核心概念
The proposed attention Kalman filter (AtKF) incorporates a self-attention mechanism to better capture dependencies in state sequences, improving the accuracy and robustness of state estimation in nonlinear systems compared to traditional Kalman filtering approaches.
要約
The paper introduces a novel Kalman filtering algorithm called the attention Kalman filter (AtKF) that integrates a self-attention mechanism to enhance state estimation performance in nonlinear systems.
Key highlights:
- AtKF uses a simplified self-attention network to capture dependencies among state sequences more effectively than traditional recurrent neural network-based approaches.
- To address the instability and inefficiency of the recursive training process inherent in Kalman filtering, the authors propose a pre-training method based on lattice trajectory piecewise linear (LTPWL) approximation and batch estimation.
- The LTPWL expression is used to linearize the nonlinear system, and a batch estimation algorithm is employed to generate pre-training data, avoiding the recursive training limitations.
- Experiments on a two-dimensional nonlinear system demonstrate that AtKF outperforms traditional filters like EKF, UKF, and particle filter, as well as the recent KalmanNet approach, in terms of estimation accuracy and robustness under noise disturbances and model mismatches.
The key innovation of this work is the integration of the self-attention mechanism within the Kalman filtering framework to better capture dependencies in state sequences, coupled with a pre-training strategy that leverages the parallel processing capabilities of the attention network to address the instability and inefficiency issues of the recursive Kalman filtering training process.
統計
The nonlinear system model is given by:
xk = α · sin(β · xk−1 + ϕ) + δ + wk
yk = a · (b · xk + c)2 + vk
where wk and vk are Gaussian white noise with covariance matrices Q and R, respectively.
引用
"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 challenge, many studies improved KF by integrating data-driven approaches, which are mainly categorized into external combination and internal embedding."
"Most current approaches employ LSTM or GRU to learn from time series data. These recurrent neural networks (RNN) perform poorly in comprehensively capturing the dependencies in time series data. Additionally, their recursive training processes suffer from instability and inefficiency."