QR Decomposition For Adaptive Filtering Application

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dc.contributor.authorOkwonu, Friday Zinzendoff
dc.date.accessioned2018-07-31T01:37:10Z
dc.date.available2018-07-31T01:37:10Z
dc.date.issued2011-05
dc.description.abstractThis thesis is designed to investigate adaptive filtering problem based on QR decomposition techniques. An adaptive filter is a self modifying digital filter that adjusts its parameters in order to minimize a defined error function. Adaptive algorithm is applied to adapt the coefficient of the used filter to nonstationary process in which the coefficient of the adaptive filter is adapted in order to minimize the error function. Adaptive filtering problem is an adaptive form of least squares problem. Recursive least squares (RLS) method recursively update the inverse of the autocorrelation matrix via matrix inversion lemma in order to compute coefficient vector and associated errors recursively. We apply QR decomposition based on Givens rotations to investigate adaptive filtering problem. Givens rotations is applied to adaptive filtering algorithm because of its iterative nature that allows easy update of the triangularized data matrix. QR decomposition of recursive least squares method (QRD-RLS) transforms data matrix to upper triangular matrix and recursively update matrix. The transformation results in a reduced form of the normal equation which can be solved for the coefficient vector via backward substitution. On the other hand, inverse QR decomposition of recursive least squares method (IQRD-RLS) updates the inverse of the upper triangular matrix and desired signal vector so that the coefficient vector can be computed directly, i.e., without backward substitution. We study the comparative performance with respect to the conditioning of the autocorrelation matrix of the problem. The mean weight error norm in used to analyze the rate of convergence and misadjustment. Simulation show that for lower condition number RLS converges fast with misadjustment comparable to the QR based methods. However, as the condition number increases RLS show evidence of reduced tractability and produce high misadjustment. On the other hand, QR decomposition based techniques converges slow but as the condition number increases misadjustment remain unchange. These results show that although QRD-RLS and IQRD-RLS converge at a slower rate, they are able to track incoming signal at a steady rate.en_US
dc.identifier.urihttp://hdl.handle.net/123456789/6073
dc.language.isoenen_US
dc.publisherUniversiti Sains Malaysiaen_US
dc.subjectAdaptive filtering problem baseden_US
dc.subjectQR decomposition techniquesen_US
dc.titleQR Decomposition For Adaptive Filtering Applicationen_US
dc.typeThesisen_US
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