An observable degree analysis method for nonlinear Systems with noise correlation

The observability in the modern control field describes whether a system can reflect the combination relationship of the state components of the system by the output measurement value. Observability is the question of whether observability is big or small with a certain value, which is of great significance to the analysis of the system. There are many methods to calculate the observability of linear systems. For the calculation of observability in the field of nonlinear systems, the complexity of nonlinear systems leads to the lack of observability theory of nonlinear systems. In the existing research on the observability of nonlinear systems, the analysis and research under the situation where the observation noise of the system is correlated with the process noise is still lacking. In the existing research of nonlinear observability, this paper considers the correlation between process noise and observation noise to be added to the analysis and calculation of nonlinear observability. Compare the observability relationship between the noise-related situation and the noise-uncorrelated situation, and further improve the analysis theory of the observability of the nonlinear system. The research and analysis of related fields have certain reference value.