On gradient adaptation with unit-norm constraints

In this correspondence, we describe gradient-based adaptive algorithms within parameter spaces that are specified by ||w||=1, where ||·|| is any vector norm. We provide several algorithm forms and relate them to true gradient procedures via their geometric structures. We also give algorithms that mitigate an inherent numerical instability for L2-norm-constrained optimization tasks. Simulations showing the performance of the techniques for independent component analysis are provided