Estimation of stochastic signals under partially missing information

• The piecewise linear interpolation filter is developed to estimate missing signals.
• A priori information can be obtained on only a few signals.
• The filter is defined in terms of pseudo-inverse matrices and therefore is always well defined.
• The proposed filter mitigates to some extent the difficulties associated with known approaches.

A new method for the estimation of a large set of stochastic signals is proposed and justified. A specific restriction is that a priori information on the set of input–output signal pairs can only be obtained, in the form of covariance matrices (or their estimates), for a small subset of signal pairs. Nevertheless it is required to estimate each reference signal. We call this procedure signal estimation under partially missing information. The conceptual foundation of the proposed filter is an optimal least squares Hadamard-quadratic estimate of the incremental change to the observed signal pairs, extended by a natural linear interpolation to an estimated value for each intermediate reference signal. The new filter is expressed in terms of Moore–Penrose pseudo-inverse matrices and therefore is always well-defined.