一般分布下的自学习滤波方法

针对Ｋａｌｍａｎ滤波存在的储多难点，在一般分布下的二阶近似最小方差估计的基础上，本文首次提出了正态严平稳假设下的自学习自适应Ｋａｌｍａｎ滤波，并相应研究了分布蜜度的离线异步自学习估计方法，文中又利用了Ｂａｙｅｓ公式得到了非线性校正项的三阶联合中心矩和四阶中心矩的自学习估计方法，并据此提出了一般分布下的自学习自适应滤波的基本公式。本文对上述理论的收敛性进行了严格证明，并指出了待研究的若干问题。

Learning Filtering Method Under A General Distribution

The learning and self-adaptive Kalman filtering with strict stationary Gaussion noise and on the basis of the minimal covariance estimation under a general distribution(non-Gaussion)proposed by res.[2]is derived for the first time.UsingBayes formula,the asynchronous learning estimation of 3rd and 4th order joint centralmoment by which a nonlinear corrective term is formed,is given.So the basic formulaof learning and self-adaptive filtering under a general distribution is finally proposed.Furthermore,the convergence proof of all above results is provided and some problemsnot to be solved are pointed out.