Improvements and Extensions of the Geometrical Dilution of Precision (GDOP) Concept for Selecting Navigation Measurements
Abstract
The optimal measurement selection problem is studied for the Global Positioning Satellite system (GPS). The fundamentals of the Geometrical Dilution of Precision (GDOP) concept are briefly reviewed, because GDOP is frequently used to rank the effectiveness of potential measurements. It is shown that GDOP does not always select the best measurements in the sense of minimum mean square navigation error. For this reason weighted least-squares and minimum variance (Kalman filter) methods are used to derive several improved measurement ranking schemes. Nonuniform measurement noise and a prior knowledge about the state are taken into account. Any specified weighted combination of the component error variances can be minimized. Eigenvalue-eigenvector theory is used to derive useful bounds and to provide geometrical insight. A purely algorithmic approach is also presented and applied to a number of representative GPS cases. In addition to the static (single time point) selection problem, the time- sequential selection problem is considered. It is shown that the choice giving the smallest instantaneous position error may not give the smallest time average position error because of the trade-off existing with velocity errors. A promising approach is formulated for the sensor substitution problem. That is, should be degraded (jammed) satellite channels be deleted from the measurements, and if so, when? Which backup sensors should be used instead? A suboptimal filtering approach using state vector partitioning is used to derive some preliminary answers to these questions.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1981
- Accession Number
- ADA108607
Entities
People
- William L. Brogan
Organizations
- University of Nebraska–Lincoln