A New Network for Particle Filtering of Multivariable Nonlinear Objects †

Piotr Kozierski, Jacek Michalski, Joanna Zietkiewicz, Marek Retinger and Wojciech Retinger and Wojciech Giernacki
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Piotr Kozierski: Faculty of Computing and Telecommunications, Institute of Computing Science, Poznan University of Technology, 60-965 Poznań, Poland
Jacek Michalski: Faculty of Control, Robotics and Electrical Engineering, Institute of Robotics and Machine Intelligence, Poznan University of Technology, 60-965 Poznań, Poland
Joanna Zietkiewicz: Faculty of Control, Robotics and Electrical Engineering, Institute of Robotics and Machine Intelligence, Poznan University of Technology, 60-965 Poznań, Poland
Marek Retinger and Wojciech Retinger: Faculty of Control, Robotics and Electrical Engineering, Institute of Robotics and Machine Intelligence, Poznan University of Technology, 60-965 Poznań, Poland
Wojciech Giernacki: Faculty of Control, Robotics and Electrical Engineering, Institute of Robotics and Machine Intelligence, Poznan University of Technology, 60-965 Poznań, Poland

Energies, 2020, vol. 13, issue 6, 1-34

Abstract: In this paper, a new object in the form of a theoretical network is presented, which is useful as a benchmark for particle filtering algorithms designed for multivariable nonlinear systems (potentially linear, nonlinear, and even semi-Markovian jump system). The main goal of the paper is to propose an object that potentially can have similar to the power system grid properties, but with the number of state variables reduced twice (only one state variable for each node, while there are two in the case of power systems). Transition and measurement functions are proposed in the paper, and two types of transition functions are considered: dependent on one or many state variables. In addition, 10 types of measurements are proposed both for branch and nodal cases. The experiments are performed for 14 different, four-dimensional systems. Plants are both linear and highly nonlinear. The results include information about the state estimation quality (based on the mean squared error indicator) and the values of the effective sample size. It is observed how the higher effective sample size resulted in the better estimation quality in subsequent cases. It is also concluded that the very low number of significant particles is the main problem in particle filtering of multivariable systems, and this should be countered. A few potential solutions for the latter are also presented.

Keywords: sequential importance resampling; multidimensional systems; particle filter; nonlinear plants; state estimation; power system grid (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
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