ION Technical Content
Direct GPS Solutions
| Abstract: | Direct (that is, noniterative) solutions to the system of GPS pseudorange equations are presented. The solutions approximate the least-squares estimate, and in the case of four satellites reduce to an exact solution. The position- bias pairs so produced have accuracy approaching that bounded by the information inequality; accordingly, these direct solutions are nearly sufficient, containing as much position information as contained in the pseudoranges themselves. Two direct solutions are derived. In the first solution, an approximation to the nonlinear least-squares cost func- tion is formulated in terms of an equation emr. The ap- proximation differs from the true cost in a manner which can be accounted for; it has the appealing property that it can be minimized directly using constrained optimization techniques. The second solution is a divide and conquer technique: the solution is formed by combining position- bias estimates based on subsets of the measured pseudor- anges. As a side result, it is shown that the least-squares position estimate based on pseudoranges is equal to that based on pseudorange differences. |
| Published in: |
Proceedings of the 49th Annual Meeting of The Institute of Navigation (1993) June 21 - 23, 1993 Royal Sonesta Hotel Cambridge, MA |
| Pages: | 457 - 466 |
| Cite this article: | Abel, Jonathan, Chaffee, James, "Direct GPS Solutions," Proceedings of the 49th Annual Meeting of The Institute of Navigation (1993), Cambridge, MA, June 1993, pp. 457-466. |
| Full Paper: |
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