Navigation Performance Using Long-Term Ephemeris Extension for Mobile Device (2013)

Broadcast ephemeris is required for a position fix while decoding broadcast ephemeris in open sky normally takes 18s, but valid just for 2 hours. Fast TTFF then becomes challenging in some tough environments such as urban canyon and indoor, where GPS signals suffer from multipath effect, signal attenuation and building blockage etc, because of the difficulty in decoding satellite ephemeris data from the broadcast navigation messages. Therefore ephemeris extension is needed. As a result, the positioning may be impossible or dramatically degraded with limited available satellites, which is not acceptable for mobile applications such as E911. This demands prediction of the GPS ephemeris, which, if available in receivers can be used to bridge the ephemeris outage period to reduce the first-time-to-fix (TTFF) and also improve positioning accuracy in challenging environments. Considering the wide variety of mobile users under some extreme cases who may have limited access to wireless network for a long time or cost and power concerns etc, a feature of ephemeris extension with sufficient precision is especially of value to location-based service provider and mobile users. 

Motivated by rapidly increasing location demands of mobile device users in GPS signal challenging conditions, more and more researches are made on long-term GPS orbit prediction – the key part of ephemeris extension. The performance of orbit prediction depends on two major components. One is satellite dynamic model and the other is satellite initial condition. Currently, three methods are adopted for determination of satellite initial condition. The first method is to acquire initial condition based on a previous set of the ephemeris. The second method is to fit the previous ephemeris with a span of fitted arc length. The third method is to use a global distributed GPS tracking network. The three methods have different merits. The first one requires less computational load and can be directly implemented in a mobile device, but the predicted orbit errors accumulate quickly. The second one has a slower accumulation of predicted orbit errors by using a span of fitted arc length instead of only one set of ephemeris, but the accuracy of the initial condition still depends on the accuracy of the fitted orbits. The third one can achieve high accuracy for the predicted orbit by directly processing raw GPS measurements from global tracking stations, but it takes high computational loads. Thus the third method can only be implemented by a server which sends the initial condition to the mobile device in which the orbit can be integrated. Some numerical investigations have been conducted to assess the accuracy of the predicted orbits with different predicted time length and different methods. Zhang et al. (2008) has demonstrated 22 m orbit error in the line-of-sight (LOS) direction for 3 days using the first method, and 9 m for 5 days using the second method by fitting a 3 days arc length of broadcast ephemeris. An example of the third method is JPL GPS predicted orbit products (http://www.gdgps.net/index.html). The median User Range Error (URE) of their products can be better than 10 m after 7 days of prediction. 

Considering that currently available ephemeris extension products in industry are good for 1-2 weeks, this paper is to investigate the possibility to extend ephemeris over an even longer period say 4 weeks, with the focus on the orbital part. First, the satellite dynamics models are first introduced, which take into account the gravity of the Earth, Sun and the Moon, as well as the solar radiation pressure model. Second, the impact of different fitted arc lengths on the quality of the initial condition of GPS satellites is analyzed. It has been demonstrated that the performance of the orbit prediction varies as a function of the selected arc length. Thus the optimal arc length is investigated to improve the accuracy of the orbit prediction while further increasing the length of orbit prediction time. Finally, the orbit prediction schemes using the abovementioned three methods for satellite initial condition determination are compared. To assess the performance of the orbit prediction, the LOS orbit errors corresponding to 50th, 68th, 95th and 100th percentile error levels are calculated using data from 8 IGS stations across Canada over a period of 28 days. When the orbit prediction scheme with an arc length of 42 h using the second method, the mean LOS orbit errors for one week prediction are 0.631m, 1.098m, 1.726m , 6.197m at 50th, 68th, 95th and 100th percentile error levels, respectively. The corresponding mean LOS orbit errors for a two week prediction are 4.061m, 6.532m, 16.932m, 42.606m. The mean LOS orbit errors for a four week prediction are 24.061m, 34.532m, 61.932m, 88.606m. The obtained results are comparable to the claimed performance by JPL for a 28-day orbital prediction, which demonstrates the feasibility of ephemeris extension for 4 weeks with sufficient accuracy to satisfy the requirement of E911 applications (50 m -1 sigma). Further longer orbit prediction will also be explored based on the obtained results.