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This paper is concerned with problems in which the interference present in a primary signal is reduced using a sum of M linearly-filtered reference signals. These latter signals contain interference components which are correlated with that present in the primary. Examples occur in antenna array processing and in multiple-axis seismometer recordings of geophysical data. In the structures of interest, the linear filters are adaptive and employ a lattice configuration. Previous work in this area has been restricted to the case of a single reference signal. The multiple-reference case is shown to have unique characteristics which do not appear in the single-dimensional case. Examples illustrating this difference are presented.