Partial observability for some distributed parameter systems

Kang, Wei; Xu, Liang

doi:10.1007/s40435-014-0087-4

Cited by 7 publications

(2 citation statements)

References 17 publications

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“…Application areas have included underwater navigation [38], [39], planetary landers [40], blood glucose modeling [41], and flow-field estimation [42], [43]. The metrics have also been adapted to analyzing the observability of subspaces of systems of partial differential equations [44], [45].…”

Section: Introductionmentioning

confidence: 99%

Empirical observability Gramian rank condition for weak observability of nonlinear systems with control

Powel

Morgansen

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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We extend observability metrics based on the empirical observability Gramian from deterministic nonlinear systems to nonlinear stochastic systems in order to capture the impact of process noise on observability. We demonstrate that the empirical observability Gramian can be used to provide an equivalent condition for a definition of stochastic observability on linear systems, and that the Gramian can be used to extend stochastic observability to nonlinear stochastic systems. We further demonstrate through simulation that consideration of process noise can reveal observability in systems that would be considered unobservable using traditional deterministic tools. Index TermsObservability, stochastic systems, nonlinear systems, Cramer-Rao bounds.

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Section: Introductionmentioning

confidence: 99%

Empirical observability Gramian rank condition for weak observability of nonlinear systems with control

Powel

Morgansen

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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“…Measuring observability quantitatively based on the observabililty Gramian is essential to the type of problems studied in this paper. For related literature, the interested readers are referred to [1,3,4,5,6,7,8,10,11,12] and references therein.…”

Section: Introductionmentioning

confidence: 99%

The Observability in Unobservable Systems

Kang¹,

Li²,

Zhao³

2022

Preprint

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In this paper, we introduce the concept of observability of targeted state variables for systems that may not be fully observable. For their estimation, we introduce and exemplify a deep filter, which is a neural network specifically designed for the estimation of targeted state variables without computing the trajectory of the entire system. The observability definition is quantitative rather than a yes or no answer so that one can compare the level of observability between different sensor locations.

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