# An Algebraic Solution of the GPS Equations

@article{Bancroft1985AnAS, title={An Algebraic Solution of the GPS Equations}, author={Stephen Bancroft}, journal={IEEE Transactions on Aerospace and Electronic Systems}, year={1985}, volume={AES-21}, pages={56-59} }

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…

## 302 Citations

GPS estimation algorithm using stochastic modeling

- Computer ScienceProceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171)
- 1998

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.

Efficient GPS Position Determination Algorithms

- Computer Science
- 2012

The stand-alone user GPS algorithm is a direct, closed- form, and efficient new position determination algorithm that exploits the closed-form solution of the GPS trilateration equations and works in the presence of pseudorange measurement noise for an arbitrary number of satellites in view.

An Efficient GPS Position Determination Algorithm

- Engineering
- 2003

: A direct, closed-form and efficient new position determination algorithm that exploits the closed-form solution of the GPS trilateration equations and works in the presence of pseudorange…

Alternative algorithms for the GPS static positioning solution

- Computer ScienceAppl. Math. Comput.
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Stochastic Modeling in GPS Estimation

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- 1999

The NAVSTAR Global Positioning System (GPS) is a space based satellite radio navigation system which provides three dimensional user positioning by solving a set of nonlinear trilateration equations…

GPS Navigation Solutions by Analogue Neural Network Least-Squares Processors

- Computer ScienceJournal of Navigation
- 2005

Two ordinary differential equation formulation schemes and corresponding circuits of neuron-like analog processors will be employed for GPS navigation processing and the solutions will be assessed and compared to those provided by the conventional method in which pseudo-inverse matrix calculation by digital computer is involved.

Estimation of relative satellite position using transformed differential carrier-phase GPS measurements

- Physics
- 2007

Techniques for applying differential carrier-phase global positioning systems to satellite formation clusters with large (approximately 100 km or more) baselines are described. Because satellites in…

The GPS filtering problem

- MathematicsIEEE PLANS 92 Position Location and Navigation Symposium Record
- 1992

The authors explore the possibility of both improved navigation accuracy and computational simplification by using nonlinear filters based on direct solutions to the GPS (Global Positioning System)…

Nonlinear Adjustment of GPS Observations of Type Pseudo-Ranges

- MathematicsGPS Solutions
- 2002

The nonlinear adjustment of GPS observations of type pseudo-ranges is performed in two steps. In step one a combinatorial minimal subset of observations is constructed which is rigorously converted…

A Minimum Variance Algorithm for Overdetermined TOA Equations with an Altitude Constraint

- Mathematics
- 2018

We present a direct (non-iterative) method for solving for the location of a radio frequency (RF) emitter, or an RF navigation receiver, using four or more time of arrival (TOA) measurements and an…

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