Conclusion

The complete set of recursions (equations (3), (5), (4), (7), (9)), along with the initializations, is formulated in the sketch of the general LSL algorithm at the end of the paper (appendix A). As in any recursive method, we have access to the residuals for all intermediate lengths of the prediction filter. The basic concept is that a residual at time T is computed from the minimization problem on the window [0,T], and does not depend on future data, which is a first way to make the algorithm adaptive. The second way is to introduce an exponential tapering, which forces the algorithm to forget the ``old data''.