Two numerical differentiation techniques for nonlinear state estimation

Quite successfully regularization methods have been used in the numerical analysis literature in approaches to the ill-posed problem of numerically differentiating a signal from its discrete, potentially uncertain, samples. One of these approaches proposed an algorithm for the computation of an optimal spline whose first derivatives are estimates of the first derivatives of the signal. These algorithms suffer from a large amount of computation they imply. We propose two versions of this smoothing spline computation algorithm which reduce the computation burden, and thus, yield two potentially valuable tools to the design problem of online nonlinear state estimators