Spline Approximation as a Tool for Estimation

The functions, which describe the time evolution of a dynamic system, are approximated by means of splines. The unknown spline coefficients are estimated by processing noisy measurements of observable system variables, by collocating the system differential equation, and by using a-priori information. The arising overdetermined linear algebraic system in the spline coefficients is solved in a weighted least squares sense, with weights equal to the inverses of the appropriate standard deviations.