The algebraic solution of the Double-System navigation equations

摘要

One new method was brought forward to solve the algebraic solution to the double-system satellite navigation equations. We established two binary quadratic equations about two satellite-station reference ranges and the matrix equations about these ranges and receiver position, where two ranges were chosen from two systems respectively. Thus the original problem is replaced by an approximate problem and for it two binary quadratic equations are obtained. Geometric and clock information is used to discard the unwanted solutions. The reference ranges, system time biases and receiver position were produced by solving these equations. Simulation indicates that our solution can solve the problem of initial position when receiver cold starts in the situations of earth-bounded and deep space. Especially in deep space where the conventional algorithm, which performs based on range-direction-cosine matrix, will probably converge to the wrong solution, our solution is still correct. In earth-bounded situation, our solution has the same precision as the conventional.