38.5 shows the date in which the test was conducted in MM/DD/YYYY format.
Figure 38.60 shows six realizations, 5 min each, of the discrepancy corresponding to Tests (a)–(f) in Table 38.5. It can be seen from Figure 38.60 that the behavior of the discrepancy is consistent across the tests. The initial discrepancy is subtracted out so that all realizations start at the origin. The inverse of the time constant for each realization was found to be
Table 38.5 Test dates, locations, and carrier frequencies
| Test | Date | Location | Frequency (MHz) | Provider |
|---|---|---|---|---|
| (a) | 01/14/2016 | 1 | 882.75 | Verizon |
| (b) | 01/20/2016 | 1 | 882.75 | Verizon |
| (c) | 08/28/2016 | 2 | 883.98 | Verizon |
| (d) | 09/02/2016 | 2 | 883.98 | Verizon |
| (e) | 08/28/2016 | 3 | 1940.0 | Sprint |
| (f) | 09/02/2016 | 3 | 1940.0 | Sprint |
38.7.3 PNT Estimation Performance in the Presence of Clock Bias Discrepancy
The clock bias discrepancy will degrade the navigation solution in two scenarios: (i) whenever the receiver is receiving signals from both sector antennas within a BTS cell and (ii) whenever the receiver is exchanging pseudorange measurements with another receiver in a different sector (e.g. in a mapper/navigator framework or a collaborative navigation framework). A practical upper bound on the introduced error in the navigation solution due to this discrepancy as well as theoretical lower bounds on the estimation error covariance for static and batch estimators are derived in [25].
Figure 38.59 Locations of the cellular CDMA BTSs: Colton, California; Riverside, California; and the University of California–Riverside (UCR).
Map data: Google Earth (Khalife et al. [12]; Khalife and Kassas [22]). Source: Reproduced with permission of Institute of Navigation, IEEE.
Figure 38.60 Six realizations, five minutes each, of the sector clock bias discrepancy for the tests in Table 38.5 (Khalife et al. [12]; Khalife and Kassas [22]).
Source: Reproduced with permission of Institute of Navigation, IEEE.
38.8 Multi‐Signal Navigation: GNSS and Cellular
The quality of the GNSS navigation solution is determined by both the pseudorange measurement noise statistics and the spatial geometry of GNSS SVs. GNSS position solutions suffer from a relatively high vertical estimation uncertainty due to the lack of GNSS SV angle diversity (SVs are usually above the receiver). To address this, an external sensor (e.g. a barometer) is typically fused with a GNSS receiver. Cellular towers are abundant and available at varying geometric configurations unattainable by GNSS SVs. For example, BTSs could be below an aerial vehicle‐mounted receiver. Therefore, fusing cellular signals with GNSS signals would yield a more accurate navigation solution, particularly in the vertical direction. This section highlights the benefits of fusing cellular signals with GNSS signals.
This section is organized as follows. Section 38.8.1 studies the dilution of precision (DOP) reduction due to fusing cellular signals with GNSS signals. Section 38.8.2 shows experimental results with ground and aerial vehicles.
38.8.1 DOP Reduction
To study the DOP reduction due to the fusion of cellular and GNSS signals, consider an environment comprising a receiver making pseudorange measurements on M GNSS SVs and N terrestrial cellular BTSs. The pseudorange measurements are fused through a WNLS estimator to estimate the states of the receiver
