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/spl ges/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.