MAML-KalmanNet: A Neural Network-Assisted Kalman Filter Based on Model-Agnostic Meta-Learning

Abstract

Neural network-assisted (NNA) Kalman filters provide an effective solution to addressing the filtering issues involving partially unknown system information by incorporating neural networks to compute the intermediate values influenced by unknown data, such as the Kalman gain in the filtering process. However, whenever there are slight changes in the state-space model (SSM), previously trained networks used in NNA Kalman filters become outdated, necessitating extensive time and data for retraining. Furthermore, obtaining sufficient labeled data for supervised learning is costly, and the effectiveness of unsupervised learning can be inconsistent. To this end, to address the inflexibility of neural network architecture and the scarcity of training data, we propose a model-agnostic meta-learning based neural network-assisted Kalman filter in this paper, called MAML-KalmanNet, by employing a limited amount of labeled data and training rounds to achieve desirable outcomes comparable to the supervised NNA Kalman filters with sufficient training. MAML-KalmanNet utilizes a pre-training approach based on specifically tailored meta-learning, enabling the network to adapt to model changes with minimal data and time without the requirement of retraining. Simultaneously, by fully leveraging the information from the SSM, MAML-KalmanNet eliminates the requirement of a large amount of labeled data to train the meta-learning initialization network. Simulations show that MAML-KalmanNet can mitigate the shortcomings existing in NNA Kalman filters regarding the requirements of abundant training data and sensitive network architecture, while providing real-time state estimation across a range of noise distributions.