基于条件高斯分布的未知输入与状态估计算法

Unknown input and state estimation based on conditional Gaussian distribution

针对未知输入同时存在于系统方程和测量方程的直接馈通线性随机系统,提出了一种同时估计未知输入和状态的算法.首先,通过将未知输入模型描述为有限方差的高斯分布,利用条件高斯分布的性质,推导出新的滤波算法,以同时得到未知输入估计和状态估计.其次,证明了当未知输入的方差趋于无穷大时,本文提出的算法等价于已有的递归三步滤波算法.最后,分析了本文算法的渐进稳定性条件,结果表明,与已有算法相比,本文的算法适用范围更广.

A simultaneous input and state estimation algorithm is proposed for linear stochastic direct feed-through systems,where the unknown input affects both state and measurement equations.First,by using a specific input model where the input is described as a Gaussian distribution with finite covariance,a new filtering formulation is derived to simultaneously obtain the input and state estimation based on the property of the conditional Gaussian distribution.Moreover,it is proved that the proposed algorithm is equivalent to the existing recursive three-step filtering algorithm when the variance of the unknown input tends to infinity.Finally,the asymptotic stability conditions of the proposed filter are discussed.It is shown that the application of this filter has a wider application range than the existing result.