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中文摘要：
包括 unscented Kalman 过滤器(UKF ) 和划分差别过滤器(DDF ) ，新西格马点过滤算法被设计在相关噪音的条件下面解决非线性的过滤问题。基于最小的均方差评价理论，非线性最佳预兆并且修正在输入噪音与测量噪音被相关的假设下面的递归的公式被导出并且能在一个统一框架被描述。然后，有相关噪音的 UKF 和 DDF 被使用 unscented 转变和秒顺序 Stirlings 插值在统一框架根据以后的平均数和协变性的近似建议。有相关噪音的建议 UKF 和 DDF 突破输入噪音和测量噪音必须被假定是在标准 UKF 和 DDF 的 uncorrelated 的限制。二个模拟例子证明为处理非线性的过滤的新算法的有效性和可行性与相关噪音发出。
英文摘要：
New sigma point filtering algorithms, including the unscented Kalman filter （UKF） and the divided difference filter （DDF）, are designed to solve the nonlinear filtering problem under the condition of correlated noises. Based on the minimum mean square error estimation theory, the nonlinear optimal predictive and correction recursive formulas under the hypothesis that the input noise is correlated with the measurement noise are derived and can be described in a unified framework. Then, UKF and DDF with correlated noises are proposed on the basis of approximation of the posterior mean and covariance in the unified framework by using unscented transformation and second order Stirling＇s interpolation. The proposed UKF and DDF with correlated noises break through the limitation that input noise and measurement noise must be assumed to be uneorrelated in standard UKF and DDF. Two simulation examples show the effectiveness and feasibility of new algorithms for dealing with nonlinear filtering issue with correlated noises.
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