Two satellites positioning algorithm based on AGPS system with two clock bias

Assisted Global Positioning System (AGPS) structure is used and Marquardt algorithm with additional earth ellipsoid equation is put forward in order to position and improve the positioning accuracy when only two satellites are captured intermittently in weak signal condition for global positioning system (GPS). AGPS provides auxiliary positioning data through General Packet Radio Service (GPRS) network. Positioning can be achieved when two satellites signals are captured twice between a short time. The big errors caused in solving the singular equation groups with Gauss-Newton algorithm can be remove by using Marquardt algorithm. In this algorithm, growth factor is used and adaptively adjusts the step according to the change of objective function. Compared to Gauss-Newton algorithm, the mean positioning bias decreases from about 500m to about 120m and there is less than 1.5 times computation increasing in Marquardt algorithm.