A variable projection method for additive components with application to GPS

A variable projection method is presented for the case of additive linear components. Specifically, the least-squares problem of minimizing /spl par/x-f(/spl phi/)-L/spl lambda//spl par//sup 2/ over parameters (/spl lambda/,/spl phi/) is reduced to that of minimizing /spl par//spl Gamma/[x-f(/spl phi/)]/spl par//sup 2/ over /spl phi/, where /spl Gamma/ is an (n-p)/spl times/n projection orthogonal to L, p being the dimension of /spl lambda/. 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.>