38.6.4.3 Aerial Vehicle Navigation
A UAV was equipped with the cellular LTE navigation receiver discussed in Section 38.6.2. When a UAV flies high enough, the received signal to the UAV does not experience multipath from the surrounding environment, except from the UAV’s body. Here, the multipath effect from the UAV’s body is negligible; therefore, tracking only the SSS yields good results, and the CRS was not used. This significantly decreases the computational burden in the receiver. It also reduces the need for a high sampling rate, which lowers the hardware cost and size. The receiver was tuned to the cellular carrier frequency of 1955 MHz, which is used by the US cellular provider AT&T.
Over the course of the experiment, the UAV was flying at an altitude of 40 m. The receiver was listening to three eNodeBs, each of which had two transmitting antennas with 20 MHz transmission bandwidth. The positions of the eNodeBs were mapped prior to the experiment with approximately 2 m accuracy. All measurements and trajectories were projected onto a 2D plane. Subsequently, only the horizontal position of the receiver was estimated. It was assumed that the receiver had access to GPS, and GPS was cut off at the start time of the experiment. Therefore, the EKF’s states were initialized with the values obtained from the GPS navigation solution. The EKF process noise and measurement noise covariances were set in a similar manner to the ground vehicle navigation experiment. The environment layout as well as the true and estimated receiver trajectories are shown in Figure 38.53. It can be seen from Figure 38.53 that the navigation solution obtained from LTE signals closely follows the GPS navigation solution. The ground‐truth trajectory was obtained from the GRID GPS SDR [58].
In an urban environment, the pseudoranges received by a ground vehicle will suffer from more multipath‐induced error compared to the pseudoranges received by a UAV with LoS conditions. However, this comparison can be made as long as the ground vehicle and UAV are navigating in the same environment, using the same eNodeBs, and following the same trajectories, except that one is on the ground while the other is airborne. In the results presented in Figures 38.52 and 38.53, the ground vehicle was equipped with a better USRP than the one on the UAV, due to payload limitations. Consequently, the LTE receiver onboard the ground vehicle was able to listen to more eNodeBs than the receiver onboard the UAV, providing the former with more measurements at a better geometric diversity than the latter. Moreover, the UAV did not use the CRS signals, which were used by the ground vehicle to aid its SSS tracking loops. These aforementioned factors resulted in the position root‐mean‐squared error (RMSE) of the ground vehicle being less than the position RMSE of the UAV.
Figure 38.52 (a) Experimental hardware and software setup and environment layout in downtown Riverside, California, showing eNodeBs’ locations and the traversed trajectory as estimated by GPS and LTE signals.
Map data: Google Earth (Shamaei et al. [65]). Source: Reproduced with permission of IEEE.
Figure 38.53 Experimental hardware setup and environment layout in Riverside, California, showing eNodeBs’ locations and the traversed trajectory as estimated by GPS and LTE signals.
Map data: Google Earth (Shamaei et al. [65]). Source: Reproduced with permission of IEEE.
38.7 BTS Sector Clock Bias Mismatch
A typical BTS transmits into three different sectors within a particular cell. Ideally, all sectors’ clocks should be driven by the same oscillator, which implies that the same clock bias (after correcting for the PN offset) should be observed in all sectors of the same cell. However, factors such as the unknown separation between the phase centers of the sector antennas and delays due to RF connectors and other components (e.g. cabling, filters, amplifiers) cause the clock biases corresponding to different BTS sectors to be slightly different. This behavior was consistently observed experimentally in different locations, at different times, and for different cellular providers [18, 22]. In the following sections, a stochastic dynamic model for the observed clock bias mismatch for different sectors of the same BTS cell is derived.
38.7.1 Sector Clock Bias Mismatch Detection
In order to demonstrate the presence of the discrepancy between sectors’ clock biases, a cellular CDMA receiver was placed at the border of two sectors of the i‐th BTS cell corresponding to the US cellular provider Verizon Wireless and was drawing pseudorange measurements from both sector antennas. The receiver had full knowledge of its state and of the BTS’s position. Subsequently, the receiver solved for the BTS clock biases
Figure 38.54 suggests that the clock biases
where ɛi is a random sequence that models the discrepancy between the sectors’ clock biases and
is the indicator function.
Note that the cdma2000 protocol requires all PN offsets to be synchronized to within 10 μs from GPS time; however, synchronization to within 3 μs is recommended [80]. Since each sector of a BTS uses a different PN offset, then the clock biases