Statistically Linearized State Estimation Algorithm with Correlated Noises

For the nonlinear state space model, it is difficult to obtain accurate closed-form solution from the recursive Bayesian framework. Therefore, in this case, through using the statistical linear regression, two algorithms with correlative noises are given based on the minimum mean-square-error estimation criterion in this paper. First, it proposes a statistical linear Kalman filter under the condition that the measurement noise and the process noise are correlated. And then it proposes a statistical linear fixed-point smoother based on the former filter. In fact, the combination of the statistical linear regression and unscented transform can ensure the development of such non-linear filter and smoother with wider scope of applicability.