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A Variational Bayesian Approach for Estimating System Parameters and Process Noise

机译：估计系统参数和过程噪声的变分贝叶斯方法

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摘要

Bayesian estimators are commonly used to estimate the state of a system over time, whether the Kalman Filter (or its derivatives), a particle filter, a sliding window approach or batch-based approach. A common assumption with all these estimators is that the parameters of the dynamics and measurement noise sources are known a-priori. To overcome this weakness, previous approaches have simultaneously estimated the system state and the covariance of the inputs. All of these approaches, however, have made the assumption that the input noise is still uncorrelated over time. In this paper, we remove this assumption by inferring both system parameters (such as the parameters for a first-order Gauss-Markov process (FOGM)) and process noise covariance simultaneously. This estimation is performed using variational inference in conjunction with a Rauch-Tung-Striebel (RTS) smoother. We demonstrate significantly improved performance over a similar RTS-based approach that estimates Q but has the time constant of the FOGM added to the system state.
机译：贝叶斯估计器通常用于估计系统随时间的状态，无论是卡尔曼滤波器（或其派生），粒子滤波器，滑动窗口方法还是基于批处理的方法。所有这些估计器的共同假设是，动力学和测量噪声源的参数是先验的。为了克服这一弱点，以前的方法已经同时估计了系统状态和输入的协方差。但是，所有这些方法都假设输入噪声随时间仍不相关。在本文中，我们通过同时推断两个系统参数（例如一阶高斯-马尔可夫过程（FOGM）的参数）和过程噪声协方差来消除该假设。此估计是使用变分推论和Rauch-Tung-Striebel（RTS）平滑器一起执行的。我们证明了与类似的基于RTS的方法相比，该方法显着提高了性能，该方法可估计Q，但将FOGM的时间常数添加到系统状态中。

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