The constellation of BeiDou Navigation Satellite System is composed of Geostationary Earth Orbit (GEO) satellites and Non-Geostationary Earth Orbit (Non-GEO) satellites. In consideration of the huge difference between GEO satellites altitude and Non-GEO satellites altitude, the global nonlinear least squres algorithm(Bancroft algorithm) is applied for BDS single point positioning in this paper. The Bancroft algorithm based on the Lorentz inner product is mainly in four dimensional space. A new algorithm to get the BDS observation weight is introduced by transforming Lorentz inner product into error equation, and then weight of the error equation is deduced. In order to testify the method, a code-minus-phase combination (CC) of BDS measurements is used to determine the code noise of GEO and Non-GEO satellites, a multipath combination (MP) is introduced to extract the multipath of pseudorange and improve the accuracy of single point positioning. The result indicates that new algorithm can improve the accuracy of BDS single point positioning.