GPS estimation algorithm using stochastic modeling

The use of direct, or closed-form, solutions of the trilateration equations for obtaining the position fix in the GPS receiver is investigated. A new closed-form position determination algorithm that works in the presence of pseudorange measurement noise and for an arbitrary number of satellites n, where n⩾4, using stochastic modeling is developed. The closed-form algorithm provides an estimate of the GPS solution, viz., user position and user clock bias, as well as the estimation error covariance. The direct algorithm is a two step procedure which, (1) entails the solution of a linear regression problem, and, (2) an update of the solution based on an additional nonlinear measurement equation. Realistic simulation experiments are performed and the direct algorithm´s performance is discussed and compared to the iterative least squares algorithm currently used in GPS