Publication:
Tensor formulations for the modelling of discrete-time nonlinear and multidimensional systems.

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Authors
Lenk, Peter John
Subjects
nonlinear system
nonlinear system modelling
Volterra series
tensor form of Volterra series
alternate coordinate systems
moving average
autoregressive
RLS algorithm
LMS algorithm
multidimensional system modelling
generalized lattice models
Levinson algorithm
Schur algorithm
2-D lattice models
nonlinear lattice models
systolic arrays
Advisors
Parker, Sydney R.
Date of Issue
1985-09
Date
September 1985
Publisher
Language
en_US
Abstract
The modelling of nonlinear and multidimensional systems from input and/or output measurements is considered. Tensor concepts are used to reformulate old results and develop several new ones. These results are verified through non-trivial computer simulations. A generalized tensor formulation for the modelling of discrete-time stationary nonlinear systems is presented. Tensor equivalents of the normal equations are derived and several efficient methods for their solution are discussed. Conditions are established that ensure a diagonal correlation tensor so that a solution can be obtained directly without matrix inversion. Using a tensor formulation, a new proof of the Generalized Lattice Theory is obtained. Tensor extensions of the Levinson and Schur algorithms are presented. New two-dimensional (2-D) lattice parameter models are derived. Using the tensor form of the Generalized Lattice Theory the 2-D multi-point error order-updates are decomposed into 0(N ) single point updates. 2-D extensions of the Levinson and Schur algorithms are given. The quarter plane lattice is considered in detail, first in a general form, then in forms which reduce the computational complexity by assuming shift-invariance. Based on the 2-D lattice, a new nonlinear lattice model is developed. The model is capable of updates in the nonlinear as well as time order.
Type
Thesis
Description
Series/Report No
Department
Electrical and Computer Engineering
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
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Citation
Distribution Statement
Approved for public release; distribution is unlimited.
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Copyright is reserved by the copyright owner
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