Abstract
For terrestrial positioning, some applications require three dimensional coordinates. The Dilution of precisions (DOPs) for position systems using range measurement are reviewed and the average values of DOPs for different deployments of base station geometries are examined. It is shown that to obtain the lowest DOPs, the base stations for different types of positioning systems need to be deployed differently. Changing the N-sided regular polygon to an (N - 1)-sided polygon with one base station in the centre of the polygon can decrease the value of DOP in general for a pseudorange time of arrival (TOA) system but not for an absolute range TOA system. The height of the base station in the centre can also change the DOP significantly. The finding can be used to optimize the deployment of the base stations for range measurement positioning systems.
Highlights
Using range measurements for positioning is the method most popular in satellite navigation systems
A Time Difference of Arrival (TDOA) system is known as a hyperbolic multilateration system as it relies on the fact that all the points where the difference in the time of arrival (TOA) radio signals from different stations is constant, its “line of position”, forms a hyperbola
In absolute range processing, the lowest Geometric DOP (GDOP) and Vertical DOP (VDOP) can be achieved (HDOP is slightly worse than the lowest value) when all the base stations have the same maximum height (5 m), while in pseudorange processing the base stations should be deployed with minimum and maximum height alternately (e.g. [0;5;0;5] when N is 4)
Summary
Using range measurements for positioning is the method most popular in satellite navigation systems. Similar examples can be found in terrestrial positioning systems [2,3,4,5] Since, in these systems, the clock error in the receiver is unknown, pseudorange rather than the absolute range is measured. If the transmitters and receiver are well synchronized or a round trip time (RTT) can be obtained, the absolute range measurement can be used for positioning [6]. DOP has been well investigated for Global Navigation Satellite Systems (GNSS) [9] [10,11,12]. Originally it was discussed in hyperbolic multilateration systems [13,14].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
