Nonlinear projection filter based on Galerkin approximation

Citation
R. Beard et al., Nonlinear projection filter based on Galerkin approximation, J GUID CON, 22(2), 1999, pp. 258-266
Citations number
33
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Aereospace Engineering
Journal title
JOURNAL OF GUIDANCE CONTROL AND DYNAMICS
ISSN journal
0731-5090 → ACNP
Volume
22
Issue
2
Year of publication
1999
Pages
258 - 266
Database
ISI
SICI code
0731-5090(199903/04)22:2<258:NPFBOG>2.0.ZU;2-H
Abstract
The conditional probability density function of the state of a stochastic d ynamic system represents the complete solution to the nonlinear filtering p roblem because, with the conditional density in hand, all estimates of the state, optimal or otherwise, can be computed. It is well known that, for sy stems with continuous dynamics, the conditional density evolves, between me asurements, according to Kolmogorov's forward equation, At a measurement, i t is updated according to Bayes formula. Therefore, these two equations can be viewed as the dynamic equations of the conditional density and, hence, the exact nonlinear filter. In this paper, Galerkin's method is used to app roximate the nonlinear filter by solving for the entire conditional density . Using a discrete cosine transform to approximate the projections required in Galerkin's method leads to a computationally realizable nonlinear filte r, The implementation details are given and performance is assessed through simulations.