量测噪声未知Markov跳变系统变分贝叶斯辅助粒子滤波
Variational Bayesian Auxiliary Particle Filter for Jump Markov Systems with Unknown Measurement Noises
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摘要: Markov跳变系统估计问题是根据带有噪声的量测序列来估计系统状态与运行模态。在实际应用中,受自身工作状态改变以及外界随机干扰的影响,传感器量测噪声发生变化导致Markov跳变系统模型失准,从而影响系统状态与运行模态估计精度。为了适应传感器量测噪声变化,本文将Markov跳变系统量测噪声协方差阵建模成一个先验概率分布为逆威沙特分布且随时间变化的离散随机过程,并定义了分布超参数传递方程。针对Markov跳变系统量测噪声参数未知条件下系统状态估计问题,本文提出了一种新的变分贝叶斯辅助粒子滤波方法,以序贯的方式分别得到Markov跳变系统运行模态、系统状态和量测噪声协方差阵近似后验概率分布。该方法首先根据边缘化粒子滤波原理,从Markov跳变系统状态、运行模态以及量测噪声方差阵的联合后验分布中边缘化运行模态变量;随后利用系统状态和量测噪声协方差阵的预测近似先验分布以及辅助粒子滤波实现对系统运行模态后验概率分布的近似;最后基于变分贝叶斯推断得到运行模态条件下系统状态和量测噪声协方差阵近似后验概率分布。在目标跟踪仿真场景下,对比实验结果表明,在计算复杂度适当增加情况下,本文算法能够保证Markov跳变系统运行模态辨识准确率,状态和量测噪声参数估计精度优于其他方法。Abstract: The jump Markov system estimation problem involves estimating the state and system mode based on a sequence of noisy measurements. In some practical applications, changes in sensor conditions and external random interferences can lead to variations in measurement noise. This variability can render the jump Markov system model inaccurate, resulting in degraded estimates of the state and system mode. To account for these changing conditions, the measurement noise covariance matrix of jump Markov systems is modeled as a discrete stochastic process, with its prior probability distribution assigned as an inverse Wishart distribution. Additionally, dynamic equations for the hyperparameters of the measurement noise covariance matrix are defined. A new variational Bayesian auxiliary particle filter is proposed to sequentially approximate the joint posterior probability distribution associated with the system mode, state, and measurement noise covariance matrix. The joint posterior distribution of the system mode, state, and noise covariance matrix is marginalized with respect to the system mode. The marginalized posterior distribution of the mode is then approximated using an auxiliary particle filter, and the state and noise covariance matrix, conditioned on each particle of the mode variable, are updated using variational Bayesian inference, with conjugacy for the state and noise covariance matrix preserved at all times. A simulation study is conducted to compare the proposed method with state-of-the-art approaches in the context of radar target tracking. The simulation results show that the estimation accuracy for the state and noise covariance matrix can be effectively improved, ensuring system mode identification accuracy at the cost of higher computational complexity.