中文摘要：

目的讨论系统噪声和测量噪声为非零均值并且互为相关情形下的带状离散随机非线性系统的状态估计问题。方法利用广义逆矩阵和矩阵的奇异值分解和带状广义离散随机非线性系统的奇异值标准形式，基于标准形式，在两种情况下，将系统分解成两个子系统，估计子系统的状态。结果推广了原有的一些结果。结论得到了该系统状态的最优预测和滤波递推方程。

英文摘要：

Aim noise. Methods To discuss a band discrete stochastic nonlinear system with nonzero mean and correlated white Using singular value decomposition of matrix and the singular values standard form of band discrete stochastic nonlinear system. Under the two cases, the band discrete stochastic system is deco subsystems based on standard form and estimating the state of subsystems. Results The original results are extended. Conclusion Optimal recursive estimation for predicting and filtering of state for this singular system are obtained.