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We present the method for constructing global ionospheric maps of TEC which relies only on dual-frequency GNSS carrier phase data, in which the ionosphere is modeled in Sun-fixed (modified dip latitude, local time) coordinate system as a spherical harmonics expansion in thin-shell layer. Inequality constraint least squares approach based on the solution of linear complimentarity problem was adopted to deal with possible non-physical negative values of vertical TEC arising in reconstructions typically for nighttime periods of low Solar activity. Suggested approach was tested on synthetic observations generated for real geometry of GNSS constellation and IGS receiving stations using NeQuick2 model for cases of high and low solar activity. Reconstruction errors proved to be below 5 TECU for high TEC values in both cases. Considered approach was also applied for the real GNSS data for several test periods and validated against different IGS GIMs, including gAGE/UPC TEC map product, which utilizes the same phasedifference approach for input data. Obtained results showed maximum inter-method deviations up to 10TECU in the regions lacking observational data.