Conditions for stability of the extended Kalman filter and their application to the frequency tracking problem

Scala, B.F. La; Bitmead, Robert R.; James, Matthew R.

doi:10.1007/bf01212364

Cited by 89 publications

(49 citation statements)

References 9 publications

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“…CAn-I which is equivalent to the requirement that the system (16,17) is observable, i.e., the state x ( t ) is uniquely determined by y(t), t 2 0. The rank condition (20) is equivalent to the pole placement property which means that for any symmetric set of n points in @, there exists a real matrix K such that A -KC has these n points as eigenvalues.…”

Section: Corollary 3 (I) Though We Restrict Attention To Observers Ofmentioning

confidence: 99%

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A dynamical control view on synchronization

Nijmeijer

2001

Physica D: Nonlinear Phenomena

137

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Section: Corollary 3 (I) Though We Restrict Attention To Observers Ofmentioning

confidence: 99%

“…The question under what conditions a matrix K can be found so that (17) is asymptotically stable can be answered using the observability rank condition. The linear system (16,17) satisfies the observability rank condition if…”

Section: Corollary 3 (I) Though We Restrict Attention To Observers Ofmentioning

confidence: 99%

A dynamical control view on synchronization

Nijmeijer

2001

Physica D: Nonlinear Phenomena

137

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“…Compared to the EKF stability proof, e.g. [4], how this variability influences certain conditions like observability, continuity and matrix invertability is not examined. Besides, switching of the covariance matrix drops pre-calculated information when shrinking and introduces initial guess when augmenting.…”

Section: A Switching Schemementioning

confidence: 99%

Filling the gap between low frequency measurements with their estimates

Wang

Kostic

Jansen³

et al. 2014

2014 IEEE International Conference on Robotics and Automation (ICRA)

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Abstract-The use of redundant sensors brings a rich diversity of information, nevertheless fusing different sensors that run at vastly different frequencies into a proper estimate is still a challenging sensor fusion problem. Instead of using the size-varying measurements and thereby the size-varying filters during each sampling period, we propose to find a substitute of the unavailable low frequency measurements such that we can avoid using different sampling frequencies in one filter. In the gap between the sampling of two low frequency measurements, the use of these substitutes produces smoother estimates. In both the proof of concept simulation and the localization experiment performed on an indoor soccer robot, our proposed approach exhibits an improved performance compared to the size-varying Kalman filter methods.

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“…There are few theoretical results to indicate when such a design will be successful. La Scala et al [9] derive sufficient conditions to ensure that the errors of the EKF will remain bounded, but their results are established for a linear observation equation. As the convergence of an EKF cannot be demonstrated, we will propose in section IV to detect problematic situations thanks to the study of the observability of the non-linear system.…”

Section: Kalman Filtering Formulationmentioning

confidence: 99%