Deconvolution of Multiple Time Series

The problem of estimating simultaneously two convolved vector time series corrupted by additive noise is considered. By regarding one of the series as being stochastic and the other as fixed, it is shown that the fixed component can be estimated by maximizing a frequency domain approximation to the likelihood. The stochastic series is estimated by using an approximation to the conditional mean evaluated at the current maximum likelihood estimators. An example involving a multiple deconvolution of seismic source and receiver functions is given.