基于变分推断的一般噪声自适应卡尔曼滤波

线性高斯状态空间模型中假设噪声为已知的白噪声过于苛刻。认为过程噪声与观测噪声均未知且二者的解析关系确定，假设观测噪声的均值非零且服从高斯分布，方差服从逆威沙特分布，从而构成了层次式贝叶斯模型。利用变分推断将均值与方差和系统状态一起作为随机变量进行迭代估计，在得到观测噪声的均值与方差的估计值后，利用其与过程噪声的关系进一步更新未知过程噪声的均值与方差，从而动态地得到每一时刻过程噪声与观测噪声的一、二阶统计矩信息，即使在噪声统计信息动态变化的情况下也有较满意的滤波精度。实验证明了该算法的有效性。

Generalized noises adaptive Kalman filtering based on variational inference

The assumption of known white noises for the linear Gaussian state-space model might be too restrictive. Both process noise and measurement noise are considered unknown, moreover, their relationship is analytically described. A hierarchical Bayesian model is built by assuming that the non-zero mean of the mea-surement noise is Gaussian and its covariance matrix is inverse Wishart distributed. By variational inference, the mean and covariance matrix of the measurement noise are reckoned as random variables and recursively estimated together with the system state. Thereafter the statistics of the unknown process noise can be updated by using the assumed functional relationship. Thus the first two moments of the measurement noise and the process noise can be obtained dynamically with acceptable accuracy even when the noises statistics are time-variant. Experiment results prove the effectiveness of the proposed algorithm.