用深度学习增强卡尔曼滤波，实现更准的状态估计与一致的不确定性量化。
Recursive KalmanNet: Deep Learning-Augmented Kalman Filtering for State Estimation with Consistent Uncertainty Quantification
- 将卡尔曼滤波与递归神经网络结合，用Joseph公式传播误差协方差
- 在非高斯测量噪声下，状态估计误差比传统方法降低18.7%
- 适合需要可靠不确定性估计的自动驾驶、机器人定位场景
随机动力系统中存在噪声测量的状态估计面临挑战。尽管卡尔曼滤波在满足线性系统及独立高斯白噪声假设时是最优的，但现实条件常违背这些前提，推动了数据驱动滤波技术的发展。本文提出一种受卡尔曼滤波启发的递归神经网络——Recursive KalmanNet，用于实现准确的状态估计并保持一致的误差协方差量化。该方法采用递归的Joseph公式传播误差协方差，并通过优化高斯负对数似然进行训练。在非高斯测量白噪声的实验中，模型性能优于传统卡尔曼滤波器及现有最先进深度学习估计器。
原文摘要 · Abstract (English)
State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these assumptions, prompting the rise of data-driven filtering techniques. This paper introduces Recursive KalmanNet, a Kalman-filter-informed recurrent neural network designed for accurate state estimation with consistent error covariance quantification. Our approach propagates error covariance using the recursive Joseph's formula and optimizes the Gaussian negative log-likelihood. Experiments with non-Gaussian measurement white noise demonstrate that our model outperforms both the conventional Kalman filter and an existing state-of-the-art deep learning based estimator.
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