标题： 自然梯度高斯近似滤波器的设计与比较测试 显示英文标题

标题： Algorithm Design and Comparative Test of Natural Gradient Gaussian Approximation Filter

摘要： 流行的贝叶斯滤波器通常依赖于线性化技术，例如 泰勒级数展开和随机线性回归，来利用标准卡尔曼滤波器的结构。 这些技术可能会在非线性和非高斯系统中引入较大的估计误差。 本文概述了滤波算法设计中的最新突破，即\textit{N}atural Gr\textit{a}dient Gaussia\textit{n} Appr\textit{o}ximation (NANO) 滤波器，并将其性能与一大类非线性滤波器进行比较。 NANO 滤波器将贝叶斯滤波解释为两个不同优化问题的解，从而可以定义最优高斯近似并推导出其相应的极值条件。 该算法设计仍然遵循贝叶斯滤波器的两步结构。 在预测步骤中，NANO 滤波器计算先验分布的前两个矩，此过程等效于矩匹配滤波器。 在更新步骤中，采用自然梯度下降法直接最小化更新步骤的目标函数，从而避免模型线性化引起的误差。 在高斯噪声、拉普拉斯噪声和β噪声环境下，对四种经典系统（包括阻尼线性振荡器、序列预测、改进的增长模型和机器人定位）进行了对比测试，以评估NANO滤波器处理非线性的能力。 此外，我们还使用卫星姿态估计示例验证了NANO滤波器对数据异常值的鲁棒性。 结果表明，NANO滤波器的性能优于常用的卡尔曼滤波器系列，例如扩展卡尔曼滤波器 (EKF)、无迹卡尔曼滤波器 (UKF)、迭代扩展卡尔曼滤波器 (IEKF) 和后验线性化滤波器 (PLF)，同时计算量相近。 显示英文摘要

摘要： Popular Bayes filters typically rely on linearization techniques such as Taylor series expansion and stochastic linear regression to use the structure of standard Kalman filter. These techniques may introduce large estimation errors in nonlinear and non-Gaussian systems. This paper overviews a recent breakthrough in filtering algorithm design called \textit{N}atural Gr\textit{a}dient Gaussia\textit{n} Appr\textit{o}ximation (NANO) filter and compare its performance over a large class of nonlinear filters. The NANO filter interprets Bayesian filtering as solutions to two distinct optimization problems, which allows to define optimal Gaussian approximation and derive its corresponding extremum conditions. The algorithm design still follows the two-step structure of Bayes filters. In the prediction step, NANO filter calculates the first two moments of the prior distribution, and this process is equivalent to a moment-matching filter. In the update step, natural gradient descent is employed to directly minimize the objective of the update step, thereby avoiding errors caused by model linearization. Comparative tests are conducted on four classic systems, including the damped linear oscillator, sequence forecasting, modified growth model, and robot localization, under Gaussian, Laplace, and Beta noise to evaluate the NANO filter's capability in handling nonlinearity. Additionally, we validate the NANO filter's robustness to data outliers using a satellite attitude estimation example. It is observed that the NANO filter outperforms popular Kalman filters family such as extended Kalman filter (EKF), unscented Kalman filter (UKF), iterated extended Kalman filter (IEKF) and posterior linearization filter (PLF), while having similar computational burden.