Relation between RLS and ARMA Lattice Filter Realization Algorithm and Its Application

Miki HASEYAMA  Nobuo NAGAI  Hideo KITAJIMA  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E77-A   No.5   pp.839-846
Publication Date: 1994/05/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Signal Processing and System Theory)
Category: 
Keyword: 
system identification,  ARMA,  RLS,  lattice filter,  frequency weighting,  

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Summary: 
In this paper, the relationship between the recursive least square (RLS) method with a U-D decomposition algorithm and ARMA lattice filter realization algorithm is presented. Both the RLS method and the lattice filter realization algorithm are used for the same applications, such as model identification, etc., therefore, it is expected that the lattice filter algorithm is in some ways related to the RLS. Though some of the proposed lattice filter algorithms have been derived by the RLS method, they do not express the relationship between RLS snd ARMA lattice filter realization algorithm. In order to describe the relation clearly, a new structure of ARMA lattice filter is proposed. Further, based on the relationship, a method of model identification with frequency weighting (MIFW), which is different from a previous method, is derived. The new MIFW method modifies the lattice parameters which are acquired without a frequency weighting and obtain the parameters of an ARMA model, which is identified with frequency weighting. The proposed MIFW method has the following restrictions: (1) The used frequency weighting is FIR filter with a low order. (2) By using the parameters of the ARMA lattice filter with ARMA (N,M) order and the frequency weighting with L order, the new ARMA parameter with the frequency weignting is with ARMA(N-L,M-L) order. By using the proposed MIFW method, the ARMA parameters estimated with the frequency weighting can be obtained without starting the computation again.