#### Technical Report USC-SIPI-117-2

“Lattice Algorithms for Recursive Instrumental Variable Methods”

by Ananthram Swami and Jerry M. Mendel

December 1987

We develop a recursive lattice algorithm for the estimation of the parameters of an AR process, using a 1-D slice of the k-th order cumulant. The cumulant matrix can be viewed as the cross-correlation of the observed process, y(n), and an associated process, z(n), and, y(n) and the other by z(n), the lattices being coupled through order- and time-update equation-conventional orthogonality conditions. Extensions to ARMA processes are discussed. The joint-process estimation problem is also treated. Some statistical analysis is carried out and convergence results are given when y(n) and z(n) can be modeled as stationary processes. The only assumption that we make about z(n) the associated process, is that the cross-correlation of y(n) and z(n) suffices for the estimation of the AR parameters, i.e., we assume that z(n) is an instrumental process Consequently, our algorithm, in fact, provides an adaptive lattice version of the multichannel recursive instrumental variable method.

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