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中文摘要：
研究了状态方程中有乘性噪声,并且观测有时滞的随机双线性系统二次滤波器设计问题。因乘性噪声导致系统参数矩阵具有随机性,并且观测方程有时滞,无法直接采用经典的Kalman滤波方法,所以本研究基于Krone-cker代数方法,首先将原系统转化为包含原系统状态和观测及其二阶Kronecker积的线性增广系统;然后基于新息重组方法将增广系统转化为无时滞系统,并利用投影定理得到增广系统系统的线性最优滤波器;最后提取增广状态估计的前n个分量,从而得到原系统的二次最优滤波器。仿真结果表明该滤波器与现有的线性最优滤波器相比,估计精度提高27%,整体性能有较大提高。
英文摘要：
The problem of quadratic filtering for a bilinear stochastic system with state-dependent multiplicative noise and single delayed measurements was studied.Due to the presence of multiplicative noises,the system parameter matrices were random.So,the classical Kalman approach could not be directly used in the presence of multiplicative noises and would delay the measurements.Based on Kronecker algebra,the original system was changed into a linear augmented system,whose states and observations included the original states,observations and their second order Kronecker product.Then,the augmented system was transformed into a delay free system via the reorganized innovation approach,and the linear optimal filter for the augmented system was designed through projection theorem.Finally,the quadratic filter of the original system was derived by extracting the first n elements of the augmented state estimation.Compared with the widely used linear optimal filter,estimation accuracy of the quadratic filter increased 27%,and the overall performance was improved.
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