Fast transversal versions of the RIV algorithm
Ananthram Swami · International Journal of Adaptive Control and Signal Processing · 1996
The system of linear equations A(n)w(n)=b(n) where A(n) is the sample cross-correlation matrix between an observed process and an instrumental variable process and b(n) is the cross-correlation vector between some desired process and the instrumental variable process, is frequently encountered. For example, the ‘normal’ equations for the AR parameters of ARMA processes based on cumulants can be interpreted as cross-correlation matrices. For a p × p matrix A(n) the recursive instrumental variable (RIV) algorithm requires computations of order p2. We develop exact fast versions which require computations of order p. This is a generalization of the fast transversal filter algorithms of Cioffi et al., who assume the matrix A to be Hermitian. Additionally, we analyse the tracking behaviour and misadjustment aspects of RIV when λ, the forgetting factor, is less than unity.