Title :
A variable projection method for additive components with application to GPS
Author :
Abel, Jonathan S.
Author_Institution :
Abel Innovations, Palo Alto, CA, USA
fDate :
7/1/1994 12:00:00 AM
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;
Journal_Title :
Aerospace and Electronic Systems, IEEE Transactions on
