Determination of GPS receiver position using Multivariate Newton-Raphson Technique for over specified cases

GPS user can fix his position by obtaining pseudoranges from a minimum of four different GPS satellites. The user position in ECEF coordinates (x_u, y_u, z_u) and the receiver clock bias with GPS Time (GPST) t_u can be obtained from the measured pseudoranges after making appropriate corrections. The receiver position can then be determined either by using linearization technique or method of least squares using Bancroft Algorithm. As it is easy to implement, most of the GPS receivers employ former method when a great degree of accuracy is not required. The latter method is found to be more accurate when pseudoranges from more than four satellites are considered. So far only Bancroft method has been suggested for the estimation of a GPS receiver position for an overspecified case when more than four satellites are observed. Here we are proposing a new method namely, Multivariate Newton - Raphson Technique (MNRT) for the estimation of a user position. Results show that the accuracy obtained using MNRT is better compared to linearization technique and is on par with the Bancroft algorithm for over specified case when pseudoranges from more than four satellites are observed. GPS data of Chitrakut station in RINEX format has been used for this purpose.