Non-Linear Non-Gaussian Gaussian and Seventh-Order Volume Kalman Filter Algorithm and Its Modeling Application

Abstract

In this paper, the Gaussian sum recursive algorithm of the nonlinear non-Gaussian state space model is derived by expressing the state noise and observation noise of the model in the form of Gaussian sum. The algorithm uses the form of Gaussian sum to approximate the non-Gaussian posterior probability density, and uses SCKF as a sub-filter to update the time and measurement of each Gaussian component to effectively solve the problem of nonlinear non-Gaussian filtering. The simulation results verify the effectiveness and correctness of the algorithm. While ensuring accuracy, EKSF and GHSF greatly reduce the amount of calculation. The simulation time is about 6.5% and 6.7% of GSPF, respectively.