Nonparametric Fixed-Interval Smoothing with Vector Splines

Abstract

A computationally efficient algorithm for nonparametric smoothing of vector signals with general measurement covariances is presented. This algorithm provides an alternative to the optimal smoothing algorithms that hinge on (possibly inaccurate) parametric state-space models. Automatic procedures that use the measurements to determine how much to smooth are developed and compared. This adaptation allows the data to speak for itself without imposing a Gauss-Markov model structure. A nonparametric approach to covariance estimation for the case of independently identically distributed (i.i.d.) measurement errors is presented. Monte Carlo simulations demonstrate the performance of the algorithm.