# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 4 Results
### Performance with No Biasing
It should be noted, that each filter's position error stays within its position uncertainty bounds, though the radiometric-only filter results show that the error is generally smaller than what the uncertainty metrics dictate that it should be. This may be indicative of over-inflating radiometric data-weighting, which would result in larger uncertainties than the available information would otherwise indicate. However, this is a single realization of error in this system, so it cannot be taken as fully representative of the system's more general error response behavior. Figure 4: Position error (blue) and RTPC uncertainty (1-\(\sigma\) (orange) and 3-\(\sigma\) (red)) for radiometric-only filter in the no-biasing setup. Figure 3: Position error (blue) and square root of the trace of the position covariance (RTPC, 1-\(\sigma\) (orange) and 3-\(\sigma\) (red)) for optical-only filter in the no-biasing setup. When applying the Magill-based gating network to this filter bank in this nominal scenario, we obtain the results depicted in Figure 6. The results show a clear preference for the fused and radiometric-only filter for the first portion of this approach phase. This makes intuitive sense because each filter is exhibiting nominal behavior (i.e., no anomalous measurement residuals), and the fused and radiometric-only filters produce solutions with significantly smaller state uncertainties. Beyond the first portion of approach, the fused filter begins to dominate the weightings because the aggregate information from both radiometric and optical data types begins to dominate over the less-informed radiometric-only solution. These results essentially tell us that the fused filter is overwhelmingly the best performing filter in the bank under the standard MME criteria (i.e., small measurement residuals and small innovations uncertainty). The weightings that come from our optimal gating network are shown in Figure 7. These weightings use a batch size of 1000 measurements (\(M=1000\)). Unlike the weightings from Magill's gating network, we do not see a clear preference for any of the filters, which is an indication of a healthy (i.e., well-modeled) filter bank. Equal weightings occur when the measurement residuals and uncertainties output from the filters in the bank are statistically consistent with each other. When one or more filters begin to be preferred by the network (i.e., large weighting), this is an indication that at least one of the filters in the bank is not behaving in a statistically consistent manner--i.e., its residuals are either too large relative to its uncertainty (leading to a low weight) or its residuals are too small relative to its uncertainty (leading to a higher weight). Unlike the Magill weighting scheme, our optimal weighting scheme focuses on prioritizing filters that output residuals that are statistically small with no preference for how small the uncertainty of that filter is. Since each filter in this scenario is properly modeled, they will each output measurement residuals that are statistically consistent with their uncertainty metrics, thus resulting in nearly equal weights  
Figure 5: Position error (blue) and RTPC uncertainty (1-\(\sigma\) (orange) and 3-\(\sigma\) (red)) for fused filter in the no-biasing setup. Figure 6: Magill gating network weights with properly modeled measurements. across the bank. In these types of scenarios, we would usually select the default filter to use for estimation purposes and conclude that no anomalies are occurring. In this instance, that default filter is the fused filter, since it is the best-informed filter.