Parameter estimation in continuous-time stochastic systems with correlated noises using the Kalman filter and Least Squares Method

Abstract

In this paper we present the problem of parameter estimation in continuous-time stochastic systems under coloured or correlated noises. The Least Squares Method (LSM) is a classical approach, but the estimation usually presents bias in stochastic systems. Here we combine this technique with a Kalman filter, that will minimize the noise effect, and will improve the estimation algorithm performance. The Instrumental Variable method will be implemented too, in order to analyse which method is more suitable for systems with coloured noises. The effectiveness of the proposed methods will be illustrated with a numerical example.