AI 中文总结
针对未知动力学下的卡尔曼滤波问题，提出基于Koopman算子的任务感知神经框架，通过双头架构联合学习线性替代与增益，实现高精度跟踪。
AI 中文摘要
近年来，人工智能辅助的卡尔曼滤波器引起了越来越多的关注。虽然诸如KalmanNet等新兴方法已被证明能在部分已知的状态空间模型中促进跟踪，但当底层动力学未知时，它们无法直接应用。为克服这一局限，我们将KalmanNet的理念扩展到未知动力学场景，开发了盲卡尔曼滤波框架，该框架在假设状态演化函数和噪声统计均不可用的情况下，从数据中同时学习预测器和校正增益。为此，我们首先引入一个任务感知的神经卡尔曼滤波框架Blind-KalmanNet，它通过一个双头神经架构将卡尔曼增益的学习原理引入预测步骤，该架构联合从数据中学习一个状态相关的线性替代模型和卡尔曼增益。基于这一公式，我们进而开发了主要框架Koopman-aided Blind-KalmanNet，该框架结合Koopman算子理论，将未知动力学提升到一个状态线性演化的潜在空间。提升后的线性预测器无缝集成到Blind-KalmanNet结构中：预训练的深度Koopman网络作为全局结构化预测器，辅以从Blind-KalmanNet继承的任务感知残差替代模型和学习到的卡尔曼增益。大量实验表明，所提出的框架在性能上可与基线方法相媲美，其中Koopman-aided Blind-KalmanNet在所有考虑的设置中均达到了最佳精度。
英文摘要
Recent years have witnessed a growing interest in AI-aided Kalman filters. While emerging methodologies, such as KalmanNet, were shown to facilitate tracking in partially known state-space models, they are not directly applicable when the underlying dynamics is unknown. To overcome this limitation, we extend the KalmanNet philosophy to the unknown-dynamics regime by developing blind Kalman filtering frameworks that learn both the predictor and the correction gain from data, assuming that the state-evolution function and the noise statistics are both unavailable. To this end, we first introduce a task-aware neural Kalman filtering framework, Blind-KalmanNet, which carries the learning principle of the Kalman gain into the prediction step through a two-head neural architecture that jointly learns a state-dependent linear surrogate and the Kalman gain from data. Building on this formulation, we then develop our main framework, Koopman-aided Blind-KalmanNet, which incorporates Koopman operator theory to lift the unknown dynamics into a latent space where the state evolves linearly. The lifted linear predictor integrates seamlessly into the Blind-KalmanNet structure: the pre-trained deep Koopman network serves as a globally structured predictor, augmented by the task-aware residual surrogate and the learned Kalman gain inherited from Blind-KalmanNet. Extensive experiments demonstrate that the proposed frameworks achieve competitive performance against baselines, with Koopman-aided Blind-KalmanNet attaining the best accuracy across all considered settings.
Comments13 pages, 6 figures
