Abstract
In dynamical processes states are only partly accessible by measurements. Most quantities must be determined via model based state estimation. Since in general only noisy data are given, this yields an ill-posed inverse problem. Observability guarantees a unique least squares solution. Well-posedness and observability are qualitative behaviours. The quantitative behaviour can be described using the concept of condition numbers, which we use to introduce an observability measure. For the linear case we show the connection to the well known observability Gramian. For state estimation regularization techniques concerning the initial data are commonly applied in addition. However, we show that the least squares formulation is well-posed, avoids otherwise possibly occuring bias and that the introduced observability measure gives a lower bound on the conditioning of this problem formulation.
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Blank, L. (2007). State Estimation Analysed as Inverse Problem. In: Findeisen, R., Allgöwer, F., Biegler, L.T. (eds) Assessment and Future Directions of Nonlinear Model Predictive Control. Lecture Notes in Control and Information Sciences, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72699-9_27
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DOI: https://doi.org/10.1007/978-3-540-72699-9_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72698-2
Online ISBN: 978-3-540-72699-9
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