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该文研究了由Fornasini-Marchesini第二(FM-II)模型描述的二维线性随机系统的最小误差方差的递推滤波问题，该系统在状态方程和观测方程中包含随机参数矩阵和噪声.首先应用矩阵分解方法将随机参数矩阵分解为确定矩阵和期望为零的随机矩阵两部分.其次，针对分解后的新系统，提出了具有无偏性和误差方差最小的两步递推滤波器的方案.然后，利用配方法得到递推滤波器的增益矩阵，并给出了一个在线的有效滤波算法.最后，通过数值仿真说明了所设计滤波的有效性.
Abstract：In this paper, the recursive filtering problem of the minimum error variance of a two-dimensional linear stochastic system described by the second Fornasini-Marchesini model is studied.The system contains stochastic parameter matrices and noises in the state equation and observation equations.Firstly, the stochastic parameter matrices are separated into deterministic and stochastic parts by using the decomposition method of matrices, and the part of stochastic matrices is with zero-mean.Secondly, a two-step recursive filter with unbiasedness and minimum error variance is proposed for the decomposed new system.Then, the gain matrix of the recursive filter is obtained using the collocation method, and an online effective filtering algorithm is presented.Finally, the effectiveness of the designed filter is demonstrated through numerical simulation.
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基本信息:
中图分类号:TN713
引用信息:
[1]戴冬梅,杨雨慧,孔淑兰.二维线性随机系统的滤波设计[J].曲阜师范大学学报(自然科学版),2026,52(02):1-8+137.
基金信息:
国家自然科学基金(61873144)
2024-12-30
2024
2025-04-10
2025-05-07
2025
1
2026-04-15
2026-04-15