Coarse-Time AGPS; Computing TOW From Pseudorange Measurements, and the Effect on HDOP

Assisted-GPS is now supported in networks, such as GSM, without precisely synchronized clocks. This has led to the concept of “coarse-time assistance,” where the AGPS assistance data provides the time to the GPS receiver, but only to an accuracy of ±2 seconds. All other assistance data (satellite orbits, approximate user position) is available, and so the AGPS device can compute position without the time-of-week (TOW) data from a satellite. In this case, the navigation equations contain five states, namely: position (three states), common-bias (one state) and time-of-day error (one state). This is one more than the usual 4 states; and thus the formula for HDOP (Horizontal Dilution of Precision) changes from the usual case. Note that the time-of-day error is not the same class of error as common-bias error; this important distinction is explained in the paper. The objective of the paper is twofold; 1) to show how to calculate position and time-of-week in a closed form solution, and 2) how HDOP changes compared to the solution with known time. The significance of this is discussed below. The 3GPP technical specification TS 25.171 specifies the minimum performance requirements for AGPS in cellular user equipment. The 3GPP specification includes requirements for both fine-time and coarse-time assistance, and thus it is important for anyone doing analysis of AGPS performance to understand both finetime and coarse-time characterizations of HDOP. Furthermore, UMTS standards now require that network elements (SLP, SMLC) calculate positions from measurement reports with imprecise time. Positioning algorithms need to use the correct HDOP value in order to correctly predict the resulting solution accuracy. This is important in reliably achieving Quality of Service thresholds that may be required. We cover the mathematics behind position computation with coarse-time and explain how this changes the formula for HDOP (in an analogous way to how HDOP changes when you change from a 2d position solution to the more general 3d solution). Lastly, we will show how the coarse-time HDOP behaves with the current GPS constellation, with the addition of other GNSS constellations (Galileo, GLONASS & Compass).