Few real-world systems are amenable to truly Bayesian filtering; nonlinearities and non-Gaussian noises can wreak havoc on filters that rely on linearization and Gaussian uncertainty approximations. This article presents the Bayesian Recursive Update Filter (BRUF), a Kalman filter that uses a recursive approach to incorporate information from nonlinear measurements. The BRUF relaxes the measurement linearity assumption of the Extended Kalman Filter (EKF) by dividing the measurement update into a user-defined number of steps. The proposed technique is extended for ensemble filters in the Bayesian Recursive Update Ensemble Kalman Filter (BRUEnKF). The performance of both filters is demonstrated in numerical examples, and new filters are introduced which exploit the theoretical foundation of the BRUF in different ways. A comparison between the BRUEnKF and Gromov flow, a popular particle flow algorithm, is presented in detail. Finally, the BRUEnKF is shown to outperform the EnKF for a very high-dimensional system.

翻译：很少有真实系统能够适用于真正的贝叶斯滤波；非线性和非高斯噪声会对依赖线性化及高斯不确定近似的滤波器造成严重影响。本文提出贝叶斯递归更新滤波器（BRUF），这是一种采用递归方法融合非线性测量信息的卡尔曼滤波器。BRUF通过将测量更新划分为用户自定义的若干步骤，放宽了扩展卡尔曼滤波器（EKF）对测量线性化的假设。该技术进一步扩展至集合滤波器，形成贝叶斯递归更新集合卡尔曼滤波器（BRUEnKF）。通过数值算例验证了两种滤波器的性能，并基于BRUF的理论基础以不同方式引入新型滤波器。详细对比了BRUEnKF与流行粒子流算法——Gromov流之间的差异。最后证明，对于极高维系统，BRUEnKF的性能优于EnKF。