ABSTRACT

This chapter presents a simple approach to the parameter estimation problem based on least squares estimation. The objective is to arrive at a practical set of formulas that can be applied to these types of problems. The chapter discusses the simplest estimation of a state variable for the scalar case. It suggests that the system identification problem will become a nonlinear sequential estimation problem. The systems identification problem or the parameter estimation problem arouses interest in all areas of engineering. The problem is to determine some or all of the system parameters based on measurements of the systems response. Thus, giving the spring-mass-damper model an initial displacement or velocity and measuring the response, one could then use this measured response to determine the effective spring constant and the effective damping constant of the tissue. This approach also has application to astronomy when one wishes to update the estimates of position and velocity as additional measurements or observations become available.