# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 4 Results
### Performance with Measurement Biasing  
Having established how these filters and gating networks perform when measurements are properly modeled, we now move toward assessing the weighting schemes' performance in the presence of measurement biasing. In order to assess the sensitivity of the filter banks to bias types, we will run different biasing scenarios where the size of the bias is varied. These scenarios are defined in Table 2. We will evaluate the effects of optical and radiometric biasing independently in the ensuing analysis. These biases are simply added to the actual measurement; however, some are representative of realistic issues in the system. The optical bias can be seen as a slight mis-modeling in the fixed orientation of the camera relative to the spacecraft attitude. The range bias can be seen as either a clock bias (spacecraft or ground-based) or transponder delay mis-model associated with the receiver electronics. The effects of a small optical bias on the optical-only and fused filters are shown in Figures 8 and 9, respectively. It is clear that even this small bias (on the order of uncertainty in the measurements) has the effect of causing the filters to have significantly higher position errors than predicted by the filter's uncertainty metrics. The solutions do not fully diverge, but larger biases could cause this to occur. The radiometric-only solution is unaffected in this scenario, since it does not process the biased optical measurements. \begin{table}
\begin{tabular}{l l l l l} \hline \hline  & \multicolumn{2}{c}{**Optical Biasing**} & \multicolumn{2}{c}{**Radiometric Biasing**} \\ \hline  & \
\begin{tabular}{l} **Sample Bias** \\ **(pix)** \\ \end{tabular} & \multicolumn{1}{c}{**Line Bias (pix)**} & \multicolumn{1}{c}{**Range Bias (m)**} &
\begin{tabular}{l} **Doppler Bias** \\ **(mHz)** \\ \end{tabular} \\ \hline No Bias & 0.0 & 0.0 & 0.0 & 0.0 \\ \hline Small Bias & 0.2 & 0.3 & 5.0 & 0.03 \\ \hline Medium Bias & 2.0 & 3.0 & 50.0 & 0.3 \\ \hline Large Bias & 20.0 & 30.0 & 500.0 & 3.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measurement Biasing Used in Simulations. Figure 7: Optimal gating network weights with properly modeled measurements. The resulting weights from the Magill gating network for these optical bias scenarios are shown in Figure 10. From these results we can make two clear conclusions: (1) the fused filter is still preferred overwhelmingly and (2) the size of the optical bias does not have a significant effect on how the Magill weights behave. Essentially, the Magill weights are unable to identify that the radiometric-only solution is the best performing filter. This is because the method for computing the weights necessitates that all measurements be used to compute filter weights, even measurements that are not processed by specific filters. This rigidness results in all three filters behaving poorly with the biased optical measurements, but because the fused filter has the smallest uncertainty it ends up rising to the top. Our optimal gating network's weights for this scenario with biased optical measurements are shown in Figure 11. The rigidity of the Magill weighting scheme is contrasted by our optimal gating network, which can be retooled to ignore unprocessed measurements when computing filter weights. The weights show a clear preference for the radio solution, and this preference becomes more significant as the size of the bias in the optical  
Figure 8: Position error (blue) and RTPC uncertainty (1-\(\sigma\) (orange) and 3-\(\sigma\) (red)) for optical-only filter in Small Optical Bias setup. Figure 10: Magill gating network weights with biased optical measurements. Figure 9: Position error (blue) and RTPC uncertainty (1-\(\sigma\) (orange) and 3-\(\sigma\) (red)) for fused filter in Small Optical Bias setup. measurement grows. As previously discussed, the fact that the filter weights deviate significantly from their nominal values (i.e., equally weighted at \(1/N\)) can be viewed as a sign of mis-modeling in the system.