Sufficient Excitation and Stable Reduced-Order Adaptive IIR Filtering
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Richard Johnson, C.
Anderson, B. D.O.
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A perturbed error system is used to describe the parameter and output error behaviors of reduced-order application of adaptive identifier/filters such as the hyperstable adaptive recursive filter (HARF). Given satisfaction of a sufficient excitation condition, this error system is shown to exhibit a bounded-input, bounded-state (BIBS) property. This implies that, despite order insufficiency, the output and parameter estimates of HARF (and similar adaptive identifier/filter algorithms) remain bounded.
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IEEE Transactions on Acoustics, Speech, and Signal Processing
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