TABLE OF CONTENTS The output error method discussed in Chapter 3 is perhaps the most widely used approach for parameter estimation. It has several nice statistical properties and is relatively easy to implement. In particular, it gives good results when the data contain only measurement noise and no process noise. However, when process noise is present in the data, a suitable state estimator is required to obtain the system states from noisy data. For a linear system, the Kalman filter is used, as it happens to be an optimal state estimator. For nonlinear systems, there is no practical optimal state estimator and an approximate filter based on system linearisation is used.
There are two approaches to handle process noise in the data: i) filtering methods, e.g., the extended Kalman filter; and ii) the filter error methods. An optimal nonlinear filter is required for computing the likelihood function exactly. The extended Kalman filter can be used for nonlinear systems and the innovations computed from this approach are likely to be white Gaussian if we can assure that the measurements are frequent.
In Chapter 4, the extended Kalman filter was applied to data with process noise for state as well as parameter estimation. The model parameters in this filtering technique are included as additional state variables (state augmentation). The most attractive feature of this approach is that it is one-pass and therefore computationally less demanding. However, experience with the use of the extended Kalman filter for parameter estimation reveals that the estimated parameter...
