Fast derivative computation using smooth X-splines

Piecewise cubic polynomials, namely X-splines, are applied as smooth approximations by regularization. The method reduces the computations while estimating the derivatives when the data has noise. The regularization parameter is chosen which helps to smooth the data and find the derivative with less computation. The convergence of the computed derivative to the exact derivative is also analyzed. Example from satellite orbit determination is used to demonstrate the efficacy for fast computation though a posteriori method is found useful to obtain satisfactory performance.