Alternative algorithms for the GPS static positioning solution

The solution for the receiver's position and clock offset from four or more GPS pseudorange measurements involves nonlinear measurement-state equations. Traditionally, these equations have been solved using an iterative gradient approach. However, closed form solutions to this problem have been available in the literature for some time (Bancroft Stephen, IEEE Transactions on Aerospace and Electronic Systems AES-21 (7) (1985) 56-59 and Lloyd D. Krause, IEEE Transactions on Aerospace Electronic Systems AES-23 (2) (1987) 225-232). Each of these algorithms has various advantages and disadvantages ranging from simplicity of implementation to computational cost to auxiliary information. Two new closed form algorithms are presented in the following sections as alternative algorithms for the solution of this problem. Since efficient algorithms exist to compute auxiliary information such as the dilution of precision parameters (DOPs), the issue examined here in comparing these new algorithms to existing algorithms is computational cost. It is shown that the two new algorithms introduced below match or exceed the computational efficiency of the previously published algorithms, particularly when more than four measurements are processed.