An adaptive signal processing system utilizes a Multistage Weiner Filter having an analysis section and a synthesis section that includes a processor. The processor includes an algorithm for generating a data adaptive linear transformation, computing an adaptive weighting w.sub.med of the data, and applying the computed adaptive weighting w.sub.med to a function of a main input signal and an auxiliary input signal to generate an output signal. A plurality of building blocks in a Gram-Schmidt cascaded canceller-type configuration sequentially decorrelate input signals from each other to produce a single filtered output signal. Each building block generates an adaptive weight w.sub.med that is applied to generate a local output signal. The effect of non-Gaussian noise contamination on the convergence MOE of the system is negligible. In addition, when desired signal components are included in weight training data they cause little loss of noise cancellation.