Statistical Analysis of Kalman Filters by Conversion to Gauss-Helmert Models with Applications to Process Noise Estimation

Petersen, Arne; Koch, Reinhard

doi:10.1109/icpr.2010.584

Cited by 7 publications

(3 citation statements)

References 6 publications

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“…Afterwards, the corresponding r i need to be derived for this case. In [ 30 ] the GHM is also used to estimate variance components for the system noise. Though, there is still the assumption of using the GMM in the measurement equation and the results cannot be used in this article.…”

Section: Orientation Determinationmentioning

confidence: 99%

“…Thus, reliability analysis based on condition equations, necessitates a new derivation of the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix in the Gauss-Helmert model (“GHM”—model with condition equations). The formulation of the system equation in the GHM can be found in [ 29 , 30 ], wherein the measurement equation and corresponding redundancy matrix are still assumed to satisfy the GMM. Hence, an important novelty of this article is the derivation of the whole Kalman filter structure in the GHM, enabling the possibility to calculate reliability measures for observations which are non-linearly included in the condition equations.…”

Section: Introductionmentioning

confidence: 99%

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Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

Ettlinger

Neuner

Burgess³

2018

Sensors

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Abstract:The topic of indoor positioning and indoor navigation by using observations from smartphone sensors is very challenging as the determined trajectories can be subject to significant deviations compared to the route travelled in reality. Especially the calculation of the direction of movement is the critical part of pedestrian positioning approaches such as Pedestrian Dead Reckoning ("PDR"). Due to distinct systematic effects in filtered trajectories, it can be assumed that there are systematic deviations present in the observations from smartphone sensors. This article has two aims: one is to enable the estimation of partial redundancies for each observation as well as for observation groups. Partial redundancies are a measure for the reliability indicating how well systematic deviations can be detected in single observations used in PDR. The second aim is to analyze the behavior of partial redundancy by modifying the stochastic and functional model of the Kalman filter. The equations relating the observations to the orientation are condition equations, which do not exhibit the typical structure of the Gauss-Markov model ("GMM"), wherein the observations are linear and can be formulated as functions of the states. To calculate and analyze the partial redundancy of the observations from smartphone-sensors used in PDR, the system equation and the measurement equation of a Kalman filter as well as the redundancy matrix need to be derived in the Gauss-Helmert model ("GHM"). These derivations are introduced in this article and lead to a novel Kalman filter structure based on condition equations, enabling reliability assessment of each observation.

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Section: Orientation Determinationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

Ettlinger

Neuner

Burgess³

2018

Sensors

View full text Add to dashboard Cite

show abstract

“…Moreover the covariance will be closer to singular the less noise is added. On the one hand, this leaves the ID unapplicable for general least squares estimators and according statistical analysis, as are described in (Petersen and Koch, 2010). On the other hand, the matrix might loose positive semidefiniteness (required for covariance matrices) due to numerical issues.…”

Section: Performance Analysismentioning

confidence: 99%

A Novel State Parametrization for Stereo-Slam

Petersen

Koch

2012

Proceedings of the International Conference on Computer Vision Theory and Applications

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This paper proposes a novel parametrization for probabilistic stereo SLAM algorithms. It is optimized to fulfill the assumption of Gaussian probability distributions for system errors. Moreover it makes full use of the contraints induced by stereo vision and provides a close to linear observation model. Therefore the position and orientation are estimated incremetally. The parametrization of landmarks is chosen as the landmarks projection in the master camera and its disparity to the projection in the slave camera. This way a minimal parametrization is given, that is predestinated for linear probabilistic estimators.

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Range-only Position Estimation with Delay Correction via Lagrange-Bürman Inversion.

Verriest

Lampe

2017

IFAC-PapersOnLine

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Statistical Analysis of Kalman Filters by Conversion to Gauss-Helmert Models with Applications to Process Noise Estimation

Cited by 7 publications

References 6 publications

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

Development of a Kalman Filter in the Gauss-Helmert Model for Reliability Analysis in Orientation Determination with Smartphone Sensors

A Novel State Parametrization for Stereo-Slam

Range-only Position Estimation with Delay Correction via Lagrange-Bürman Inversion.

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