# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 4 Results
### Dynamical Model Mis-Modeling
In initial analysis, this increased sensitivity does not seem to be associated with simulation geometry (i.e., net attitude control thrust orientation with respect to Earth and optical targets), but it may be due to the uncertainties present in the filter. The optical filter has larger state uncertainties, in general, which can make it less sensitive to dynamic mis-modeling and it has fewer parameters than radiometric data (e.g., clock error, transponder bias, etc.) that could improperly absorb the dynamic mis-modeling. Figure 17: Position error (blue) and RTPC uncertainty (1-\(\sigma\) (orange) and 3-\(\sigma\) (red)) for optical-only filter with attitude thruster mis-modeling. The Magill gating network weights for our filter bank with 6 filters are shown in Figure 20. These results show that the Magill gating network overwhelmingly favors the properly modeled fused filter (fused-Q). This makes sense because this filter is properly modeled and fully-informed, so it would have small residuals and small uncertainties. By strongly favoring the fused-Q filter over the fused filter, we can postulate that there is mis-modeling in the system because the lower uncertainty filter (the fused) should be preferred if no mis-modeling were present--it is hard to validate this fully, though, because the Magill weights have been shown to be unable to reliably detect mis-modeling through our previous examples. There is a tradeoff between increasing dynamic uncertainty parameters in the filter. By increasing these parameters, we essentially lessen statistical constraints on the data, which allow the filter to absorb more error, which can yield smaller measurement residuals; however, this comes with higher estimate uncertainties, generally. The Magill gating network accounts for the size of the measurement residual and the innovations' uncertainty, which means adding dynamic uncertainty to the system can yield results that are difficult to predict. Figure 19: Position error (blue) and RTPC uncertainty (1-\(\sigma\) (orange) and 3-\(\sigma\) (red)) for fused filter with attitude thruster mis-modeling. Figure 20: Magill gating network weights with attitude thruster mis-modeleing. The weights from our optimal gating network are shown in Figure 21. The results clearly indicate an anomaly is occurring due to the fact the weights are consistently different from one another. We see that this gating network indicates a preference primarily for the optical filters, and secondarily to the properly modeled fused and radiometric-only filters. The dynamically mis-modeled fused and radiometric-only filters have the least priority. These results are fairly intuitive based on our previous analysis. We previously saw that the optical filters were generally unaffected by the dynamic mis-modeling, so we would expect them to rank highly in the gating network. Similarly, the properly modeled radiometric-only and fused filters, should perform well because they are not subject to any unaccounted biasing. However, two results are odd: (1) the optical filters outperform the properly modeled radiometric-only and fused filters and (2) the effects of the dynamic mis-modeling seem to diminish over time. In the former case, this seems to imply that the optical filters produce lower residuals than the other two properly modeled filters in a \(\chi^{2}\)-sense. This is somewhat confirmed by the position tracking results (Figure 17), which shows position error for the optical filter is generally below the 1-\(\sigma\) bound. This might imply that the uncertainty metrics from the optical filter are too large in this scenario. In the latter case, this result is somewhat un-intuitive because we saw that position error in the fused and radiometric-only filters actually grows over time, so we would expect their residuals to grow commensurately. This result would lead to drops in the weights for these two filters, not increases as we have observed. This type of result warrants more study and should be addressed in future work.