A variable projection method for additive components with application to GPS

Author

Abel, Jonathan S.

Author_Institution

Abel Innovations, Palo Alto, CA, USA

Volume

30

Issue

3

fYear

1994

fDate

7/1/1994 12:00:00 AM

Firstpage

928

Lastpage

930

Abstract

A variable projection method is presented for the case of additive linear components. Specifically, the least-squares problem of minimizing ||x-f(φ)-Lλ||² over parameters (λ,φ) is reduced to that of minimizing ||Γ[x-f(φ)]||² over φ, where Γ is an (n-p)×n projection orthogonal to L, p being the dimension of λ. Applications to signal modeling and Global Positioning System (GPS) navigation are given. In the case of GPS, it is shown that least-squares point position estimates based on pseudoranges are equal to those based on pseudorange differences

Keywords

least squares approximations; linear systems; minimisation; parameter estimation; radionavigation; satellite relay systems; signal processing; GPS; Global Positioning System; additive components; least-squares point position estimates; least-squares problem; minimisation; navigation; pseudoranges; signal modeling; variable projection method; Amplitude estimation; Frequency estimation; Frequency measurement; Global Positioning System; Least squares approximation; Navigation; Noise level; Noise measurement; Nonlinear filters; Parameter estimation;

fLanguage

English

Journal_Title

Aerospace and Electronic Systems, IEEE Transactions on

Publisher

ieee

ISSN

0018-9251

Type

jour

DOI

10.1109/7.303764

Filename

303764