A COMPARATIVE-STUDY OF MAXIMUM-LIKELIHOOD ESTIMATORS FOR NONLINEAR DYNAMICAL SYSTEM MODELS

Estimating nonlinear stochastic dynamical system models from discrete observation is discussed. Nonlinear dynamical system models with obser vation noise as well as system noise is practically useful for describ ing the time evolution of dynamic phenomena. The models will work only if their parameters are set appropriately. Then, the models must be e stimated from real data which are almost always observed at discrete t imes. Generally nonlinear models in continuous time are not easy to es timate. With linear approximation of a nonlinear dynamical system mode l, it can be transformed into a discrete state space model. Using the discretized model together with the Kalman filter algorithm, the param eters of the model can be estimated from discrete observation via maxi mum likelihood technique. What linear approximation is used is critica l for performance of estimation. This paper considers two linear appro ximations; the first order linear approximation used in the extended K alman filter and a second order linear approximation based on Ito's fo rmula. Applying these linear approximations to Van der Pol's random os cillation and Rayleigh's random oscillation, we make a numerical compa rison of the performance of the two maximum likelihood estimators by M onte Carlo experiments. In addition, it is also important for estimati ng continuous time models from discrete observation to evaluate how mu ch the performance of estimation is dependent on time interval of disc rete observation. We examine the influence of time interval on estimat ion.