FAST TRANSVERSAL VERSIONS OF THE RIV ALGORITHM

The system of linear equations A(n)w(n) = b(n), where A(n) is the samp le cross-correlation matrix between an observed process and an instrum ental variable process and b(n) is the cross-correlation vector betwee n some desired process and the instrumental variable process, is frequ ently encountered. For example, the 'normal' equations for the AR para meters of ARMA processes based on cumulants can be interpreted as cros s-correlation matrices. For a p x p matrix A(n) the recursive instrume ntal variable (RIV) algorithm requires computations of order p(2). We develop exact fast versions which require computations of order p. Thi s is a generalization of the fast transversal filter algorithms of Cio ffi et al., who assume the matrix A to be Hermitian. Additionally, we analyse the tracking behaviour and misadjustment aspects of RIV when l ambda , the forgetting factor, is less than unity.