Optimal State Estimation Method Based on Convex Combination

As the basis of modern control theory, state variables are widely used to describe and analyze the internal characteristics of the system, and the optimal state estimation algorithm is the key. Based on the idea that weighted average can smooth errors, this paper proposes an optimal state estimation method based on convex combination, and analyzes its effectiveness from algorithm design, theoretical analysis, and simulation experiments. Firstly, the convex combination of random variables is derived; secondly, the numerically complete equivalence between the optimal estimation based on the convex combination of random variables and likelihood estimation is analyzed; finally, the equivalence between the optimal state estimation method based on convex combination and the classical univariate Kalman filter algorithm is proved.