KALMAN FILTER OPTIMIZED CUBIC SPLINE FUNCTIONS FOR DIGITAL SMOOTHING

The potential of a computational procedure for the automatic selection of the optimal knot distributions of spline functions for smoothing of noisy data has been investigated. The procedure is based on the use of cubic truncated power bases as linear estimators of the smoothing spline functions, and on the Kalman filter algorithm for computing the best least-squares values of the power basis coefficients. The optimal placement of the knots is selected by examination of the innovations sequence and through a strategy suitable for testing the model validity for each set of incoming data. The theory of the method is described, and its application to smoothing of both synthetic and experimental signals is illustrated.