KalmanFormer: using transformer to model the Kalman Gain in Kalman Filters.

Area of Science:

• Signal Processing
• Machine Learning
• Control Systems

Background:

• Accurate state estimation is crucial for dynamic systems.
• Traditional Kalman Filters (KF) excel in linear/Gaussian systems but struggle with non-linear dynamics and model uncertainties.
• Real-world applications often present non-linearities and incomplete system information.

Purpose of the Study:

• To develop a robust state estimator for non-linear dynamic systems.
• To overcome limitations of classical Kalman Filters in practical scenarios.
• To improve state estimation accuracy under partial information.

Main Methods:

• Introduction of KalmanFormer, a hybrid model-driven and data-driven state estimator.
• Integration of a Transformer framework within the classical Kalman Filter.
• Learning the Kalman Gain directly from data, bypassing the need for prior noise parameter knowledge.

Main Results:

• KalmanFormer demonstrated superior performance compared to the Extended Kalman Filter (EKF) in numerical experiments.
• Achieved higher accuracy in tracking hidden states of dynamic systems.
• Showcased resilience to system non-linearities and imprecise model parameters.

Conclusions:

• The hybrid KalmanFormer effectively addresses limitations of traditional Kalman Filters.
• Leveraging data through Transformer enhances state estimation robustness and accuracy.
• KalmanFormer offers a promising solution for state estimation in complex, real-world dynamic systems.