Efficient implementation of the multistage Wiener filter for multiple beam applications

A new implementation of the multistage Wiener filter (MWF) is developed for constrained filtering applications, such as radar surveillance, that require the formation of many filter vectors. The MWF is a "signal-dependent" reduced rank adaptive filter, which means that it uses the steering vector to form its basis for rank reduction. Signal-dependent processing provides a performance improvement, but typically causes computer operations to grow linearly with the number of filters. The algorithm introduced in this paper uses a single SVD in order to impose a diagonal structure on the data matrix. By using Householder reflections for the MWF blocking matrix the diagonal structure is preserved and exploited during subsequent calculations. The new algorithm takes advantage of the recently discovered connection between the MWF and the method of conjugate gradients. Timing results demonstrate more than an order of magnitude speed improvement over the conventional MWF.