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An Iterative Method Based on the Marginalized Particle Filter for Nonlinear B-Spline Data Approximation and Trajectory Optimization

Jauch, Jens; Bleimund, Felix; Frey, Michael; Gauterin, Frank

Abstract:
The B-spline function representation is commonly used for data approximation and trajectory definition, but filter-based methods for nonlinear weighted least squares (NWLS) approximation are restricted to a bounded definition range. We present an algorithm termed nonlinear recursive B-spline approximation (NRBA) for an iterative NWLS approximation of an unbounded set of data points by a B-spline function. NRBA is based on a marginalized particle filter (MPF), in which a Kalman filter (KF) solves the linear subproblem optimally while a particle filter (PF) deals with nonlinear approximation goals. NRBA can adjust the bounded definition range of the approximating B-spline function during run-time such that, regardless of the initially chosen definition range, all data points can be processed. In numerical experiments, NRBA achieves approximation results close to those of the Levenberg–Marquardt algorithm. An NWLS approximation problem is a nonlinear optimization problem. The direct trajectory optimization approach also leads to a nonlinear problem. The computational effort of most solution methods grows exponentially with the trajectory length. ... mehr

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Verlagsausgabe §
DOI: 10.5445/IR/1000094540
Veröffentlicht am 13.05.2019
Coverbild
Zugehörige Institution(en) am KIT Institut für Fahrzeugsystemtechnik (FAST)
Publikationstyp Zeitschriftenaufsatz
Jahr 2019
Sprache Englisch
Identifikator ISSN: 2227-7390
KITopen-ID: 1000094540
Erschienen in Mathematics
Band 7
Heft 4
Seiten Article: 355
Bemerkung zur Veröffentlichung Gefördert durch den KIT-Publikationsfonds
Vorab online veröffentlicht am 16.04.2019
Schlagworte nonlinear; recursive; iterative; B-spline; approximation; marginalized particle filter; Rao-Blackwellized particle filter; multiobjective; trajectory; optimization
Nachgewiesen in Web of Science
Scopus
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