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Nonlinear state estimation based on improved high-degree cubature Kalman filter for fermentation process

As high-dimensional nonlinear systems, some state variables of fermentation processes are unmeasurable, and nonlinear state estimation such as the high-degree cubature Kalman filter can be used to obtain the estimations of these variables. However, the high-degree cubature Kalman filter may suffer filter failure when dealing with high-dimensional systems. To solve the problem that the numerical stability of the high-degree cubature Kalman filter will decline with the increasement of dimension, an improved high-degree cubature Kalman filter is proposed. In this paper, arbitrary degree cubature rule is given and the improved high-degree cubature Kalman filter algorithm based on diagonalization of matrix is derived. Furthermore, the implementation process of the improved algorithm is constructed in industrial yeast fermentation process to demonstrate the performance of using the improved high-degree cubature Kalman filter.