Quantization effects and stabilization of the fast-Kalman algorithm

Papaodysseus, C; Alexiou, C; Roussopoulos, G; Panagopoulos, A

dc.contributor.author	Papaodysseus, C	en
dc.contributor.author	Alexiou, C	en
dc.contributor.author	Roussopoulos, G	en
dc.contributor.author	Panagopoulos, A	en
dc.date.accessioned	2014-03-01T01:16:59Z
dc.date.available	2014-03-01T01:16:59Z
dc.date.issued	2001	en
dc.identifier.issn	11108657	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/14304
dc.subject	Adaptive algorithms	en
dc.subject	Finite-precision error in RLS algorithms	en
dc.subject	Kalman filtering	en
dc.subject	Quantization error in fast-Kalman algorithm	en
dc.subject	Recursive least squares filtering	en
dc.subject.other	Acoustic noise	en
dc.subject.other	Adaptive algorithms	en
dc.subject.other	Kalman filtering	en
dc.subject.other	Recursive functions	en
dc.subject.other	Finite-precision errors	en
dc.subject.other	Recursive least square (RLS) schemes	en
dc.subject.other	Adaptive filtering	en
dc.title	Quantization effects and stabilization of the fast-Kalman algorithm	en
heal.type	journalArticle	en
heal.identifier.primary	10.1155/S1110865701000014	en
heal.identifier.secondary	http://dx.doi.org/10.1155/S1110865701000014	en
heal.publicationDate	2001	en
heal.abstract	The exact and actual cause of the failure of the fast-Kalman algorithm due to the generation and propagation of finite-precision or quantization error is presented. It is demonstrated that out of all the formulas that constitute this fast Recursive Least Squares (RLS) scheme only three generate an amount of finite-precision error that consistently propagates in the subsequent iterations and eventually makes the algorithm fail after a certain number of recursions. Moreover, it is shown that there is a very limited number of specific formulas that transmit the generated finite-precision error, while there is another class of formulas that lift or ""relax"" this error. In addition, a number of general propositions is presented that allow for the calculation of the exact number of erroneous digits with which the various quantifies of the fast-Kalman scheme are computed, including the filter coefficients. On the basis of the previous analysis a method of stabilization of the fast-Kalman algorithm is developed and is presented here, a method that allows for the fast-Kalman algorithm to follow very difficult signals such as music, speech, environmental noise, and other nonstationary ones. Finally, a general methodology is pointed out, that allows for the development of new algorithms which, intrinsically, suffer far less of finite-precision problems.	en
heal.journalName	Eurasip Journal on Applied Signal Processing	en
dc.identifier.doi	10.1155/S1110865701000014	en
dc.identifier.volume	2001	en
dc.identifier.issue	3	en
dc.identifier.spage	169	en
dc.identifier.epage	180	en