An approach to stabilizing the fast array RLS adaptive filter using homogeneous coordinates in projective geometry

The fast array RLS (FARLS) adaptive filter employs a circular and hyperbolic rotation to transform from a pre-array to a post-array. The algorithm is known to be numerically unstable for finite-precision implementations. It is believed that the difficulty lies in the numerical computation of the hyperbolic rotation. We propose the use of homogeneous coordinates in projective geometry to transform the hyperbolic rotation to a circular rotation. This rotation (being circular) is numerically stable. However, the transformation to the new circular representation in the projective coordinates is still numerically difficult. Nevertheless, this method may lead to a new approach that completely circumvents the instability.