How to Deal with Parameter Estimation in Continuous-Time Stochastic Systems

In this paper, we present some options to deal with the problem of parameter estimation in continuous-time stochastic systems under white, and coloured noise perturbations using classical methods. Least-squares method (LSM) is one of the most widely used estimation methods, in continuous and discrete time systems, but it presents a bias problem. The instrumental variable method (IV), even though is considered the best option when a noise is present in the system dynamics, cannot completely minimize its effect in continuous time. Here, we propose to combine these algorithms with two auxiliary techniques: the Kalman filter and the equivalent control. These techniques working in parallel with the LSM and IV estimation algorithm will reduce the bias, the noise effect in the estimated parameters, and are very easy to implement. The effectiveness of the proposed methods is illustrated in a numerical example.