Parameter estimation using Kalman filters with constraints

We suggest incorporating dynamical information such as locations of unstable fixed points into parameter estimation algorithms in order to improve the method of reconstructing dynamics from time series data. We show how the process of reconstruction using nonlinear filters such as the extended Kalman filter can be easily modified to take advantage of the additional information. We demonstrate the methods using data from two systems exhibiting chaotic dynamics - the Chua circuit and Chen's equations. In both cases we find the models reconstructed using constraints that better approximate the unstable fixed point structure of the underlying systems.