发表机构
The University of Texas at Tyler; The Ohio State University（德克萨斯大学泰勒分校; 俄亥俄州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出混合递归估计器 UKN，通过添加 NoiseNet 和 GainNet 组件优化 UKF，在合成与真实飞行数据基准测试中，其状态估计误差、RMSE 及协方差校准效果均优于对比算法。
AI 中文摘要
非线性动力学系统的状态估计通常采用无迹卡尔曼滤波器（Unscented Kalman filter, UKF），该滤波器通过确定性 sigma 点传播状态矩，并在每一步报告后验协方差。然而在实际应用中，未知且时变的噪声统计特性以及模型失配会同时降低估计精度和协方差校准效果。现有的学习型滤波器虽能提升精度，但大多基于扩展卡尔曼滤波器构建，要么放弃显式协方差，要么学习不确定性却未校正由失配引起的增益偏差。本文提出无迹卡尔曼网（Unscented KalmanNet, UKN），这是一种混合递归估计器，在保留 UKF 显式 sigma 点协方差递归结构的同时，添加两个结构不同的学习组件：NoiseNet 将时变过程噪声和测量噪声协方差预测为固定基线的有界乘性修正项，确保正定性；GainNet 对解析增益应用有界残差修正。一种感知校准的训练目标通过自适应权重将状态误差与协方差一致性、新息一致性项相结合，联合优化精度和校准效果。在三个合成系统和 UZH-FPV 真实飞行数据上，将 UKN 与 UKF、卡尔曼网（KalmanNet）、贝叶斯卡尔曼网（Bayesian KalmanNet）进行基准测试，结果显示 UKN 在全部四个测试案例中实现了最低的聚合状态估计误差，在合成案例中相比 UKF 将均方根误差（RMSE）降低了 26.4% 至 49.7%；对 11 次飞行的留一序列交叉验证显示，其平均位置 RMSE 和速度 RMSE 分别降低了 22.4% 和 34.3%。UKN 还具有最低的折间变异性，其归一化估计误差平方和（NEES）与经验覆盖率相比其他滤波器最接近标称值。
英文摘要
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.
