# Anomaly Detection in Autonomous Deep-Space Navigation via Filter Bank Gating Networks
## 2 Related Work  
Filter banks provide a platform to test many different filter models on the same input data. The filter models can differ from each other in a number of different ways, including: measurement model parameters, fidelity of the measurement models, measurement weightings (i.e., uncertainties), the set of measurements that are processed by the filter, dynamical model parameters, fidelity of the dynamical model, maneuver models, a priori state uncertainties, etc. By passing this data through different models, we can better understand the nature of the underlying true model by determining which filters in the bank perform best in a given scenario. The metric for measuring which filters in the bank are the most important is its weighting, which is obtained through a gating network or weighting schemes. Based on each filter's performance (or the properties of the input), it is assigned a weighting between 0 and 1, such that the sum of all weightings is equal to 1. Typically, these weightings are used to weight the state estimate from each filter in a weighted summation that produces a final optimal state estimate that is a linear combination from each filter's output. Alternatively, the weightings can be used as signals for anomalies and mis-modeling in the system. For instance, if a sudden bias appeared in the measurements obtained from a certain camera, then we would expect the weighting for filters that process those measurements to decrease--an indication of anomalous behavior. How effectively weights respond to anomalies is a function of several things, including: the type of gating network that is used, the filter's sensitivity to the anomaly, and the size of the anomaly. The type of gating network that is used can often differ based on the type of filter bank that is being employed. The two types that have been focused on in the existing literature are the MoE and MME methods. The MoE method [34] is a method commonly used within the field of neural networks, which are often leveraged in applications like machine learning. The MoE method leverages the idea of divide and conquer, which attempts to break up complicated problems into many smaller and simpler pieces whose individual results can be combined to solve the larger problem. Essentially, the bank is trained such that each filter within the bank becomes an expert that focuses on a specific piece of input (i.e., measurement) state space. When an input comes into that filter's area of expertise, it would be ranked highly by the gating method, thus dominating the final bank's state estimate. It's important to note two traits of MoEs at this point: (1) the gating network values are entirely based on the input values and parameters that are trained ahead of time (via methods like classification and regression tree [CART] with the expectation-maximization [EM] approach [34]); and (2) as a result, the MoE gating network weights do not reflect how the filters are performing, just how much of an expert the filters are for the given input. We are looking for an algorithm that tracks how well filters are performing in real-time so we want to make the gating network focus on filter performance in addition to the input values. This adjustment pushes the algorithm more into the realm of Multiple Model Estimation, but we still utilize concepts from the area of MoEs in this research. MME [35; 36] is a form of optimal state estimation where instead of operating a single filter to process measurements, a bank of filters is used in which each filter has a different model. The estimators can differ in the dynamical model, the measurement models, the process noise parameters, the measurements' uncertainty parameters, the estimation algorithm, etc. Each estimator is given the same measurement vector, they each process it with their unique setup, and then a weight is computed for each estimator to reflect how likely each estimator is to reflect the true model of the system.