用深度学习改进非线性滤波，既更准又保持可信的不确定性估计。
Unscented KalmanNet: Structure-Preserving Deep Learning with Calibrated Posterior Uncertainty under Incomplete Physics and Unknown Noise
- 在无迹卡尔曼滤波基础上加入可学习模块，分别校正模型偏差和噪声变化
- 在合成数据和真实飞行数据上，状态估计误差比传统方法降低26.4%~49.7%
- 同时保证后验协方差校准，适合对可靠性要求高的实际系统应用
非线性状态估计需融合基于模型的预测与带噪观测。当动力学不完整且噪声统计未知、时变时，该融合过程会降低精度与统计一致性。现有学习辅助滤波器多将准确性与不确定性估计分开处理，限制了其修正模型失配引起的偏差能力，同时难以保持显式的校准后验协方差。本文提出无迹卡尔曼网（UKN），一种基于模型的深度学习架构，扩展无迹卡尔曼滤波（UKF）以学习两类滤波误差的机制，同时保留显式后验协方差传播。NoiseNet学习时变过程与测量协方差作为基线协方差的有界乘性修正，确保正定性；GainNet学习分析式UKF增益的有界残差修正，补偿模型失配导致的偏差。一种校准感知训练目标通过自适应加权耦合状态误差、后验协方差与创新一致性项，联合优化准确性和校准性。UKN在三个合成系统和真实飞行UZH-FPV数据上对比UKF、KalmanNet与Bayesian KalmanNet进行评测。所有四个案例中均达到最低状态估计误差，在合成案例中相比UKF降低RMSE 26.4%–49.7%。11次飞行的留一序列交叉验证显示，平均位置与速度RMSE分别降低22.4%和34.3%。UKN还表现出最低的跨序列波动，归一化NEES与经验覆盖率最接近名义值，优于其他报告协方差的滤波器。结果表明，结构化学习适配能提升估计精度并维持校准的不确定性。
原文摘要 · Abstract (English)
Nonlinear state estimation requires sequentially fusing model-based predictions with noisy measurements. Under imperfect dynamics and unknown, time-varying noise statistics, this fusion can degrade in both accuracy and statistical consistency. Existing learning-aided filters largely treat accuracy and uncertainty estimation separately, limiting their ability to correct model-mismatch-induced bias while retaining an explicit, calibrated posterior covariance. This paper introduces Unscented KalmanNet (UKN), a model-based deep learning architecture that extends the Unscented Kalman Filter (UKF) with learned mechanisms for these two sources of filtering error while preserving explicit posterior covariance propagation. NoiseNet learns time-varying process and measurement covariances as bounded multiplicative corrections to baseline covariances, guaranteeing positive definiteness, while GainNet learns a bounded residual correction to the analytical UKF gain to compensate for model-mismatch-induced bias. A calibration-aware training objective couples state error with posterior covariance and innovation consistency terms through adaptive weighting, jointly optimizing accuracy and calibration. UKN is benchmarked against UKF, KalmanNet, and Bayesian KalmanNet on three synthetic systems and real-flight UZH-FPV data. It achieves the lowest state-estimation error in all four examples and reduces RMSE by 26.4-49.7% compared with UKF in the synthetic cases. Leave-one-sequence-out cross-validation over 11 flights shows 22.4% and 34.3% reductions in mean position and velocity RMSE, respectively. UKN also yields the lowest fold-to-fold variability, with dimension-normalized NEES and empirical coverage closest to nominal values among covariance-reporting filters. These results show that structured learned adaptation improves estimation accuracy while retaining calibrated uncertainty.
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