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• W2182922659 abstract "Steepest descent gradient algorithms for unbiased equation error adaptive infinite impulse response (IIR) filtering are analyzed collectively for both the total least squares and mixed least squares-total least squares framework. These algorithms have a monic normalization that allows for a direct filtering imple- mentation. We show that the algorithms converge to the desired filter coefficient vector. We achieve the convergence result by ana- lyzing the stability of the equilibrium points and demonstrate that only the desired solution is locally stable. Additionally, we describe a region of initialization under which the algorithm converges to the desired solution. We derive the results using interlacing rela- tionships between the eigenvalues of the data correlation matrices and their respective Schur complements. Finally, we illustrate the performance of these new approaches through simulation. error filtering with operation count complexity that is similar to the ubiquitous least mean square (LMS) algorithm (26). Several of the TLS or mixed LS-TLS algorithms have operation counts of ) or high (15)-(17). We additionally desire algorithms that provide a direct filtering implementation, i.e., the filter calculation provides a parameter estimate that does not require additional scaling prior to application, unlike the unit-norm algorithms that require a post-calculation monic normalization (18)-(20). Much work (21), (23)-(25) has recently been published to propose stable, simple LMS-like algorithms for equation error filtering. The algorithms of (23) and (24) consider only the TLS scenario, whereas the algorithm of (25) only considers the mixed LS-TLS scenario. Furthermore, the algorithm of (21) fails to be stable (22), whereas none of the algorithms presented in (23)-(25) demonstrate a complete stability proof. In this paper, we present an complexity algorithm for unbiased equation error filtering based on the TLS or mixed LS-TLS methodology for which we establish stable adaptation behavior. Our algorithm is based on a gradient descent of a cost function known to give unbiased results in either the TLS or mixed LS-TLS scenario, depending on a suitably chosen diag- onal weighting matrix. Additionally, we impose a monic nor- malization on the update that is key to ensuring stability in the adaptation process. We explore the algorithm's stability by cal- culating the performance in the neighborhood of the equilibrium points. We also demonstrate guaranteed convergence to the de- sired solution given proper initialization of the parameter vector and a sufficiently small constant update gain factor. We derive the results using interlacing relationships between the eigen- values of the data correlation matrices and their respective Schur complements." @default.
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• W2182922659 date "2004-01-01" @default.
• W2182922659 modified "2023-09-27" @default.
• W2182922659 title "Analysis of Gradient Algorithms for TLS-Based" @default.
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