Original scientific paper
https://doi.org/10.7305/automatika.53-4.248
Polynomial Filtering: To any degree on irregularly sampled data
Pieter V. Reyneke
; Fastar Research Group Dept. Radar and Imaging Systems, Denel Dynamics, Nellmapius Rd, Irene, 0157, Centurion, SA
Norman Morrison
; Department of Electrical Eng., University of Cape Town, 7700, Cape Town, SA
Derrick G. Kourie
; Dept. of Computer Science, University of Pretoria, Roper Str, 0002, Pretoria, SA
Corné de Ridder
; School of Computing, University of South Africa, Preller Str 1, 0001, Pretoria, SA
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.
Keywords
Radar tracking filters; Polynomial approximation; Smoothing; State estimation; Satellite tracking; Discrete time filters; Laguerre processes; Legendre processes; Polynomial approximation; Smoothing methods; Interpolation; Extrapolation
Hrčak ID:
94026
URI
Publication date:
5.12.2012.
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