# Polynomial filtering : to any degree on irregularly sampled data

 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 en_US 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. dc.description.abstract Polinomni filtri en_US 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. 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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