# Performance Characterization of GNSS/IMU/DVL Integration under Real Maritime Jamming Conditions
## 5 Results
### Lab Experiment
The measurements affected by the jamming signal show comparable behavior with fewer measurements for low elevation angles but only slightly overall increased standard deviations. Interestingly, the effect of the jamming signal on the standard deviation of the pseudorange measurements is rather minor, and this seems to be counterintuitive compared to the expected behavior of a typical receiver in the presence of a jammer. For the highest jamming signal power, only an increase by a factor of about 1.3 for the standard deviation can be observed. As an overbound for all data, including both jamming scenarios, the following functional dependence of the standard deviation \(\sigma\) and the elevation angle \(\alpha\) was determined (see Figure 7):  
\[\sigma=A\times(\sin(\alpha))^{-B} \tag{7}\]  
with \(A=0.85\) m and \(B=0.6\). Elevation-dependent functions have often been applied in geodetic applications for expressing the expected noise of GNSS observations [46; 47]. Finding the unknown parameters \(A\) and \(B\) constitutes a nonlinear regression problem, solved here by applying a least-squares adjustment. In Figure 8, for the same measurements as in Figure 7, the standard deviation as a function of the CN0 is shown. Interestingly, in the absence of the jammer, the reference data show an almost linear dependency on CN0. A linear fit leads to a slope of \(a=-0.06\) m/dBHz and an offset of \(b=3.95\) m. This linear dependency is different from a suggested exponential dependency as reported in literature [48; 49]. To some extent, this could be explained by a new firmware of the receiver and a different antenna used compared to our previous work [49]. Comparing the curve for Scenario A with the scenario without jamming, mainly a parallel shift towards smaller CN0 values without a significant increased pseudorange error can be found. This finding is consistent with the analysis of Figures 6 and 7. Furthermore, the curve for Scenario B is mainly shifted towards smaller CN0 values; it also starts at slightly higher standard deviations for the pseudorange error (the right-most end of the line starts at a higher error value with increasing jammer power), and error deviation increases faster with decreasing CN0 values. Figure 6: 2D histogram plot of carrier-to-noise density ratio (CN0) versus elevation angle without jamming (**left**); for Scenario A (**middle**) and Scenario B (**right**). Summarizing the results of Figure 8, one can conclude that, for the used receiver, the functional dependency of the standard deviation of the pseudorange error on the carrier-to-noise density, as is observed for the unjammed scenario, is rather an indirect correlation. The receiver tracking noise error, which should strongly depend on CN0, is small compared to other dominating errors, such as iononspheric, tropospheric, and multipath errors, at least for CN0 \(>\) 40 dBHz. For the usage of pseudorange measurements within a tightly coupled KF, this leads to an unexpected conclusion that a CN0-based weighting scheme, calibrated for the unjammed scenario, could result in overestimation of the pseudorange errors in the vicinity of a jammer. Interestingly, the main impact of the applied sweeping PPD jammer on the used geodetic receiver is the reduction of the number of tracked satellites, while the pseudorange error statistics is only slightly effected. As expected, the receiver's reported CN0 directly correlates with the applied jamming signal strength. Therefore, the dependency of the CN0 on the elevation angle is a good candidate for an indicator of the presence of a jamming signal in the environment. Of course, as the CN0  
Figure 8: Recorded dependency of the pseudorange error statistics on the receiver reported CN0 value for lab experiment. Figure 7: Measured dependency of the pseudorange error statistics (standard deviation) on the elevation angle in the lab experiment. dependency is setup-specific, the relationship between the reported CN0 and the elevation angle has to be determined for each sensor configuration separately.