Impact analysis between observable degrees and estimation accuracy of Kalman filtering

It is well known that estimation performance of the Kalman filtering (KF) depends closely on systemic observability. Moreover, observable degree is usually used to measure the ability of observability on systemic state variables in control and estimation systems. Thereby, there should be a corresponding relation between the estimation performance of the KF and the observable degree. Unfortunately, value of the observable degree can tend to be infinite for most current computational ways and there must be a performance upper bound for the KF estimate. There is a clear impact between the observable degree and the filtering accuracy. Two common approaches to compute observable degree of estimation systems are briefly introduced in this paper, i.e., eigenvalues and eigenvectors analysis method for mean squared error (MSE) and singular value decomposition (SVD) method of observability matrix. Furthermore, the corresponding impact relation between the filtering performance and observable degree is expressly discussed by considering influences from system parameters to the observable degree and the estimation accuracy, respectively. Finally, two simulation examples are given to verify the analysis results obtained in this paper.