Mixed H2/H∞ estimation: posteriori and priori adaptive filtering

We examine the possibility of combining H² (least-mean-squares) performance with H^∞-optimal performance in adaptive filtering. It is shown that the resulting adaptive algorithms allow for a trade-off between average and worst-case performances and are most applicable in situations in which, because of modelling errors, the exact statistics of the underlying signals are not known. A nonlinear adaptive filter that recursively minimizes the LMS error over all filters that guarantees a prespecified worst-case H^∞ bound. A simple example is presented to compare the algorithm´s behaviour with the H^∞ adaptive filter and other mixed algorithms.