Linear solution of the three-station positioning equation reconstructed based on the path difference equation

Abstract

For a three-station path difference positioning system with an arbitrary planar layout, if the solution analysis is directly based on the path difference equation, the radial distance unknowns in the equation are difficult to directly eliminate. Once the conversion relationship between the polar coordinate system and the Cartesian coordinate system is utilized, the differential equation system can be transformed into a mixed variable equation system, which includes both the three radial distances in the polar coordinate system and the two coordinate variables in the Cartesian coordinate system. Take the radial distance of the main station as the quantity to be solved, and use the path difference equation to express the radial distance of the secondary station as a function of the radial distance of the main station. By selecting the appropriate station coordinates, an unknown variable in the Cartesian coordinate system can be eliminated. By combining mixed equations, another unknown variable in the Cartesian coordinate system can be further eliminated. Thus, a definite solution equation containing only the radial distance of the main station is obtained.