Gaussian Filter Estimation Framework for Nonlinear Systems with Multiple Non-Ideal Scenarios

This paper concerns a Gaussian filter estimation framework for nonlinear systems with multiple non-ideal scenarios. Multiple non-ideal scenarios can be modeled by stochastic uncertainty, correlated noise and packet dropout compensation. The stochastic uncertainty of the system is embodied in the multiplicative noise of synchronous correlation in the process equation and the measurement equation. The correlated noise is described by the process noise and observation noises at the same time. When the estimator does not receive any measurement data, the prediction compensation mechanism is used to compensate the measurement information. Firstly, in the time update process, a two-step prediction method based on projection theorem can simultaneously achieve decorrelation of multiplicative noise, process noise and measurement noise. Then, during the measurement update, the measurement information provided based on the prediction compensation mechanism is used to update the measurement based on the projection theorem. A recursive Gaussian filter estimation framework is designed. Finally, the proposed estimation framework is numerically implemented based on the third-degree spherical-radial cubature rule. Two simulation examples show that the proposed algorithm achieves numerical stability and effectiveness when applied to state estimation problem.