NDLI: A classification of algorithms for ARMA models and ladder realizations

Content Provider	IEEE Xplore Digital Library
Author	Morf, M. Lee, D. Nickolls, J. Vieira, A.
Copyright Year	1977
Description	Author affiliation: Stanford University, Stanford, CA (Morf, M.)
Abstract	Applications of linear systems modeling have recently developed quite rapidly in speech modeling, seismic data processing, and other areas. Due to the diversity of these developments, there exists a plethora of methods for estimating the parameters of linear models given input-ouput data, transfer functions, or covariance functions. This paper attempts a systematic classification of existing least-squares modeling methods. Within this framework, we shall point out some recently developed algorithms that have many computational advantages over existing ones. In particular, the methods of interest will be classified according to how the input/output data is acessed and according to its type. Data can be accessed either sequentially or in blocks; the data can be either input/output signals, transfer functions, or covariance functions. Since we consider state-space, autoregressive-moving average models, and the related ladder realizations, we shall distinguish the following three classes of algorithms: Riccali or square-root type methods, recently developed "fast" algorithms, and their ladder forms. While the first class typically requires computations of $O(n^{3})$ or $O(n^{2})$ with n equal to the number of model parameters, the "last" forms only require operations and storage of O(n). The ladder realizations have several advantages, such as lowest complexity and their stability "by inspection" properties. In the appendices, we present an example of our new exact least-squares recursions for ladder forms, and show how to obtain stable partial minimal realizations of the joint impulse response - and covariance - matching type.
Starting Page	13
Ending Page	19
File Size	457116
Page Count	7
File Format	PDF
DOI	10.1109/ICASSP.1977.1170231
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1977-05-09
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Classification algorithms Transfer functions Contracts Information systems Laboratories Stability Inspection Time factors History Technological innovation
Content Type	Text
Resource Type	Article

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