1. A method for operating a positioning system comprising an estimation circuit and a processing unit to determine a location of a target, comprising: obtaining, by the estimation circuit, a plurality of guess distance values of a plurality of satellites, respectively; utilizing, by the estimation circuit, satellite signals received from the plurality of satellites to estimate a plurality of pseudo range values of the plurality of satellites, respectively; comparing, by the processing unit, the guess distance values with the pseudo range values respectively, to generate a residual vector; applying, by the processing unit, a rank-based approach based on the residual vector to generate a calculation result; deriving, by the processing unit, an error effect component from the calculation result; generating, by the processing unit, a compensated residual vector by compensating the residual vector based on the error effect component and the residual vector; calculating, by the processing unit, the position of the target based on the compensated residual vector; and outputting, by the processing unit, the calculated position of the target.