Time-Dependent State Prediction for the Kalman Filter Based on Recurrent Neural Networks

Traditional formulations of the well-established Kalman filter build upon prediction models which are linear and Gaussian, moreover they usually adopt the Markov property which excludes any form of long-term temporal dependencies. However, targets might follow specific behavioural patterns based on, e.g., their origin or destination, therefore time dependencies become highly relevant. In this article, the recently developed Mnemonic Kalman Filter is analysed which predicts the full Gaussian density of a target based on its previous position using a recurrent neural network with Long Short-Term Memory. For comparison, a simpler Long Short-Term Memory Kalman Filter is introduced which only provides a prediction of the target state vector. The presented experiments suggest that the learning-based approaches are highly relevant for time-dependent scenarios with low detection rates or possible occlusions. Furthermore, uncertainty estimation plays an important role in the filtering process.