Abstract
In many applications, a priori information on a large set of signals of interest can only be obtained for a few signals, p, while information on other signals is missing. At the same time, it is required to estimate each reference signal. The signal is a stochastic vector and the observations are noisy. The conceptual foundation of the proposed filter is an optimal least squares linear estimate of the incremental change to the p signal pairs, extended by a natural interpolation to an estimated value of each reference signal. The new filter is expressed in terms of the Moore-Penrose pseudo-inverse matrices and therefore is always well-defined.