Localizing in Urban Canyons using Joint Doppler and Ranging and the Law of Cosines Method

William W. Jun, Kar-Ming Cheung, E. Glenn Lightsey, Charles Lee

Abstract:	The performance of Global Navigation Satellite System (GNSS) based navigation can be limited in urban canyons and other regions with narrow satellite visibility. These regions may only allow for less than the minimum of four satellites to be visible, leading to a decay of positional knowledge. A scheme with Joint Doppler and Ranging (JDR) and relative positioning, known as the Law of Cosines (LOC) method, is introduced in this paper that utilizes Doppler and pseudorange measurements from a minimum of two GNSS satellites to obtain a position fix. The user’s GNSS receiver was assumed to output both corrected pseudorange and Doppler shift measurements for each tracked satellite. The velocity vector of each satellite was calculated using broadcast satellite ephemerides. Additionally, the location of the reference station was known and Doppler measurements from the GNSS receiver at the reference station were transmitted to the user. Ephemerides from eight GNSS satellites were simulated with the user and reference station approximately 12 km apart in San Francisco. Gaussian error sources were modelled and randomized in Monte Carlo simulations, adding error to the receiver’s known satellite ephemeris, satellite velocity, Doppler, and pseudorange measurements. Each unique pair of 2 satellites was employed for the positioning of the user using the LOC method for over 10,000 Monte Carlo simulations. With reasonable assumptions on measurement error, the average 2D topocentric Root-Mean-Square-Error (RMSE) performance of all pairs of satellites was 23 meters, reducing to 10 meters by removing specific pairs with poor geometry. However, with a new technique called Terrain Assisted – JDR (TA-JDR), which uses accurate topographic information of the user’s region as a faux pseudorange measurement, the average RSME of the satellite pairs was reduced to approximately 7 meters. The use of the JDR-LOC scheme and its variants may not only be useful in urban canyons, but also in other GPS-denied unfriendly environments. Ultimately, the JDR-LOC scheme was capable of achieving navigational solutions with an RMSE as low as 7 meters for users with limited GNSS satellite visibility, with only the use of a GNSS receiver and a reference station.
Published in:	Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019) September 16 - 20, 2019 Hyatt Regency Miami Miami, Florida
Pages:	140 - 153
Cite this article:	Jun, William W., Cheung, Kar-Ming, Lightsey, E. Glenn, Lee, Charles, "Localizing in Urban Canyons using Joint Doppler and Ranging and the Law of Cosines Method," Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, Florida, September 2019, pp. 140-153. https://doi.org/10.33012/2019.16897
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In