Position, Navigation, and Timing Technologies in the 21st Century. Группа авторов

      With the exception of GNSS receivers mounted on high‐flying aerial vehicles and SVs, all GNSS SVs are typically above the receiver [85]; that is, the elevation angles in H_sv are theoretically limited between 0° and 90°. Moreover, GNSS receivers typically ignore signals arriving from GNSS SVs below a certain elevation mask (typically 0° to 20°), since such signals are heavily degraded due to the ionosphere, troposphere, and multipath. When using GNSS together with cellular signals for navigation, the elevation angle span may effectively double to be between −90° and 90°. For ground vehicles, useful measurements can be made on cellular towers at elevation angles of . For aerial vehicles, cellular BTSs can reside at elevation angle as low as , for example, if the vehicle is flying directly above the BTS.

To compare the DOP of a GNSS‐only navigation solution with a GNSS + cellular navigation solution, a receiver position expressed in an Earth‐Centered Earth‐Fixed (ECEF) coordinate frame was set to . The elevation and azimuth angles of the GPS SV constellation above the receiver over a 24 hour period was computed using GPS SV ephemeris files from the Garner GPS Archive [86]. The elevation mask was set to el_{sv, min} ≡ 20^°. The azimuth and elevation angles of three towers, which were calculated from surveyed terrestrial cellular CDMA tower positions in the receiver’s vicinity, were and . The resulting VDOP, HDOP, GDOP, and associated number of available GPS SVs for a 24 hour period starting from midnight, September 1, 2015, are plotted in Figure 38.61. These results were consistent for different receiver locations and the corresponding GPS SV configurations. The following can be concluded from these plots for using N ≥ 1 cellular towers. First, the resulting VDOP using GPS + N cellular towers is always less than the resulting VDOP using GPS alone. Second, using GPS + N cellular towers prevents large spikes in VDOP when the number of GPS SVs drops. Third, using GPS + N cellular towers also reduces both HDOP and GDOP. Additional analysis is given in [7, 8].

Figure 38.61 Figure (a) represents the number of GPS SVs with an elevation angle > 20° as a function of time. Figures (b)–(d) correspond to the resulting VDOP, HDOP, and GDOP, respectively, of the navigation solution using GPS only, GPS + 1 cellular tower, GPS + 2 towers, and GPS + 3 towers (Morales et al. [7]).

      Source: Reproduced with permission of Z. Kassas (International Technical Meeting Conference).

      38.8.2 GPS and Cellular Experimental Results

      38.8.2.1 Ground Vehicle Navigation

A ground‐vehicle‐mounted receiver was placed in an environment comprising N cellular CDMA towers. The states of the towers , where , were collaboratively estimated by mapping receivers in the navigating receiver’s vicinity. The mapping receivers had knowledge of their own states from GPS. The pseudoranges made by the receiver on the N cellular towers along with the estimates produced by the mapping receivers were fed to a least‐squares estimator to produce an estimate of the receiver’s states and an associated estimation error covariance matrix P, from which the VDOP, HDOP, and GDOP were calculated and are tabulated in Table 38.6 for M GPS SVs and N cellular towers. A sky plot of the GPS SVs is shown in Figure 38.62(a). The tower locations, receiver location, and a comparison of the resulting 95th‐percentile estimation uncertainty ellipsoids of for {M, N} = {5, 0} and {5, 3} are illustrated in Figure 38.62(b). The corresponding vertical errors were 1.82 m and 0.65 m, respectively. Hence, adding three cellular towers to the navigation solution that used five GPS SVs reduced the vertical error by 64.3%.

      38.8.2.2 Aerial Vehicle Navigation

A UAV was flown in a cellular environment comprising three cellular CDMA BTSs and two LTE eNodeBs, whose states were estimated by mapping receivers in their environment [6]. The UAV was equipped with the cellular CDMA and LTE navigation receivers discussed in Sections 38.5 and 38.6, respectively, which produced pseudorange measurements to all five towers. The UAV was also equipped with the GRID SDR that produced pseudorange measurements to seven GPS SVs. The towers’ state estimates and GPS and cellular tower pseudoranges were used to estimate the UAV’s 3D position and clock bias through a nonlinear least‐squares estimator. Figure 38.63 illustrates the environment and the resulting 95th‐percentile uncertainty ellipsoids associated with the position estimate using (i) seven GPS SVs and (ii) seven GPS SVs along with three cellular CDMA BTSs and two LTE eNodeBs. Note that the volume of the GPS‐only navigation solution uncertainty ellipsoid V_GPS was reduced upon fusing the five cellular pseudoranges to 0.16(V_GPS).

Table 38.6 DOP values for M GPS SVs + N

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