卡尔曼滤波器中噪声估计的脆弱性：优化可以处理模型误设定
The Fragility of Noise Estimation in Kalman Filter: Optimization Can Handle Model-Misspecification
摘要：
卡尔曼滤波器（KF）参数传统上由噪声估计确定，因为在KF假设下，当参数对应于噪声协方差时，状态预测误差最小。然而，噪声估计仍然是黄金标准，无论假设如何-即使它不等同于误差最小化。我们证明，即使是看似简单的问题可能包括多个假设违反-这是有时甚至很难注意到。我们从理论上和经验表明，即使是轻微的违规行为可能会在很大程度上改变最佳参数。我们提出了一个基于梯度的方法，随着Cholesky参数化显式优化的状态预测误差。我们在3个不同领域的数十个实验中显示出对噪声估计的一致改进。最后，我们证明了优化使KF与LSTM模型竞争-即使在非线性问题中。
英文摘要：
The Kalman Filter (KF) parameters are traditionally determined by noise estimation, since under the KF assumptions, the state prediction errors are minimized when the parameters correspond to the noise covariance. However, noise estimation remains the gold-standard regardless of the assumptions - even when it is not equivalent to errors minimization. We demonstrate that even seemingly simple problems may include multiple assumptions violations - which are sometimes hard to even notice. We show theoretically and empirically that even a minor violation may largely shift the optimal parameters. We propose a gradient-based method along with the Cholesky parameterization to explicitly optimize the state prediction errors. We show consistent improvement over noise estimation in tens of experiments in 3 different domains. Finally, we demonstrate that optimization makes the KF competitive with an LSTM model - even in non linear problems.
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