应用SVD分解简化卡尔曼增益计算的理论研究

Study on the theory of reducing Kalman filter gain matrix with SVD decomposition

在总结前人关于卡尔曼滤波简化的基础上,提出了一种新的简化方法,即利用矩阵的奇异值将数据矩阵进行SVD分解,从而得到能够描述原状态向量的新的较少维数向量的有效秩,根据该有效秩,不仅可以得到和前人相一致的简化表达形式,而且可以得到舍去部分的表达公式.经过和HAMSOM模式结合,利用渤海区域的SST进行同化实验验证,证明SVD分解简化可行.推求得到的附加的舍去误差公式为定性的讨论舍去部分的影响提供了理论基础.

A new scheme based on the reduction principle of predecessor's research, was developed to reduce the calculating amount of the Kalman gain matrix with SVD decomposition. With the new scheme, the main parts of the data array and its order and the formula of truncated error were obtained. On the basis of the reduced order, the reduced model for computing the covariance matrix was developed. The results of twin experiments indicated that the data after data assimilation were close to the observations and that the scheme was correct.