Figure 38.48 DLL performance as a function of C/N0 for non‐coherent discriminators: dot‐product discriminator (solid line) and early‐power‐minus‐late‐power discriminator (dashed line), Bn, DLL = {0.05, 0.005} Hz, and teml = 1 (Shamaei et al. [74]).
Source: Reproduced with permission of IEEE.
38.6.3.3 Code Phase Error Analysis in Multipath Environments
Sections 38.6.3.1 and 38.6.3.2 evaluated the ranging accuracy with coherent and non‐coherent baseband discriminators in the presence of additive white Gaussian noise. However, multipath is another significant source of error, particularly for ground receivers. Multipath analysis and mitigation for navigation with LTE signals is an ongoing area of research [3, 11, 15, 19, 63, 73, 74, 76–79].
38.6.4 Cellular LTE Navigation Experimental Results
This section presents experimental results for navigation with cellular LTE signals. Section 38.6.4.1 analyzes the pseudorange obtained with the SSS and CRS signals produced by the receiver discussed in Section 38.6.2. Sections 38.6.4.2 and 38.6.4.3 present navigation results with aerial and ground vehicles, respectively.
38.6.4.1 Pseudorange Analysis
This section evaluates the pseudorange obtained by the receiver discussed in Section 38.6.2. To this end, the pseudorange variation from GPS is compared with the pseudorange variation due to (i) only tracking the SSS and (ii) aiding the SSS tracking loops with the CRS. The receiver was mounted on a ground vehicle and was tuned to the carrier frequencies of 1955 and 2145 MHz, which are allocated to the US LTE providers AT&T and T‐Mobile, respectively [63]. The transmission bandwidth was measured to be 20 MHz. The vehicle‐mounted receiver traversed a total trajectory of 2 km while listening to the 2 eNodeBs simultaneously as illustrated in Figure 38.49. The position states of the eNodeBs were mapped beforehand. Figures 38.50 and 38.51 show (a) the change in the pseudoranges between the receiver and the 2 eNodeBs, (b) the error between the GPS pseudorange and the LTE pseudoranges, and (c) the distance error cumulative distribution function (CDF) of the LTE pseudoranges.
Figure 38.49 LTE environment layout and experimental hardware setup. Map data: Google Earth (Shamaei et al. [63]).
Source: Reproduced with permission of Z. Kassas (International Technical Meeting Conference).
Figure 38.50 (a) Estimated change in pseudorange and estimated CIR at t = 13.04 s for eNodeB 1. The change in the pseudorange was calculated using (1) SSS pseudoranges, (2) SSS+CRS pseudoranges, and (3) true ranges obtained using GPS. (b) Pseudorange error between (1) GPS and SSS and (2) GPS and SSS+CRS. (c) CDF of the error in (b) (Shamaei et al. [63]).
Source: Reproduced with permission of Z. Kassas (International Technical Meeting Conference).
Figure 38.51 (a) Estimated change in pseudorange and estimated CIR at t = 8.89 s and t = 40.5 s for eNodeB 2. The change in the pseudorange was calculated using (1) SSS pseudoranges, (2) CRS pseudoranges, and (3) true ranges obtained using GPS. (b) Pseudorange error between (1) GPS and SSS and (2) GPS and SSS+CRS. (c) CDF of the error in (b) (Shamaei et al. [63]).
Source: Reproduced with permission of Z. Kassas (International Technical Meeting Conference).
The error in the pseudorange obtained by tracking the SSS is mainly due to multipath. The estimated CIR at t = 13.04 s for eNodeB 1 and t = 8.89 s and t = 40.5 s for eNodeB 2 show several peaks due to multipath, which are dominating the line‐of‐sight (LoS) peak. These peaks contributed a pseudorange error of around 330 m at t = 13.04 s for eNodeB 1 and around 130 m at t = 8.89 s for eNodeB 2. These results highlight the importance of utilizing the CRS signals to correct for multipath‐induced errors.
38.6.4.2 Ground Vehicle Navigation
A car was equipped with the cellular LTE navigation receiver discussed in Section 38.6.2. The receiver was tuned to the cellular carrier frequencies 739 MHz and 1955 MHz, which are used by the US cellular provider AT&T. The PLL, FLL, and DLL noise‐equivalent bandwidths were set to 4, 0.2, and 0.001 Hz, respectively. The adaptive threshold approach proposed in [65] was adopted to mitigate multipath.
All measurements and trajectories were projected onto a 2D plane. 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 standard deviation of the initial uncertainty of position and velocity were set to be 5 m and 0.01 m/s, respectively [55]. The standard deviation of the initial uncertainty of the clock bias and drift were set to be 0.1 m and 0.01 m/s, which were obtained empirically. The clock oscillators were modeled as oven‐controlled crystal oscillators (OCXOs) with