The nonlinear and stochastic relationship between noise covariance parameter values and state estimator performance makes optimal filter tuning a very challenging problem. Popular optimization-based tuning approaches can easily get trapped in local minima, leading to poor noise parameter identification and suboptimal state estimation. Recently, black box techniques based on Bayesian optimization with Gaussian processes (GPBO) have been shown to overcome many of these issues, using normalized estimation error squared (NEES) and normalized innovation error (NIS) statistics to derive cost functions for Kalman filter auto-tuning. While reliable noise parameter estimates are obtained in many cases, GPBO solutions obtained with these conventional cost functions do not always converge to optimal filter noise parameters and lack robustness to parameter ambiguities in time-discretized system models. This paper addresses these issues by making two main contributions. First, we show that NIS and NEES errors are only chi-squared distributed for tuned estimators. As a result, chi-square tests are not sufficient to ensure that an estimator has been correctly tuned. We use this to extend the familiar consistency tests for NIS and NEES to penalize if the distribution is not chi-squared distributed. Second, this cost measure is applied within a Student-t processes Bayesian Optimization (TPBO) to achieve robust estimator performance for time discretized state space models. The robustness, accuracy, and reliability of our approach are illustrated on classical state estimation problems.

翻译：噪声协方差参数值与状态估计器性能之间的非线性和随机关系，使得最优滤波器调参成为一个极具挑战性的问题。基于优化的传统调参方法易陷入局部最优，导致噪声参数辨识不佳与状态估计次优。近年来，基于高斯过程贝叶斯优化的黑箱技术通过利用归一化估计误差平方和归一化新息误差统计量推导卡尔曼滤波自动调参的代价函数，已被证明能克服上述诸多问题。尽管该方法在许多情况下可获得可靠的噪声参数估计，但采用这些传统代价函数得到的贝叶斯优化解并不总能收敛至最优滤波器噪声参数，且对时间离散化系统模型中的参数模糊性缺乏鲁棒性。本文通过两项主要贡献解决这些问题：首先，我们证明归一化新息误差和归一化估计误差平方仅当估计器调参正确时服从卡方分布。因此，卡方检验不足以确保估计器已被正确调参。我们利用这一发现将归一化新息误差和归一化估计误差平方的常规一致性检验扩展为对非卡方分布施加惩罚项。其次，将该代价度量应用于学生t过程贝叶斯优化框架，以在时间离散化状态空间模型中实现鲁棒的估计器性能。通过经典状态估计问题验证了所提方法的鲁棒性、准确性与可靠性。