CAJ | 학술논문

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。
선성고사상태공간모형중가설조성위이지적백조성과우가각。인위과정조성여관측조성균미지차이자적해석관계학정，가설관측조성적균치비령차복종고사분포，방차복종역위사특분포，종이구성료층차식패협사모형。이용변분추단장균치여방차화계통상태일기작위수궤변량진행질대고계，재득도관측조성적균치여방차적고계치후，이용기여과정조성적관계진일보경신미지과정조성적균치여방차，종이동태지득도매일시각과정조성여관측조성적일、이계통계구신식，즉사재조성통계신식동태변화적정황하야유교만의적려파정도。실험증명료해산법적유효성。
The assumption of known white noises for the linear Gaussian state-space model might be too re-strictive.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 esti-mated 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-vari-ant.Experiment results prove the effectiveness of the proposed algorithm.