Tradeoffs in the estimation problem with respect to two performance criteria

We study a class of suboptimal group filters derived from a filter with a diagonal impulse response matrix to which off-diagonal entries are being added in a systematic way. Two different approaches of trading off computational and stochastical performances of the resulting filters are discussed. The systematic procedures-both in the time and in the spectral domains-are for achieving a desired tradeoff between the two criteria. Examples of filtering of 1st order Markov processes out of a white noise are given. The results are compared with the optimal Wiener filter under similar conditions. It is shown that for group filters and 1st order Markov processes, significant computational gains can be achieved at the expense of small deviations from the optimal stochastical performance