Polynomial filtering : to any degree on irregularly sampled data

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dc.contributor.author Reyneke, Pieter V.
dc.contributor.author Morrison, Norman
dc.contributor.author Kourie, Derrick G.
dc.contributor.author De Ridder, Corne
dc.date.accessioned 2013-02-15T10:04:43Z
dc.date.available 2013-02-15T10:04:43Z
dc.date.issued 2012
dc.description.abstract Conventionally, polynomial filters are derived for evenly spaced points. Here, a derivation of polynomial filters for irregularly spaced points is provided and illustrated by example. The filter weights and variance reduction factors (VRFs) for both expanding memory polynomial (EMP) and fading-memory polynomial (FMP) filters are programmatically derived so that the expansion up to any degree can be generated. (Matlab was used for doing the symbolic weight derivations utilizing Symbolic Toolbox functions.) Order-switching and length-adaption are briefly considered. Outlier rejection and Cramer-Rao Lower Bound consistency are touched upon. In terms of performance, the VRF and its decay for the EMP filter is derived as a function of length (n) and the switch-over point is calculated where the VRFs of the EMP and FMP filters are equal. Empirical results verifying the derivation and implementation are reported. en_US
dc.description.abstract Polinomni filtri uobicˇajeno se rade za ravnomjerno raspored¯ene tocˇke u prostoru. U ovom radu dana je derivacija polinomnih filtara za neravnomjerno raspored¯ene tocˇke. Težinske vrijednosti filtra i faktori smanjenja varijance (VRF-ovi) za polinom proširene memorije (EMP) i polinom oslabljenje memorije (FMP) su programski podržani tako da se može napraviti ekspanzija do bilo kojeg stupnja. Kratko su razmotreni i promjena poretka i adaptacija dužine filtra. Dotaknute su i metode odbijanja jako raspršenih rezultata i Cramer-Raove konzistencije donje granice. VRF i njegovo opadanje za EMP filtar izvedeno je kao funkcija duljine (n) i izraˇcunata je toˇcka prijelaza gdje su VRF-ovi od EMP i FMP filtara jednaki. Predoˇceni su empirijski rezultati koji verificiraju izvod i implementaciju. en_US
dc.description.librarian am2013 en_US
dc.description.uri https://automatika.korema.hr/index.php/automatika/index en_US
dc.identifier.citation Reyneke, PV, Morrison, N, Kourie, DG & De Ridder, C 2012, 'Polynomial filtering : to any degree on irregularly sampled data', Automatika, vol. 53, no. 4, pp. 382-397. en_US
dc.identifier.issn 0005-1144 (print)
dc.identifier.issn 1848-3380 (online)
dc.identifier.other 10.7305/automatika.53-4.248
dc.identifier.uri http://hdl.handle.net/2263/21017
dc.language.iso en en_US
dc.publisher KoREMA - Croatian Society for Communications, Computing, Electronics, Measurement and Control en_US
dc.rights Creative Commons Attribution License en_US
dc.subject Radar tracking filters en_US
dc.subject Polynomial approximation en_US
dc.subject Smoothing en_US
dc.subject State estimation en_US
dc.subject Satellite tracking en_US
dc.subject Discrete time filters en_US
dc.subject Laguerre processes en_US
dc.subject Legendre processes en_US
dc.subject Polynomial approximation en_US
dc.subject Smoothing methods en_US
dc.subject Interpolation en_US
dc.subject Extrapolation en_US
dc.subject Filtri za prac´enje radara en_US
dc.subject Polinomna aproksimacija en_US
dc.subject Izgladivanje en_US
dc.subject Procjena stanja en_US
dc.subject Pracenje satelita en_US
dc.subject Diskretni vremenski filtri en_US
dc.subject Laguerreovi procesi en_US
dc.subject Legendreovi procesi en_US
dc.subject Aproksimacija polinomom en_US
dc.subject Metode izgladivanja en_US
dc.subject Interpolacija en_US
dc.subject Ekstrapolacija en_US
dc.title Polynomial filtering : to any degree on irregularly sampled data en_US
dc.title.alternative Polinomno filtriranje : postizanje bilo kojeg stupnja na nepravilno uzorkovanim podacima en_US
dc.type Article en_US


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