Nonparametric Fixed-Interval Smoothing of Nonlinear Vector-Valued Measurements

Abstract

The problem of estimating a smooth vector-valued function given noisy nonlinear vector-valued measurements of that function is addressed. A nonparametric optimality criterion for this estimation problem is presented, and a computationally efficient iterative algorithm for its solution is developed. The criterion is the natural generalization of previously published work on vector splines with linear measurement models. The algorithm provides an alternative to the extended Kalman filter, as it does not require a parametric state-space model. An automatic procedure that uses the measurements to determine how much to smooth is presented. The algorithm's subpixel estimation accuracy is demonstrated on the estimation of a curved edge in a noisy image and on a biomedical image-processing application.