Figure 38.19 Plot of σ, the standard deviation of Δt, as a function of the carrier‐to‐noise ratio
Source: Reproduced with permission of IEEE.
38.5.4.1 Pseudorange Analysis
The variation in the pseudorange obtained by the receiver discussed in Section 38.5.2 is compared to the variation in the true range between a mobile receiver and cellular CDMA BTSs. For this purpose, the receiver was mounted on two platforms: (i) an unmanned aerial vehicle (UAV) and (ii) a ground vehicle [12, 18, 25].
UAV Results: Figure 38.20 shows the BTS environment, the UAV trajectory, and the experimental hardware setup. Signals from two cellular BTSs corresponding to the US cellular provider Verizon Wireless were tracked. The BTSs transmitted at a carrier frequency of 883.98 MHz and their positions were mapped prior to the experiment [37, 39]. The ground‐truth reference for the UAV trajectory shown in Figure 38.20 was taken from its onboard navigation system, which uses GPS, an INS, and other sensors. The distance D between the UAV and each BTS was calculated using the navigation solution produced by the UAV’s navigation system and the known BTS position. The pseudorange ρ was obtained from the cellular CDMA receiver that was mounted on the UAV. In order to validate the resulting pseudoranges, the variation of the pseudorange Δρ ≜ ρ − ρ(0) and the variation in distance ΔD ≜ D − D(0) are plotted in Figure 38.21 for the two BTSs, where ρ(0) is the initial value of the pseudorange, and D(0) is the initial distance between the UAV and the BTS. It can be seen from Figure 38.21 that the variations in the pseudoranges closely follow the variations in distances. The difference between ΔD and Δρ for a particular BTS is due to the variation in the clock bias difference
Figure 38.20 BTS environment and experimental hardware setup for the UAV experiment. Map data: Google Earth (Khalife et al. [12]).
Source: Reproduced with permission of IEEE.
Figure 38.21 Variation in pseudoranges and the variation in distances between the receiver and two cellular CDMA BTSs for the UAV experiment (Khalife et al. [12]).
Source: Reproduced with permission of IEEE.
Ground Vehicle Results: Figure 38.22 shows the BTS environment, ground vehicle trajectory, and the experimental hardware setup. Signals from two cellular BTSs corresponding to the US cellular provider Verizon Wireless were tracked. The BTSs transmitted at a carrier frequency of 882.75 MHz, and their positions were mapped prior to the experiment [37, 39]. The ground‐truth reference for the ground vehicle trajectory in Figure 38.22 was obtained from the Generalized Radionavigation Interfusion Device (GRID) GPS SDR [58]. The change in the true range and the change in pseudorange are plotted in Figure 38.23, similarly to the UAV experiment. It can be seen from Figure 38.23 that the variations in the pseudoranges closely follow the variations in distances. The difference between ΔD and Δρ for a particular BTS is due to the variation in the clock bias difference
38.5.4.2 Ground Vehicle Navigation
Two cars (mapper and navigator) were equipped with the cellular CDMA navigation receiver discussed in Section 38.5.2. The receivers were tuned to the cellular carrier frequency 882.75 MHz, which is a channel allocated to the US cellular provider Verizon Wireless. The mapper was stationary and was estimating the clock biases of the 3 BTSs via a WLS estimator as discussed in Section 38.4.1. The BTSs’ positions were known to the mapper, and the position states were expressed in a local 3D frame whose horizontal plane passes through the three BTSs and is centered at the mean of the BTSs’ positions. The height of the navigator was known and constant in the local 3D frame over the trajectory driven and was passed as a constant parameter to the estimator. Hence, only the navigator’s 2D position and its clock bias were estimated through the WNLS described in Section 38.4.1. The weights of the WNLS were calculated using Eq. (38.17) with