# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 4 Results
### Performance with Measurement Biasing
Because the radiometric solution is clearly preferred, we can assume that the source of the mis-modeling is something to which the optical-only and fused filters have greater sensitivity (e.g., biasing in the optical measurement model). These results show that the Magill weights are largely insensitive to optical biasing, while our new gating network is able to clearly identify the presence of a problem while also indicating the potential source of the issue. Moving forward, we will investigate how these gating networks and filters perform in the presence of radiometric measurement biasing. The position uncertainty and error due to a Large Radiometric Measurement Bias (Table 2) for the radiometric-only and fused filters are shown in Figures 12 and 13. Neither filter diverges because a large portion of the radiometric biases are absorbed by different parameters in the filter (e.g., ranging errors can be absorbed by clock error parameters); however, the effect of the biases can still be seen. The radiometric-only filter position error drifts noticeably outside of the 3-\(\sigma\) bounds. The biases' effects on the fused filter are more subtle. Essentially, the additional un-biased optical information helps constrain the solution to stay near the true trajectory, which gives an advantage over the radiometric-only solution. However, when comparing the fused filter's performance in the no bias scenario setup, we can see a slight increase in position error that is attributable to the presence of these radiometric measurement biases. Figure 11: Optimal gating network weights with biased optical measurements. Small (solid lines), medium (dotted lines), and large (dashed lines) biasing cases are included. Figure 12: Position error (blue) and RTPC uncertainty (1-\(\sigma\) (orange) and 3-\(\sigma\) (red)) for radiometric-only filter in Large Radiometric Bias setup. Further investigating the effect of these radiometric biases, the clock phase uncertainty and error statistics from the fused filter are shown in Figure 14. When processing un-biased radiometric data, the fused filter outputs clock errors that are near 0-\(\sigma\) in size; however, when the large radiometric bias is introduced the filter now outputs clock error in the range of 1-2 \(\sigma\). More specifically, the clock error is approximately 2 \(\upmu\)s, which is what should be expected from the 500 m range bias that we introduced. Essentially, this result shows that the filter absorbed the range bias into the clock error modeling in a way that is not statistically anomalous. This is why the fused filter is still able to output accurate state estimates despite being given biased radiometric data. By turning down the clock phase uncertainty, we would be able to better detect smaller radiometric errors; however, it is important not set the clock uncertainty too low where the filter becomes susceptible to divergence from realistic/anticipated clock errors. The weights from the Magill gating network for these biased radiometric data scenarios are shown in Figure 7:0 Once again, we find that that the Magill weights overwhelmingly prefer the fused filter despite the introduction of biased measurements. This makes sense, since the fused filter is still able to output statistically healthy estimates and it still produces the smallest uncertainty in its estimate. It is interesting to note that the size of the radiometric bias does have a noticeable effect on how quickly the filter weights converge to their steady-state values. As the size of the bias increases, we find that the filter weights more quickly favor the fused filter over the radiometric-only filter--the optical-only is always low-weighted due to its high uncertainty metrics. This makes intuitive sense because the radiometric-only solution is more significantly compromised by the radiometric data  
Figure 7:1 Clock phase error and uncertainty for fused filter in Large Radiometric Bias setup.