perform the reliability analyses and (d) study the efficiency of FDIR behavior for future grid using logical properties. The detailed analysis and prediction (done for the fault occurrence scenario) mainly focus in determining the (1) the probability of switching failures of FDIR in smart grid; (2) the probability of isolating the defective switch from the system within limited time and (3) the probability of restoring the system automatically within the minimum possible interval. KeywordsFDIR • Ethernet • Smart grid • Markov model • Model checking • Stochastic analysis Abbreviations FDIR Fault detection, isolation and restore supply of system FTU Feeder terminal unit CB Circuit breaker DFA Distributed feeder automation FASM FDIR message start ISOM Isolation message result RESM Restoration message result IED Intelligent electrical device

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Section: Introductionmentioning

confidence: 99%

Ethernet-Based Fault Diagnosis and Control in Smart Grid: A Stochastic Analysis via Markovian Model Checking

Uddin

Alghamdi

Uddin

et al. 2019

J. Electr. Eng. Technol.

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Low-Complexity Square-Root Unscented Kalman Filter Design Methodology

Dutt

Acharyya

2023

Circuits Syst Signal Process

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Quantitative verification of Kalman filters

Evangelidis

Parker

2021

Form. Asp. Comput.

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Kalman filters are widely used for estimating the state of a system based on noisy or inaccurate sensor readings, for example in the control and navigation of vehicles or robots. However, numerical instability or modelling errors may lead to divergence of the filter, leading to erroneous estimations. Establishing robustness against such issues can be challenging. We propose novel formal verification techniques and software to perform a rigorous quantitative analysis of the effectiveness of Kalman filters. We present a general framework for modelling Kalman filter implementations operating on linear discrete-time stochastic systems, and techniques to systematically construct a Markov model of the filter's operation using truncation and discretisation of the stochastic noise model. Numerical stability and divergence properties are then verified using probabilistic model checking. We evaluate the scalability and accuracy of our approach on two distinct probabilistic kinematic models and four Kalman filter implementations.

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Quantitative Verification of Numerical Stability for Kalman Filters

Cited by 5 publications

References 17 publications

Ethernet-Based Fault Diagnosis and Control in Smart Grid: A Stochastic Analysis via Markovian Model Checking

Ethernet-Based Fault Diagnosis and Control in Smart Grid: A Stochastic Analysis via Markovian Model Checking

Low-Complexity Square-Root Unscented Kalman Filter Design Methodology

Quantitative verification of Kalman filters

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