FlexKalmanNet: A Modular AI-Enhanced Kalman Filter Framework Applied to Spacecraft Motion Estimation

TL;DR

FlexKalmanNet is introduced, a novel modular framework that bridges the gap between a deep fully connected neural network with Kalman filter-based motion estimation algorithms by integrating a deep fully connected neural network with Kalman filter-based motion estimation algorithms.

Abstract

The estimation of relative motion between spacecraft increasingly relies on feature-matching computer vision, which feeds data into a recursive filtering algorithm. Kalman filters, although efficient in noise compensation, demand extensive tuning of system and noise models. This paper introduces FlexKalmanNet, a novel modular framework that bridges this gap by integrating a deep fully connected neural network with Kalman filter-based motion estimation algorithms. FlexKalmanNet's core innovation is its ability to learn any Kalman filter parameter directly from measurement data, coupled with the flexibility to utilize various Kalman filter variants. This is achieved through a notable design decision to outsource the sequential computation from the neural network to the Kalman filter variant, enabling a purely feedforward neural network architecture. This architecture, proficient at handling complex, nonlinear features without the dependency on recurrent network modules, captures global data patterns more effectively. Empirical evaluation using data from NASA's Astrobee simulation environment focuses on learning unknown parameters of an Extended Kalman filter for spacecraft pose and twist estimation. The results demonstrate FlexKalmanNet's rapid training convergence, high accuracy, and superior performance against manually tuned Extended Kalman filters.

Figures (8)

• Figure 1: Forward pass of the computational graph of FlexKalmanNet. The flow of activations during a forward pass is illustrated via the solid arrows. Dashed arrows represent data flows that are relevant for the framework, but not part of the computational graph. The backward pass for the gradients goes in the opposite direction of the illustrated solid lines.
• Figure 2: Hyperparameter grid search mapped to the best validation loss for DS1. Each column represents a variable in the hyperparameter space that has more than one available value. Sweeps are traversing these columns from the left hand side to the right hand side, mapping their hyperparameters to their best validation loss as root mean squared error. The color map indicates the magnitude of the loss relative to the minimum and maximum loss values of all sweeps. Plot generated via Weights and Biases wandb.
• Figure 3: Convergence behavior of the RMSE losses during training with DS2. Two RMSE losses of each epoch during the training of the DFCNN model using DS2 are presented: The loss from the training phase, blue, and the loss of the validation phase, orange.
• Figure 4: Convergence behavior of the learned parameters during training with DS2. The $20$ noise covariance terms that the DFCNN is learning from the DS2 are tracked over each epoch and depicted in this graph.
• Figure 5: EKF results using the trained parameters for DS1 applied on DS1. Each of the four subplots depicts one of the four motion components from the state vector: orientation, position, angular velocity and translational velocity. In every subplot, the EKF estimate and the corresponding measurement or ground truth are plotted, denoted as $\hat{x}$, $\tilde{x}$ and $x$, respectively.