Least Squares Approximation
The celebrated concept of least squares approximation is introduced in this chap-ter. Least squares can be used in a wide variety of categorical applications, including: curve fitting of data, parameter identification, and system model realization. Many examples from diverse fields fall under these categories, for instance determining the damping properties of a fluid-filled damper as a function of temperature, identification of aircraft dynamic and static aerodynamic coefficients, orbit and attitude determination, position determination using triangulation, and modal identification of vibratory systems. Even modern control strategies, for instance certain adaptive controllers, use the least squares approximation to update model parameters in the control system. The broad utility implicit in the aforementioned examples strongly confirms that the least squares approximation is worthy of study.