Abstract
In this paper, we have studied the nonlinear observability theory and its relationship with nonlinear estimation problems. We first presented a necessary and sufficient condition for local observability of nonlinear systems. Based on the sufficient condition for local observability, we developed a global observability condition for a class of nonlinear systems. We have found that the observability of a nonlinear system is necessary for the existence of an unbiased, bounded-variance state estimate. However, different from the linear counterpart, the converse is not true in general. A sufficient condition for asymptotic observability for nonlinear systems is given. This condition also assures the asymptotic convergence, in both the almost sure and the mean square sense, of the maximum likelihood estimate to the true state vector.
This work was supported by the Department of the Army.
The United States Government assumes no responsibility for the information presented.
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© 1982 Springer-Verlag
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Lee, T.S., Dunn, K.P., Chang, C.B. (1982). On observability and unbiased estimation of nonlinear systems. In: Drenick, R.F., Kozin, F. (eds) System Modeling and Optimization. Lecture Notes in Control and Information Sciences, vol 38. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006143
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DOI: https://doi.org/10.1007/BFb0006143
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