# Performance Characterization of GNSS/IMU/DVL Integration under Real Maritime Jamming Conditions
## 5 Results
### Results of the Maritime Jamming Campaign
#### 5.2.2 Tightly and Loosely Coupled UKF Results  
After the discussion of the GPS single point positioning results in the last paragraph, now the results of both loosely and tightly coupled UKF using GPS, IMU, and Doppler velocity log (DVL), as introduced in Section 3, will be analyzed. In this section, we focus on positioning results using the constant noise model as the simplest possible measurement model for the GPS measurements, with a comparison of the results of the different noise models provided afterward. In Figure 11, the positioning results are presented for an example of 8 min time span with \(>\)3 min when no SPP solution can be obtained (portside antenna, around 6:50 UTC (see Figure 9), as the number of satellites drops temporarily below four due to the proximity to the jammer. The GPS outage starts after a segment with an already relatively bad GDOP due to a decreased number of satellites, as can be seen from the HPE for the pure GPS SPP solution between \(t=1\) and \(t=2\) min. Both tightly and loosely coupled UKFs show good smoothing behavior within the first 2 min of that segment and keep their horizontal positioning error significantly below 2 m. Within the time interval, when the number of satellites drops below four, the loosely coupled UKF starts to drift away linearly, while the tightly coupled UKF still nicely follows the vessel track, keeping the HPE below 2 m. This example is an excellent demonstration of a great advantage of a tightly coupled architecture when compared to a simpler loosely coupled technique in a real application scenario, where the pseudorange measurements are exploited even in the case where fewer then four satellites are available. For the loosely coupled UKF, the drift during the GNSS outage is apparently linear in time. This is expected when a classical GNSS/IMU integration is augmented with the velocity measurements (DVL can be seen as an odometer). This proves to be a great advantage of DVL augmentation when compared to a more classical IMU/GNSS approach, where inertial sensors typically show position drift to be cubic in time. In Figure 12 the positioning results are shown for the complete scenario (approximately 2 h). In order to evaluate the UKF with the most challenging scenario, we have used here the GPS measurements from the midship antenna, which showed the largest GPS single point positioning errors (see Figure 9). During the first passing of the jammer, both tightly and loosely coupled filter showed a comparable performance with the number of the tracked satellites dropping very fast to one or even to zero satellites. In this challenging case the position solution of a tightly coupled UKF also shows a linear drift exactly due to the same reason as the loosely coupled UKF described above. Apparently, an available single range measurement is not sufficient to constrain the estimated position  
Figure 10: Mean HPE versus GDOP for all three antennas together. Error bars mark the 1\(\sigma\) values. of the filter. This could be, at least to some extent, explained by the fact that both the position and the receiver clock offset have to be estimated. An interesting idea for a future measurement campaign would be to investigate the performance gain of a tightly coupled UKF when a more stable Rubidium oscillator is used as the reference of the receiver's clock. During the second jammer passing, the number of tracked satellites varies several times around four, with a maximum of 6 and a minimum of 0 satellites. Here, the tightly coupled filter still shows some advantages, although the loosely coupled filter performs reasonably well. The largest difference between the filters can be observed during the third passing of the jammer. During that time span with a GPS outage, for a short period of time, four satellites were tracked. The GDOP for this four satellite constellation is larger than 50 (outside the scale of Figure 9d), and the largest positioning errors (\(\mathrm{HPE}\approx 200\) m) occur.