Efficient GPS Position Determination Algorithm

The use of detect, or closed-form solutions of the trilateration equations used to obtain the position fix in GPS receivers is investigated. The paper is concerned with the development of an efficient new position determination algorithm that uses the closed-form solution of the trilateration equations and works in the presence of pseudorange measurement noise and for an arbitrary number of satellites. in addition, an initial position guess is not required and good estimation performance is achieved even under high GDOP conditions. A two step GPS position determination algorithm which 1) entails the solution of a linear regression problem and, 2) an update of the solution based on one nonlinear measurement equation is developed. The closed-form solution of the linear regression in step 1 provides an estimate of the GPS solution, viz., user position and user clock bias, as well as the estimation error covariance. in the update step 2, only two to three iterations are required, as opposed to five iterations which are normally required in the standard iterative least square algorithm currently used in GPS. The two step algorithm also provides a data driven prediction of the pseudorange measurement noise strength and the estimation error covariance. The mathematical derivation of the novel and efficient solution algorithm for the GPS pseudorange equations using stochastic modeling is validated in a realistic simulation experiment based on 5000 Monte Carlo runs. The algorithm's performance is discussed and compared to the conventional iterative least squares algorithm currently used in GPS.Air Force Inst of Tech Wright-Patterson AFB OH is the author of 'Efficient GPS Position Determination Algorithm', published 1999 under ISBN 9781423545996 and ISBN 1423545990.