Effect of the Error in the Line-of-Sight Unit Vector on Pseudolite-Based Positioning Systems

Changdon Kee, Hyoungmin So, Jeonghan Kim, Haeyoung Jun, Per Enge, and Sam Pullen

Abstract:	This paper presents the Line-of-Sight (LoS) unit vector error caused by the position uncertainty of a GPS user and GPS satellite and its affect on GPS accuracy. Especially, we emphasize the case of a pseudolite-based positioning system, where the distance between a user and pseudolite transmitters is very short. For GPS navigation, the LoS unit vector should be calculated using GPS satellite positions, and we estimate user position using this. However, the user position error, caused by thermal noise or multipath, also creates LoS unit vector error. It also causes range error, which could affect GPS positioning accuracy. It is widely known that the LoS unit vector error is negligible because the distance between a user and each GPS satellite is very long compared to the position uncertainty of the GPS user. The same is true of Differential GPS or DGPS. Thus, there is no problem in using the DGPS solution as an initial point without considering the effect of LoS error. For example, it is used to calculate the cycle ambiguity using Least Square Ambiguity Search Technique (LSAST) in Carrier-Phase Differential GPS (CDGPS). However, in pseudolite-based positioning system, the pseudolites may be located very close to the user. In this case, the LoS unit vector error due to the position error is not negligible and affects the range and position accuracy. If the distance between the user and the pseudolites is too short, the LoS unit vector error causes a large error in the DGPS solution such that it cannot be used as an initial point in LSAST. Because the LoS error is reflected in the observation equation in the same manner as measurement error, it is impossible to resolve the exact cycle ambiguity. As a result, the true ambiguity could be outside of the integer ambiguity candidates. Therefore, in order to use LSAST in pseudolite-based positioning system without considering the effect of LoS error, pseudolites must be as far from the user as possible. In this paper, we examine the minimum distance between the user and the pseudolites. Simulation results show that, in our case study, the pseudolites should be located at least 760 meters from the user. Unless the pseudolites located outside of this threshold, it is impossible to achieve centimeter-level CDGPS accuracy using the pseudolites. This paper can be used to design the constellation of pseudolites for indoor and outdoor system, for example, L1/L5 Airport Pseudolites (APLs) in LAAS and JPALS.
Published in:	Proceedings of the 2004 National Technical Meeting of The Institute of Navigation January 26 - 28, 2004 The Catamaran Resort Hotel San Diego, CA
Pages:	181 - 189
Cite this article:	Kee, Changdon, So, Hyoungmin, Kim, Jeonghan, Jun, Haeyoung, Enge, Per, Pullen, Sam, "Effect of the Error in the Line-of-Sight Unit Vector on Pseudolite-Based Positioning Systems," Proceedings of the 2004 National Technical Meeting of The Institute of Navigation, San Diego, CA, January 2004, pp. 181-189.
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