I. Introduction

Having Dealt in the previous chapter with the formulation of nonlinear state-space model postulates to define the cause effect relationship purported to underlie the physical phenomenon, and having elaborated on the simulation (i.e., computation of system responses) using numerical procedures, we now turn our attention to the first of the two central methods of aircraft parameter estimation, namely the output error method. The other method, called the filter error method, will be discussed in the next chapter. Both of these methods belong to a general class of output error, also called response curve fitting, methods. The class of estimation methods called the equation error methods will be considered separately. In this class of output error methods, model parameters are adjusted iteratively to minimize the error between the measured variables (system output) and the estimated (model predicted) responses. The method, however, leads to a nonlinear optimization problem, in which the computational burden is relatively high. The method of weighted least squares, the simplest among this class, accounts for measurement noise. However, it assumes a priori specification of the weighting matrix. Based on probability theory, a more profound formulation called the maximum-likelihood principle was provided by Fisher.1 3 It can handle both process and measurement noise, and has several desirable statistical properties of a good estimator. This chapter considers the case where we assume that the process noise is negligible and that the measurements are corrupted by additive measurement noise only. It leads to the output error method (OEM). The...