Estimation of parameters in the state space model of stochastic RL electrical circuit

Abstract

Purpose -The purpose of this paper is to consider the stochastic differential equation of the RL electrical circuit as the dynamic model of a state space system when the current in the circuit is hidden and corrupted by the measurement noise. Estimation of the corrupted current and the values of missing or unknown parameters (resistance, the observed current variance in the measurement model, the mean and variance of the current prior distribution) which are the main concern in electrical engineering is considered. Design/methodology/approach -Optimal filtering is proposed for estimation of the hidden current from the noisy observations. Also, the problem of analyzing this model based on estimation of the unknown parameters is addressed from the likelihood-based and Bayesian perspective. Findings -Computational techniques for parameter estimation are carried out by the Maximum likelihood (ML) approach using Expectation-Maximization type optimization and Bayesian Monte Carlo perspective using Metropolis-Hastings scheme. The explicit formulas for the ML estimator are obtained and it is shown that the smoothers, the filters and the predictions for the current have the best confidence intervals, respectively. Some numerical simulation examples which are performed by R programming software are considered to show the efficiency and applicability of the proposed approaches. Results show an excellent estimation of the parameters based on these approaches. Practical implications -Due to the fact that in an empirical situation of electrical engineering, observing the current in the circuit regardless of the measurement noise and knowing the exact value of the parameters are unrealistic assumptions, this paper can be used in various types of real time projects. Originality/value -To the best of the authors' information, the problem of analyzing the state space model of RL electrical circuit has not been studied before. Furthermore, the estimation of the hidden current as the state of the system and estimation of the unknown parameters of the model via both ML and Bayesian approaches have been investigated for the first time in the present study.

Skew Normal State Space Modeling of RC Electrical Circuit and Parameters Estimation based on Particle Markov Chain Monte Carlo

“…The assumption of skew normal measurement noise in the model makes variation (non-Gaussian) to the modeling of this circuit in comparison with the work (RL electrical circuit) which is considered in (Farnoosh and Hajrajabi, 2013) and makes the model be applicable in various types of real time projects. The SMC filter is proposed to track the hidden charge from the noisy observation.…”

“…Farnoosh and Hajrajabi, (2013) considered the state space modeling of stochastic RL electrical circuit and parameter estimation via ML and Bayesian approach. In this paper, the mathematical model of the RC electrical circuit as a series resistor-capacitor circuit is considered as stochastic differential equation (SDE) by adding some randomness to the ordinary differential equation.…”