# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
###### Abstract  
This study investigates methods for autonomous navigation of a deep-space spacecraft where one-way radiometric and on-board optical information are fused to create a fully informed state estimate. The specific focus is on using filter bank methods (i.e., Multiple Model Estimation [MME] and Mixture of Experts [MoE]) to detect when measurement and/or dynamical mis-modeling occurs. We develop a new \(\chi^{2}\)-based gating network for a filter bank that may be used to identify poorly performing filters (i.e., those with low weights), which may be used as a signal for mis-modeling in the system. In addition to defining and deriving this new weighting scheme, numerical simulations based on NASA's InSight mission demonstrate this new algorithm's performance with and without measurement and dynamical mis-modeling present. spacecraft navigation; anomaly detection; Multiple Model Estimation; filter bank; autonomous navigation +
Footnote †: journal: Applied Sciences  
operated in deep-space with a specific focus on cruise and approach mission phases. This work can be viewed as an extension of [PERSON] et al. [2], who quantified the performance of radiometric and optical fused autonomous navigation. Our approach to this problem utilizes filter bank methods (e.g., Multiple Model Estimate [MME] and Mixture of Experts [MoE])--collections of estimators (i.e., filters) that are each modeled slightly differently, and each estimator processes the available information to produce an independent state estimate. On top of the filter bank is a gating network (i.e., weighting scheme) that assigns a time-variable weight to each filter, which indicates how important that filter is to the overall solution. This weighting may also be viewed as an indicator of how well the filters are performing, so it may be used as an indicator of mis-modeling in the system. In this paper, we develop a new optimal gating network, which focuses on supporting radiometric and optical fused estimation for autonomously navigated spacecraft. These weights are used to both identify the presence of mis-modeling in the system as well as characterize the root cause of the mis-modeling--a graphical example of this process is shown in Figure 1.  
The general problem we are addressing in this study (anomaly detection and characterization) has many different approaches beyond the neural-network based method we are pursuing in this study. Many approaches deal specifically with the problem of maneuver detection and characterization--i.e., the identification and reconstruction of a dynamic anomaly while tracking a target. A number of classical methods (e.g., dynamic model compensation, polynomial acceleration model estimation, etc.) [3; 4; 5] and input estimation techniques [6; 7; 8] rely on detecting dynamic anomalies via statistical tests on measurement residuals, and then characterize the anomaly by estimating dynamic parameters associated with the anomaly. System identification methods [9; 10; 11] are commonly applied to the characterization of mis-modeled systems. These approaches tend to focus on reconstructing a system by measuring how a system responds to commanded inputs, though some methods [12; 13] do not require direct knowledge of the inputs. However, these methods are not always generally applicable especially for deep-space spacecraft navigation problems where there are significant constraints on tracking data and input resources (e.g., power and fuel). A number of spacecraft focused approaches exist [14; 15; 16; 17], though they tend to focus on specific applications which are not related to deep-space navigation.