Using SDP relaxation for optimization of the satellites set chosen for positioning

A GNSS (global navigation satellite system) navigation receiver, comprising:

• a plurality of radio frequency tracts receiving GNSS signals from at least five satellites, wherein at least two of the five satellites belong to one constellation, and the remaining satellites belong to at least one other constellation;
• a digital section including a processor configured to process the GNSS signals to measure code and phase measurements for each of the satellites and each of the GNSS signals;
• the processor configured to select a subset of the GNSS signals as an optimal set for coordinate calculation,
• wherein the selecting is based on Semi-Definite Programming (SDP) relaxation as applied to an optimization of a PDOP (positional dilution of precision) criterion, wherein the SDP relaxation minimizes a linear criterion subject to a linear matrix inequality constraint;
• the processor configured to calculate coordinates of a receiver based on the code and phase measurements of the selected subset;
• and
• the processor configured to output the calculated coordinates.