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This paper is focused on the nonlinear state estimation problem with finite-step correlated noises and packet loss. Firstly, by using the projection theorem repeatedly, the mean and covariance of process noise and measurement noise in the condition of measurements before the current epoch are calculated. Then, based on the Gaussian approximation recursive filter (GASF) and the prediction compensation mechanism, one-step predictor and filter with packet dropouts are derived, respectively. Based on these, a nonlinear Gaussian recursive filter is proposed. Subsequently, the numerical implementation is derived based on the cubature Kalman filter (CKF), which is suitable for general nonlinear system and with higher accuracy compared to the algorithm expanded from linear system to nonlinear system through Taylor series expansion. Finally, the strong nonlinearity model is used to show the superiority of the proposed algorithm.

Gaussian Recursive Filter for Nonlinear Systems with Finite-step Correlated Noises and Packet Dropout Compensations