# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 4 Results
### Simulation Description  
Our simulations in this section focus on application of our algorithm to a deep-space navigation problem where different observables are fused together to form a fully-informed navigation solution--the primary use-case for which this algorithm was developed. Spacecraft navigation problems have a unique set of qualities relative to other navigation problems--mostly related to things like the data-sparse nature of the tracking data (i.e., long gaps between observation windows are common), the limitations on controllability of the system due to power and fuel scarcity, the need for highly precise sensors and clocks, and the level of dynamical knowledge that is needed to successfully predict the motion of the spacecraft. Deep-space navigation (i.e., beyond the Earth-moon system) has its own unique challenges including: even longer delays between observation windows, long communication delays with the ground and low-signal communications (due to large Earth-spacecraft distances), highly non-linear dynamics in dynamically unknown systems (e.g., asteroid proximity operations), and the limited ground communication infrastructure there is to communicate with all of the currently operating deep-space missions (one of the major motivations behind autonomous navigation research).  
Deep space missions typically rely on Earth-based radiometric data types for tracking (e.g., ranging based on light-travel times, Doppler, and differenced one-way ranging at different receiver locations), but can also use on-board observables from spacecraft-mounted cameras and light detection and ranging (LIDAR) sensors. Typically, the radiometric data is two-way (ground->spacecraft->ground) in order to improve data quality by removing spacecraft clock errors; however, one-way observables are feasible with a highly-stable/accurate on-board clock like DSAC. For this analysis, we will focus on one-way radiometric data and optical data because these better support autonomous spacecraft navigation, which is a prime use-case for this research. Fusing radiometric and optical data types into a single navigation solution can often be difficult due to the data types being so independent with each other. However, this independence is powerful from an information standpoint, so it is desirable to develop a method for robust autonomous fused navigation.  
To test our algorithm in a realistic deep-space navigation problem, we developed a scenario based on NASA's InSight mission--specifically, the final 45 days of the Martian approach phase. Table 1 defines our nominal filter setup--specifically where it differs from the model described by [PERSON] et al. [2]. For completeness, our nominal filter setup includes the following parameters: spacecraft cartesian position and velocity; solar pressure scale factor; attitude control thruster magnitudes and direction; impulsive burn parameters for trajectory correction maneuvers; Earth pole motion and universal time (UT1); Tropospheric and Ionospheric delay terms; spacecraft clock offset and drift terms; ranging biases; gravitational parameters for the Earth, Moon, and Mars; ephemerides for the Earth, Mars, Deimos, Phobos, and other optical targets (i.e., asteroids); and deep space network station locations. In the measurement biasing analysis, we use the same general filter setup for each filter in the filter bank with only difference being what measurements are being processed by each filter and bias terms that are specific to specific data types (e.g., removing range bias terms from the optical-only filter). For the dynamic mis-modeling analysis, we make specific changes to the attitude thrusting and process noise models in each filter, which are defined described in Section 4.4.