Exact analysis of the finite precision error generation and propagation in the FAEST and the fast transversal algorithms: A general methodology for developing robust RLS schemes

Papaodysseus, C; Koukoutsis, E; Stavrakakis, G; Halkias, CC

dc.contributor.author	Papaodysseus, C	en
dc.contributor.author	Koukoutsis, E	en
dc.contributor.author	Stavrakakis, G	en
dc.contributor.author	Halkias, CC	en
dc.date.accessioned	2014-03-01T01:12:52Z
dc.date.available	2014-03-01T01:12:52Z
dc.date.issued	1997	en
dc.identifier.issn	0378-4754	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/12273
dc.subject	White Noise	en
dc.subject	kalman filter	en
dc.subject.classification	Computer Science, Interdisciplinary Applications	en
dc.subject.classification	Computer Science, Software Engineering	en
dc.subject.classification	Mathematics, Applied	en
dc.subject.other	FILTERS	en
dc.subject.other	NORMALIZATION	en
dc.title	Exact analysis of the finite precision error generation and propagation in the FAEST and the fast transversal algorithms: A general methodology for developing robust RLS schemes	en
heal.type	journalArticle	en
heal.identifier.primary	10.1016/S0378-4754(97)00004-9	en
heal.identifier.secondary	http://dx.doi.org/10.1016/S0378-4754(97)00004-9	en
heal.language	English	en
heal.publicationDate	1997	en
heal.abstract	In this paper, an analysis for the actual and deeper cause of the finite precision error generation and accumulation in the FAEST-5p and the fast transversal filtering (FTF) algorithm is undertaken, on the basis of a new methodology and practice. In particular, it is proved that, in case where the input data in these algorithms is a white noise or a periodic sequence, then, out of all the formulas that constitute these two schemes, only four specific formulas generate an amount of finite precision error that consistently makes the algorithms fail after a certain number of iterations. If these formulas are calculated free of finite precision error, then all the results of the two algorithms are also computed error-free. In addition, it is shown that there is a very limited number of specific formulas that transmit the finite precision error generated by these four formulas. Moreover, a number of very general propositions is presented that allow for the calculation of the exact number of erroneous digits with which all the quantities of the FAEST and FTF schemes are computed, including the filter coefficients. Finally, a general methodology is introduced, based on the previous results, that allows for the development of new RLS algorithms that, intrinsically, suffer less of finite precision numerical problems and that therefore are, in practice, suitable for high quality fast Kalman filtering implementations.	en
heal.publisher	ELSEVIER SCIENCE BV	en
heal.journalName	Mathematics and Computers in Simulation	en
dc.identifier.doi	10.1016/S0378-4754(97)00004-9	en
dc.identifier.isi	ISI:A1997XV39700003	en
dc.identifier.volume	44	en
dc.identifier.issue	1	en
dc.identifier.spage	29	en
dc.identifier.epage	41	en