The role of the likelihood function in the estimating of chaos models (Q2744939)

The present paper tries to show that the likelihood function can be a useful tool for the identification of continuous-time chaos models defined by deterministic differential equations with two types of noise processes, such as the system noise and the observation noise. The authors describe a form of nonlinear Kalman filter, called the local linearization (LL) filter, and demonstrate its usefulness both in discretizing the basic model and in estimating model parameters. By making use of the concept of innovation process it is explained how the likelihood may be defined in forms of the innovations from the LL filter. The effect of using the LL filter is illustrated on simulated Lorenz chaos and Rikitake two disk dynamo chaos data.