A variable projection method is presented for the case of additive linear components. Specifically, the least-squares problem of minimizing parallel-to x - f(phi) - Llambda parallel-to 2 over parameters (lambda, phi) is reduced to that of minimizing parallel-to GAMMA[x - f(phi)] parallel-to 2 over phi, where GAMMA is an (n - p) x n projectIon orthogonal to L, p being the dimension of 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.