噪声相关的Kalman—Bucy滤波器

The Kalman-Bucy Recursive Filtering Formulas of Related Noises

本文应用T.Kailath的新息法于线性滤波问题。导出了当系统噪声和观测噪声相关时,不仅含有随机干扰输入,而且还有确定性输入的Kalman-Bucy滤波器。设有状态向量随机微分方程: x_i=A_ix_i+B_(ii)u_i+B_i~■W_t,x_■=0 及现测方程: y_i=C_ix_i+v_i 这里w_i和v_i依赖白噪声过程,且 R_(is)^(wv)=s_iδ(t-s),R_(is)~w=Q_iδ(t-s),R_(i■)~v=R_iδ(t-s) S_i≥0,Q_t≥0,R_t>0,则状态X_t的最优线性估计X_t满足及此处 M_i=-(P_i^xC_i^x+B_iS_i)R_i^(-1)

In this paper, we applied T.Kailath's innovation approach to the linear filtering problem. Suppose that, the state evolves according to the vector stochastic differential equation and the observed vector process is w_i and v_i are dependent white noise processes with Q_i≥0, R_i>0. Then the optimal linear estimation of the state x_i satisfies and where