Smoothing and Interpolating Noisy GPS Data with Smoothing Splines

On Mixed Interpolating-Smoothing Splines and the ν-Spline

Approximating data with weighted smoothing splines∗

Given a data set (ti, yi), i = 1, . . . , n with the ti ∈ [0, 1] non-parametric regression is concerned with the problem of specifying a suitable function fn : [0, 1] → R such that the data can be reasonably approximated by the points (ti, fn(ti)), i = 1, . . . , n. If a data set exhibits large variations in local behaviour, for example large peaks as in spectroscopy data, then the method must ...

Smoothing with Cubic Splines

A spline function is a curve constructed from polynomial segments that are subject to conditions or continuity at their joints. In this paper, we shall present the algorithm of the cubic smoothing spline and we shall justify its use in estimating trends in time series. Considerable effort has been devoted over several decades to developing the mathematics of spline functions. Much of the intere...

Smoothing Noisy Data with Spline Functions *

I t is shown how to choose the smoothing parameter when a smoothing periodic spline of degree 2m -1 is used to reconstruct a smooth periodic curve from noisy ordinate data. The noise is assumed "white" , and the true curve is assumed to be in the Sobolev space W,(*ra) of periodic functions with absolutely continuous v-th derivative, v = 0, t . . . . . 2 m I and square integrable 2m-th derivativ...

Control theoretic smoothing splines

In this paper some of the relationships between optimal control and statistics are examined. We produce generalized, smoothing splines by solving an optimal control problem for linear control systems, minimizing the -norm of the control signal, while driving the scalar output of the control system close to given, prespecified interpolation points. We then prove a convergence result for the smoo...