A novel general methodology for studying and remedying finite precision error with application in Kalman filtering

Papaodysseus, C; Alexiou, C; Panagopoulos, Th; Roussopoulos, G; Kravaritis, D

dc.contributor.author	Papaodysseus, C	en
dc.contributor.author	Alexiou, C	en
dc.contributor.author	Panagopoulos, Th	en
dc.contributor.author	Roussopoulos, G	en
dc.contributor.author	Kravaritis, D	en
dc.date.accessioned	2014-03-01T01:18:33Z
dc.date.available	2014-03-01T01:18:33Z
dc.date.issued	2003	en
dc.identifier.issn	1436-3240	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/15078
dc.subject	Finite precision error	en
dc.subject	Kalman type algorithms instability	en
dc.subject	Kalman type algorithms stabilization	en
dc.subject	Quantization error	en
dc.subject	RLS algorithms	en
dc.subject.classification	Engineering, Environmental	en
dc.subject.classification	Engineering, Civil	en
dc.subject.classification	Environmental Sciences	en
dc.subject.classification	Statistics & Probability	en
dc.subject.classification	Water Resources	en
dc.subject.other	error correction	en
dc.subject.other	Kalman filter	en
dc.subject.other	least squares method	en
dc.title	A novel general methodology for studying and remedying finite precision error with application in Kalman filtering	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00477-002-0116-2	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00477-002-0116-2	en
heal.language	English	en
heal.publicationDate	2003	en
heal.abstract	Least squares (LS) techniques, like Kalman filtering, are widely used in environmental science and engineering. In this paper, a new general approach is introduced for the study of the generation, propagation and accumulation of the quantization error in any algorithm. This methodology employs a number of fundamental propositions demonstrating the way the four operations addition, multiplication, division and subtraction, influence quantization error generation and transmission. Using these, one can obtain knowledge of the exact number of erroneous digits with which all quantities of any algorithm are computed at each step of it. This methodology offers understanding of the actual cause of the generation and propagation of finite precision error in any computational scheme. Application of this approach to all Kalman type LS algorithms shows that not all their formulas are equivalent concerning the quantization error effects. More specifically, few generate the greater amount of quantization error. Finally, a stabilization procedure, applicable to all Kalman type algorithms, is introduced that renders all these algorithms very robust.	en
heal.publisher	SPRINGER-VERLAG	en
heal.journalName	Stochastic Environmental Research and Risk Assessment	en
dc.identifier.doi	10.1007/s00477-002-0116-2	en
dc.identifier.isi	ISI:000183840000001	en
dc.identifier.volume	17	en
dc.identifier.issue	1-2	en
dc.identifier.spage	1	en
dc.identifier.epage	19	en