Mixed H/sup 2//H/sup /spl infin// estimation: posteriori and priori adaptive filtering

We examine the possibility of combining H/sup 2/ (least-mean-squares) performance with H/sup /spl infin//-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/sup /spl infin// bound. A simple example is presented to compare the algorithm's behaviour with the H/sup /spl infin// adaptive filter and other mixed algorithms.