【摘要】 线性随机卡尔曼-布西滤波问题要求系统方程和观测方程中的系数为有界区间上的有界函数,将系统方程中的扩散系数从有界区间上的有界函数推广为L2空间中的函数,这种情况下需要解决以下问题:推广后的系统方程的解是否存在唯一,以推广后的系统方程的系数作为积分因子的一部分的某个积分是否有意义,证明了上述问题仍然成立,并且得到了推广后的线性滤波问题的解满足的随机微分方程.更多还原

【Abstract】 The diffusion coefficient in the system equations is generalized to the function in the space from a bounded function in a bounded interval in this paper.So the following issues are needed to solve:whether the solution of the generalized system is unique.The other is that whether the diffusion coefficient in the generalized system equations is meaningful as the part of the integrating factor.The above problems are proved still valid.The obtained solution of the generalized linear filtering problem can satisfy the stochastic differential equation.更多还原