TABLE OF CONTENTS To address the parameter estimation problem, we begin with the assumption that the data are contaminated by noise or measurement errors. We use these data in an identification/estimation procedure to arrive at optimal estimates of the unknown parameters that best describe the behaviour of the data/system dynamics. This process of determining the unknown parameters of a mathematical model from noisy input-output data is termed 'parameter estimation'. A closely related problem is that of 'state estimation' wherein the estimates of the so-called 'states' of the dynamic process/system (e.g., power plant or aircraft) are obtained by using the optimal linear or the nonlinear filtering theory as the case may be. This is treated in Chapter 4.
In this chapter, we discuss the least squares/equation error techniques for parameter estimation, which are used for aiding the parameter estimation of dynamic systems (including algebraic systems), in general, and the aerodynamic derivatives of aerospace vehicles from the flight data, in particular. In the first few sections, some basic concepts and techniques of the least squares approach are discussed with a view to elucidating the more involved methods and procedures in the later chapters. Since our approach is model-based, we need to define a mathematical model of the dynamic (or static) system.
The measurement equation model is assumed to have the following form:
| (2.1) |  |
where y is ( m 1) vector of true outputs and z is ( m 1) vector that denotes the measurements (affected by noise)...
