Parameter-Estimation Approaches for Inherently Unstable/Augmented Aircraft

In certain practical applications, it is required to estimate the parameters of the open loop system (which might be inherently unstable) from the data generated when the system is operating in a closed loop. The feedback causes correlations between the input and output variables and identifiability problems. In the augmented system, the measured responses would not display the modes of the system adequately as the feedback is generating controlled responses. The complexity of the estimation problem is more when the basic system is unstable because the integration of the state model could lead to numerical divergence and the measured data would be usually corrupted by process and measurement noises. The EEM does not involve direct integration of the system’s equations and hence can be used for parameter estimation of such unstable systems. The EKF-UD approaches can be used for parameter estimation of unstable systems because of the inherent stabilization properties of the filters [1]. OEM poses some difficulties when applied to highly unstable systems since the numerical integration of the unstable state model equa­tions would lead to divergence. One can provide artificial stabilization in the model (in the software algorithm) used for parameter estimation resulting in the feedback – in-model method. This requires good engineering judgment. Another way to cir­cumvent this problem is to use measured states in the estimation, leading to the stabilized output error method (SOEM) [1]. The FEM is the most general approach to the problem of parameter estimation. FEM treats the errors arising from data

correlation as process noise, which is suitably accounted for by the KF part of FEM. A detailed exposition of FEM is given in Refs. [1,5].