TABLE OF CONTENTS The estimation before modelling (EBM) methodology is essentially a two-step approach [1 3]. In the first step, the extended Kalman filter is used for state estimation. The filtered states or their derivatives/related variables are used in the next step of regression analysis. Thus, the parameter estimation is separated into two independent steps. This is unlike the output error method, where parameter estimation is accomplished in essentially one-step, though in an iterative manner. In the output error method, the model structure has to be defined a priori whereas in estimation before modelling, this is taken care of in the second step only. Often smoothing techniques are used in the first step to minimise errors from the extended Kalman filter. The main advantage of the EBM approach is that state estimation is accomplished before any modelling is done. For state estimation, usual system dynamics, which might have only a descriptive mathematical model, is used. In the second step of regression analysis, one can evolve the most suitable detailed mathematical model, the parameters of which are estimated using the least squares method. It is here that model selection criteria play an important role. Another advantage of the estimation before modelling approach is that it can be used to handle data from inherently unstable/augmented systems. In addition, this approach has great utility for aircraft parameter estimation.
In state reconstruction, the nonlinear functions arise due to augmentation of the state vector with unknown sensor bias and scale factors, which also need to be...
