Abstract: An adaptive filter is implemented by a computer (10) processing an input signal using a recursive least squares lattice (RLSL) algorithm (12) to obtain forward and backward least squares prediction residuals. A prediction residual is the difference between a data element in a sequence of elements and a prediction of that element from other sequence elements. Forward and backward residuals are converted at (14) to interpolation residuals which are unnormalised Kalman gain vector coefficients. Interpolation residuals are normalised to produce the Kalman gain vector at (16). The Kalman gain vector is combined at (18) with input and reference signals x(t) and y(t), which provides updates for the filter coefficients or weights to reflect these signals as required to provide adaptive filtering.