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.

Citation

Farnoosh, R. and Hajrajabi, A. (2013), "Estimation of parameters in the state space model of stochastic RL electrical circuit", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 32 No. 3, pp. 1082-1097. https://doi.org/10.1108/03321641311306141