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 uncorrelated 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.
