Position, Navigation, and Timing Technologies in the 21st Century

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).

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 38.6for 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%.

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 38.5and 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 38.63illustrates 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 GPSwas reduced upon fusing the five cellular pseudoranges to 0.16( V GPS).

Table 38.6 DOP values for M GPS SVs + N cellular towers

Figure 38.62 (a) Sky plot of GPS SVs: 14, 18, 21, 22, and 27 used for the 5 SV scenarios. For the 4 SV scenario, SVs 14, 21, 22, and 27 were used. The elevation mask, el sv, min, was set to 20° (dashed red circle). (b) Top: Cellular CDMA tower locations and receiver location. Bottom: Uncertainty ellipsoid (yellow) of navigation solution from using pseudoranges from five GPS SVs and uncertainty ellipsoid (blue) of navigation solution from using pseudoranges from five GPS SVs and three cellular CDMA towers. Map data: Google Earth (Morales et al. [7]).

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

Traditional integrated navigation systems, particularly onboard vehicles, integrate GNSS receivers with an INS. When these systems are integrated, the long‐term stability of a GNSS navigation solution complements the short‐term accuracy of an INS. GNSS–INS fusion architectures with loosely coupled, tightly coupled, and deeply coupled estimators are well studied [87]. Regardless of the coupling type, the errors of a GNSS‐aided INS will diverge in the absence of GNSS signals, and the rate of divergence depends on the quality of the IMU. Cellular signals could be used in place of GNSS signals to aid an INS [44]. This section outlines how cellular signals could be used to aid an INS in the absence of GNSS signals. Additional details can be found in [4, 45, 88, 89].

This section is organized as follows. Section 38.9.1discusses how to aid the INS with cellular signals in a radio SLAM fashion. Sections 38.9.2and 38.9.3present simulation and experimental results, respectively, of a UAV navigating in a radio SLAM fashion, while aiding its INS with ambient cellular signals.

Figure 38.63 Experimental results comparing the navigation solution uncertainty ellipsoids produced by (1) GPS alone and (2) GPS and cellular CDMA and LTE. Map data: Google Earth (Kassas et al. [6]).

Source: Reproduced with permission of IEEE.

To correct INS errors using cellular pseudoranges, an EKF framework similar to a traditional tightly coupled GNSS‐aided INS integration strategy can be adopted, with the added complexity that the cellular towers’ states (position and clock error states) are simultaneously estimated alongside the navigating vehicle’s states (position, velocity, attitude, IMU measurement error states, and receiver clock error states). This framework is composed of two modes:

Mapping ModeThe EKF produces estimates and associated estimation error covariances of both the navigating vehicle and the cellular towers’ states (augmented in ) using both GNSS SV and cellular pseudoranges. Between aiding corrections, the EKF produces the state prediction and prediction error covariance P− using the INS and receiver and cellular transmitter clocks models. When an aiding source is available, either GNSS SV or cellular pseudoranges, the EKF produces a state estimate update and associated estimation error covariance P+.