A systolic array for RLS and CRLS estimation

The linear least squares problem is one of the oldest problems in applied mathematics, with numerous applications throughout modern engineering. In the traditional information matrix approach to recursive least squares (RLS) estimation, a triangular factor R of A is updated to a triangular factor R of R_ of A_, by means of orthogonal transformations, and then a triangular backsolve is performed to get the updated least squares solution x__LS. It is well known that these two separate computational steps as such cannot be pipelined on a parallel processor array. The authors focus on an alternative covariance matrix approach to RLS estimation, and show how a parallel implementation can be derived. Furthermore, it is shown how to extend this covariance-type algorithm/architecture to constrained RLS (CRLS) estimation