# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 4 Results
### Dynamical Model Mis-Modeling
Overall, the weights from this gating network do tell us that an anomaly is occurring in the system. The gating networks preference for the optical filters seems to indicate that the problem is something to which the optical data is relatively insensitive. Furthermore, the gating network's secondary preference for the higher dynamic uncertainty filters seems to indicate the issue may be dynamic in nature. By combining these inferences, we can hypothesize that there is a dynamic mis-modeling in the system that acts in a manner to which radiometric data is especially sensitive. This once again shows the utility of this gating network in its abilities to both identify the presence of mis-modeling and provide a means for characterizing what that mis-modeling may be. As a final test of this gating network's capabilities, we consider an extension to the dynamic mis-modeling problem. Our previous example focused on whether the gating network could identify mis-modeling when half of the filter's in the bank were properly modeled and the other half under-represented dynamic variations in the attitude thruster model. In this next example, we mis-model all six filters in the same manner--we increase the true nominal attitude thruster magnitude by a factor of ten, while keeping the original values in the filters. This results in a modeling error on the order of \(1\times 10^{-11}\) km/s\({}^{2}\). We then remove the attitude thruster magnitude-specific parameters from the filters as well as the temporal estimation of the SRP parameter (just estimated as a bias now), and instead we add parameters for a batched (1-day batch length) polynomial acceleration model to the filters to account for mis-modeled accelerations (i.e., process noise). The standard  
Figure 21: Optimal gating network weights with attitude thruster mis-modeling. filters (i.e., fused, radio, and optical) all use an a priori sigma of \(5\times 10^{-12}\) km/s\({}^{2}\) for this polynomial acceleration model (termed low-uncertainty filters going forward) while the high-uncertainty filters (i.e., fused-Q, radio-Q, and optical-Q) all use an a priori sigma of \(5\times 10^{-11}\) km/s\({}^{2}\). This filter setup is designed to detect dynamic mis-modeling when the filter weights begin to favor the high uncertainty models. The error and uncertainty behaviors for this setup are similar to what we have seen previously. The low-uncertainty radiometric and fused filters have position errors that quickly diverge outside the 3-\(\sigma\) tracking envelopes due to the mis-modeling. The low-uncertainty optical filter does experience some degraded tracking (especially right before entry), but it is clearly less sensitive to the mis-modeling than the filters that use radiometric data. The high-uncertainty filters perform much better than their low-uncertainty counterparts. The error remains bounded by the uncertainty envelopes, which indicates that the higher uncertainty polynomial acceleration model is appropriately compensating for the mis-modeled attitude control thruster models. The Magill gating network metrics for this scenario are also similar to the previous example. This gating network overwhelmingly favors the high-uncertainty fused filter, since it is the only fully-informed filter that outputs measurement residuals that are not too large relative to its expected level of uncertainty. Once again, however, this result is hard to draw a conclusion from, since we have already shown the Magill weights do not reliably detect the presence of anomalies. The filter weights from our optimal gating network are shown in Figure 22. Other than in the middle of the arc, several things are apparent in these results: (1) anomalous behavior is detectable due to the filters deviating from equal weighting, (2) the low-uncertainty fused and radiometric-only solutions are the worst performing filters, (3) the filter that is the most consistently highly-weighted is the optical high-uncertainty filter, and (4) all three low-uncertainty filters have low weights right before entry.