A closed-form algorithm for eliminating user position biases caused by satellite constellation changes

In GPS positioning, the user position is derived by the pseudo-range measurements and the user-satellite geometric matrix. When the satellite constellation changed, either gaining or losing satellites, it may cause the user position biases. The instantaneous biases in position solution are not desirable in some applications. An algorithm called position bias filter has been proposed to solve the problem. Also, a modified algorithm is designed to reduce the computation burden of original algorithm by a recursive method. In this paper, we propose a closed-form algorithm for eliminating the user position biases. The algorithm remains the low computation in a few satellites change (less than four) of satellite constellation without recursive calculation.