# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 4 Results
### Dynamical Model Mis-Modeling  
To investigate the efficacy of our new gating network in detecting the presence of dynamic mis-modeling, we will introduce more dynamic variations in the truth data and then slightly adjust the filter bank to include filters with varied parameters for acceleration estimation. In terms of truth data changes, we significantly increase the error in the attitude control thrusting such that each thruster has a random constant bias drawn from a zero-mean normal distribution with a standard deviation of 3\(\times\) the nominal thrust level ( \(5\times 10^{-12}\) km/s\({}^{2}\)) and daily temporal variations in the magnitude that are drawn from a zero-mean normal distribution with a standard deviation of 10\(\times\) the nominal thrust level. We leave the attitude thruster direction uncertainty untouched relative to the nominal scenario setup. In order to enable detection of dynamic mis-modeling in our filter bank, we introduce variations of our existing three filters where the new versions have different uncertainties on attitude control thruster magnitude parameters. Our standard filters (radio, optical, and fused) remain unchanged relative to the scenario setup, so they have large errors in \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Case** & **Radio Filter** & **Optical Filter** & **Fused Filter** \\ \hline Ideal & 0.3333 & 0.3333 & 0.3333 \\ \hline No Bias & 0.3354 & 0.3272 & 0.3374 \\ \hline Small Bias—Optical & 0.4186 & 0.2923 & 0.2891 \\ \hline Medium Bias—Optical & 0.9008 & 0.0638 & 0.0354 \\ \hline Large Bias—Optical & 0.9679 & 0.0316 & 0.0004 \\ \hline Small Bias—Radio & 0.3354 & 0.3272 & 0.3374 \\ \hline Medium Bias—Radio & 0.3350 & 0.3280 & 0.3370 \\ \hline Large Bias—Radio & 0.3047 & 0.3899 & 0.3054 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average Optimal Gating Network Weights for Biased Measurement Scenarios. their attitude control thrusting models--they only model a 3% bias and a 5% daily variation in the attitude thruster magnitudes. The new filters (radio-Q, optical-Q, and fused-Q) are all modeled properly--they model a 300% bias and a 1000% daily variation in the attitude thruster magnitudes, while thrusters in reality would never be this poorly behaved, this type of scenario is reminiscent of the Mars Climate Orbiter crash, where a units modeling error led to significant modeling issues in the attitude control system. It should be noted that these modeling errors only occur during attitude thrusting, so the errors are not constant, and thus will not be as detectable as a comparably-sized constant bias in acceleration. The intent of this exercise is to see whether these dynamically mis-modeled filters are de-weighted by our gating network in a way that would allow us to detect the anomaly as well as determine the cause of the anomaly. Before investigating how the gating networks react to the introduction of this attitude thruster mis-modeling, we first want to quantify the effect of this dynamic mis-modeling on the individual filters. Figures 17-19 show the position error and uncertainty metrics that results from the optical-only, radiometric-only, and fused filters that are dynamically mis-modeled. The optical-only filter (Figure 17) seems relatively unaffected by the presence dynamic mis-modeling--this is a different truth realization from the no-biasing case, but the position error is similarly well-bounded by its uncertainty envelope. Conversely, the radiometric-only filter (Figure 18) is noticeably affected by the dynamic mis-modeling. Position tracking error begins to steadily increase over time (relative to the uncertainty bounds) until it exceeds the 3-\(\sigma\) bound for an extended period. The fused filter (Figure 19) exhibits similar behavior--Its position error grows beyond the 3-\(\sigma\) bound for an extended period, but it begins to recover near entry as the optical data becomes more information rich. These results tell us that radiometric data is far more sensitive to this type of dynamic mis-modeling than optical data.