Learning algorithms and underlying basic mathematical ideas are presen
ted for the problem of adaptive blind signal processing, especially in
stantaneous blind separation and multichannel blind deconvolution/equa
lization of independent source signals. We discuss recent developments
of adaptive learning algorithms based on the natural gradient approac
h and their properties concerning convergence, stability, and efficien
cy. Several promising schemas ale proposed and reviewed in the paper.
Emphasis is given to neural networks or adaptive filtering models and
associated online adaptive nonlinear learning algorithms. Computer sim
ulations illustrate the performance of the developed algorithms. Some
results presented in this paper are new and are being published for th
e first time.