# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 4 Results
### Performance with No Biasing  
The filter bank we consider in this subsection, includes three filters. This includes an optical-only filter (only processes optical data), a radiometric-only filter (only processes radiometric data), and a fused filter (processes both optical and radiometric data). The intent of this filter bank is to identify when optical and radiometric are in conflict with one another--a strong indication of mis-modeling in the system. Beyond this we would like to identify which data type is mis-modeled, and ideally be able to determine the cause of the mis-modeling. We begin our analysis by evaluating the filter performance in the absence of measurement biasing. The position error and uncertainty for each filter in the bank are shown in \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Uncertainty** & **Model Notes** \\ \hline
3D Inertial Mars-Relative Position & 100.0 km (diagonal) & — \\ \hline
3D Inertial Mars-Relative Velocity & 0.1 m/s (diagonal) & — \\ \hline Solar Pressure Scale Factor & 0.11 (Bias, 1-\(\sigma\)) & Modeled with a constant random bias and stochastic varying component that is estimated in discrete patches that are correlated in time \\ \hline Attitude Thruster Acceleration Magnitude & 3\% (Bias, 1-\(\sigma\)) & Modeled with constant bias and temporally varying component that is estimated in discrete batches that are correlated in time \\ \hline Attitude Thruster Orientation & 3.0 deg & Modeled with a constant random bias \\ \hline Earth Pole & \(5.5\times 10^{-6}\) deg (Bias, 1-\(\sigma\)) & Modeled with a constant random bias and stochastic varying component that is estimated in discrete batches that are correlated in time \\ \hline Earth UT1 & \(3.0\times 10^{-3}\) deg (Bias, 1-\(\sigma\)) & Modeled with a constant random bias and stochastic varying component that is estimated in discrete batches that are correlated in time \\ \hline Trypospheric Dry/Wet & 1 cm (Bias, 1-\(\sigma\)) & Modeled with a constant random bias and stochastic varying component that is estimated in discrete patches that are correlated in time \\ \hline Trypospheric Dry/Wet & 1 cm (Bias, 1-\(\sigma\)) & Modeled with a constant random bias and stochastic varying component that is estimated in discrete batches that are correlated in time \\ \hline Trypospheric Dry/Wet Delays & 1 cm (Temporal, 1-\(\sigma\)) & Modeled with a constant random bias and stochastic varying component that is estimated in discrete batches that are correlated in time \\ \hline Trypospheric Dry/Wight Delays & 55/15 cm [Day] (Bias, 1-\(\sigma\)) & Modeled with a constant random bias and stochastic varying component that is estimated in discrete batches that are correlated in time \\ \hline Ionospheric Day/Night Delays & 55/15 cm [Day] (Bias, 1-\(\sigma\)) & Modeled with a constant random bias and stochastic varying component that is estimated in discrete batches that are correlated in time \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Nominal Filter Setup Used in Simulations. Figures 3-5. In these results, we see that the optical-only filter (Figure 3) tracks the spacecraft at a level of 10-50 km (1-\(\sigma\)) until right before entry, where uncertainty deceases to the sub-kilometer level over the course of a few days. Conversely, the radiometric-only filter (Figure 4) tracks consistently at the 10 km level (1-\(\sigma\)) until immediately before entry where position uncertainty rapidly decreases to the sub-kilometer level, while radiometric-only tracking generally has a smaller square root of the trace of the position covariance (RTPC) level than the optical-only tracking, it should be noted that there is a period right before entry where optical-only tracking begins to outperform the radiometric-only tracking. The fused filter (Figure 5) consistently outperforms the other two filters throughout the duration of the simulation. Position uncertainty ranges between 1 and 10 km (1-\(\sigma\), RTPC), generally decreasing with time, until about 4-days before entry when position tracking improves significantly.