Nonlinear Kalman Filtering based on Self-Attention Mechanism and Lattice Trajectory Piecewise Linear Approximation

The traditional Kalman filter (KF) is widely applied in control systems, but it relies heavily on the accuracy of the system model and noise parameters, leading to potential performance degradation when facing inaccuracies. To address this issue, introducing neural networks into the KF framework offers a data-driven solution to compensate for these inaccuracies, improving the filter's performance while maintaining interpretability. Nevertheless, existing studies mostly employ recurrent neural network (RNN), which fails to fully capture the dependencies among state sequences and lead to an unstable training process. In this paper, we propose a novel Kalman filtering algorithm named the attention Kalman filter (AtKF), which incorporates a self-attention network to capture the dependencies among state sequences. To address the instability in the recursive training process, a parallel pre-training strategy is devised. Specifically, this strategy involves piecewise linearizing the system via lattice trajectory piecewise linear (LTPWL) expression, and generating pre-training data through a batch estimation algorithm, which exploits the self-attention mechanism's parallel processing ability. Experimental results on a two-dimensional nonlinear system demonstrate that AtKF outperforms other filters under noise disturbances and model mismatches.