An Algebraic Solution of the GPS Equations
- 1 January 1985
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Aerospace and Electronic Systems
- Vol. AES-21 (1) , 56-59
- https://doi.org/10.1109/taes.1985.310538
Abstract
The global positioning system (GPS) equations are usually solved with an application of Newton's method or a variant thereof: Xn+1 = xn + H-1(t - f(xn)). (1) Here x is a vector comprising the user position coordinates together with clock offset, t is a vector of tour pseudorange measurements, and H is a measurement matrix of partial derivatives H = fx· In fact the first fix of a Kalman filter provides a solution of this type. If more than four pseudoranges are available for extended batch processing, H-1 may be replaced by a generalized inverse (HTWH)-1HTW, where W is a positive definite weighting matrix (usually taken to be the inverse of the measurement covariance matrix). This paper introduces a new method of solution that is algebraic and noniterative in nature, computationally efficient and numerically stable, admits extended batch processing, improves accuracy in bad geometric dilution of precision (GDOP) situations, and allows a "cold start" in deep space applications.Keywords
This publication has 1 reference indexed in Scilit:
- A Novel Procedure for Assessing the Accuracy of Hyperbolic Multilateration SystemsIEEE Transactions on Aerospace and Electronic Systems, 1975