Embedded cubature Kalman filter with adaptive setting of free parameter

•This paper devotes to solving the problem of the choice of free parameter in ECKF.•An adaptive method is proposed based on maximum likelihood criterion.•A third-degree AECKF is obtained by using the proposed adaptive method.•A fifth-degree AECKF based on the fifth-degree ECR is developed.•Simulation results show the superior performance of the proposed methods.

The choice of free parameter in embedded cubature Kalman filter (ECKF) is important, and it is difficult to choose an optimal value in practice. To solve this problem, an adaptive method is proposed to determine the value of free parameter of ECKF based on maximum likelihood criterion. By incorporating this method in the third-degree ECKF, a new third-degree adaptive ECKF (AECKF) algorithm is obtained. To further improve the accuracy of the third-degree AECKF, a new fifth-degree AECKF based on the fifth-degree embedded cubature rule is developed. Simulation results show that the proposed algorithms have higher estimation accuracy than existing methods.