In　some　complex　environments,　nonline-of-sight　(or　multipath)　usually　introduces　an　additional　path　delay　to　the　pseudorange,　which　is　known　to　be　one　of　the　most　dominant　sources　of　accuracy　degradation　in　global　navigation　satellite　systems　(GNSSs).　The　additional　path　error　is　non-Gaussian.　Different　techniques,　including　antenna-based,　receiver-based,　and　poster-receiver,　have　been　proposed　for　mitigating　the　influence　of　multipath.　However,　the　estimated　additional　path　delay　obtained　by　classical　algorithms,　such　as　maximum　likelihood　or　Bayesian　estimation,　often　has　a　certain　deviation　from　the　real-additional　path　delay.　For　more　accurate　estimation,　we　first　restrict　the　additional　path　error　in　a　relatively　wide　interval;　then,　the　position　estimation　is　converted　into　a　constrained　separable　nonlinear　least　squares　problem.　We　propose,　in　this　paper,　a　two-stage　estimation　algorithm　for　global　positioning　system　positioning.　At　the　first　stage,　we　ignore　the　additional　path　error　and　obtain　a　relatively　accurate　initial　position.　Then,　based　on　the　result　obtained　at　the　first　stage,　we　include　the　additional　path　error　in　the　estimation　problem　and　estimate　it　by　variable　projection　(VP)　method.　Numerical　results　show　that　the　proposed　algorithm　based　on　the　VP　method　can　effectively　mitigate　multipath　interference.