Systematic estimation of state noise statistics for extended Kalman filters

The successful application of model-based control depends on the information about the states of the dynamic system. State-estimation methods, like extended Kalman filters (EKF), are useful for obtaining reliable estimates of the states from a limited number of measurements. They also can handle the model uncertainties and the effect of unmeasured disturbances. The main issue in applying EKF remains that one needs to specify the confidence in the model in terms of process noise covariance matrix. The information about the model uncertainties can effectively and systematically calculate the process noise covariance matrix for an EKF. Two systematic approaches are used for this calculation. The first is based on a Taylor series expansion of the nonlinear equations around the nominal parameter values, while the second accounts for the nonlinear dependence of the system on the fitted parameters by Monte Carlo simulations that can easily be performed on-line. The value of the process noise covariance matrix obtained is not limited to a diagonal form and depends on the current state of the dynamic system. Thus the a-priori information regarding the uncertainty in the model is utilized and the need for extensive tuning of the EKF is eliminated. The application of these techniques to example processes is also discussed. The accuracy of this methodology is compared very favorably with the traditional methods of trial-and-error turning of EKF.