中文摘要：

利用数据同化方法研究了Lorenz混沌系统中的非线性问题.提出了一种基于Cholesky分解的降秩平方根滤波算法,可以改善数据同化中的滤波发散现象.通过对卡尔曼滤波误差协方差矩阵进行Cholesky分解,降低协方差矩阵的计算量和存储量,提高滤波的收敛速度.在Lorenz混沌系统上研究了降秩平方根滤波的性能,通过敏感性分析试验,讨论了降秩平方根滤波的稳定性,验证了算法的有效性,比较了降秩平方根滤波与集合卡尔曼滤波的同化性能.结果表明,在Lorenz混沌系统的短期预报实验中,降秩平方根滤波的同化性能优于集合卡尔曼滤波.

英文摘要：

Data assimilation methods are used to study the nonlinear problems in Lorenz chaotic system. A reduced rank square root filter algorithm（RRSQRT） based on Cholesky decomposition is proposed, which can alleviate the filtering divergence phenomenon in data assimilation. Using Kalman filtering error covariance matrix Cholesky decomposition, it can reduce the amount of calculation and storage of covariance matrix and improve the convergent speed of filtering. With the Lorenz chaotic system, sensitivity analysis tests are conducted to research the performance of singular square root filter, the stability of the singular square root filter is discussed and the effectiveness of the algorithm is verified. The assimilation performance between RRSQRT and ensemble Kalman filter（EnKF） BFQis compared. The results show that the RRSQRT is better than EnKF in short time forecast experiment with Lorenz chaotic system.