In adaptive signal processing, joint process estimation plays
an important role in various estimation problems. It is well
known that a joint process estimator consists of two struc-
tures, namely the orthogonalizer and the regression filter. In
literature, orthogonalization step is performed either by or-
thogonal transformations or by linear predictors. While the
orthogonal transformations do not preserve entropy; the
predictors, such as the lattice, do preserve it. However, the
steady-state performance of such linear predictors is not as
good as those of the orthogonal transformations. Lattice
filters do not perform perfect orthogonalization when they
operate as gradient-based adaptive predictors. In this work,
adaptive escalator predictor is proposed to be used as the
orthogonalizer of the joint process estimator. The proposed
method preserves the entropy and achieves perfect orthogo-
nalization at all times. Moreover it has good steady-state
performance compared to those structures utilizing gradient
adaptive lattice filters.