Motion Tomography via Occupation Kernels

Russo, Benjamin P.; Kamalapurkar, Rushikesh; Chang, Dongsik; Rosenfeld, Joel A.

doi:10.48550/arxiv.2101.02677

Cited by 3 publications

(2 citation statements)

References 6 publications

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“…In addition, the MT method is applied to facilitate assimilation of the Lagrangian data stream collected by the underwater vehicles to Eulerian flow prediction model [20]. [21] generalizes the MT algorithm by parameterizing the flow field using the occupation kernels.…”

Section: Introductionmentioning

confidence: 99%

Laplacian regularized motion tomography for underwater vehicle flow mapping with sporadic localization measurements

Meriam,

Mengxue,

Fumin

2024

Auton Robot

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Localization measurements for an Autonomous Underwater Vehicle (AUV) are often difficult to obtain. In many cases, localization measurements are only available sporadically after the AUV comes to the sea surface. Since the motion of AUVs is often affected by unknown underwater flow fields, the sporadic localization measurements carry information of the underwater flow field. Motion tomography (MT) algorithms have been developed to compute a underwater flow map based on the sporadic localization measurements. This paper extends MT by introducing Laplacian regularization in to the problem formulation and the MT algorithm. Laplacian regularization enforces smoothness in the spatial distribution of the underwater flow field. The resulted Laplacian regularized motion tomography (RMT) algorithm converges to achieve a finite error bounded. The performance of the RMT and other variants of MT are compared through the method of data resolution analysis. The improved performance of RMT is confirmed by experimental data collected from underwater glider ocean sensing experiments.

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Section: Introductionmentioning

confidence: 99%

Laplacian regularized motion tomography for underwater vehicle flow mapping with sporadic localization measurements

Meriam,

Mengxue,

Fumin

2024

Auton Robot

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“…In particular, like kernel functions, occupation kernels provide a function theoretic analog of their respective measures in a RKHS. Hence, occupation kernels themselves can be leveraged as basis functions for approximation, and indeed occupation kernels have been used in precisely that manner for motion tomography in [8] as well as for a regression approach to fractional order nonlinear system identification in [9]. Occupation kernels are also leveraged as basis functions for the construction of eigenfunctions for finite rank representations of Liouville operators in a continuous time Dynamic Mode Decomposition routine in [10].…”

Section: Introductionmentioning

confidence: 99%

Control Occupation Kernel Regression for Nonlinear Control-Affine Systems

Abudia,

Channagiri,

Rosenfeld

et al. 2021

Preprint

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This manuscript presents an algorithm for obtaining an approximation of nonlinear high order control affine dynamical systems, that leverages the controlled trajectories as the central unit of information. As the fundamental basis elements leveraged in approximation, higher order control occupation kernels represent iterated integration after multiplication by a given controller in a vector valued reproducing kernel Hilbert space. In a regularized regression setting, the unique optimizer for a particular optimization problem is expressed as a linear combination of these occupation kernels, which converts an infinite dimensional optimization problem to a finite dimensional optimization problem through the representer theorem. Interestingly, the vector valued structure of the Hilbert space allows for simultaneous approximation of the drift and control effectiveness components of the control affine system. Several experiments are performed to demonstrate the effectiveness of the approach.

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Laplacian Regularized Motion Tomography for Underwater Vehicle Flow Mapping with Sporadic Localization Measurements

Ouerghi

Hou

Zhang

2022

Preprint

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Localization measurements for an Autonomous Underwater Vehicle (AUV) are often difficult to obtain. In many cases, localization measurements are only available sporadically after the AUV comes to the sea surface. Sincethe motion of AUVs is often affected by unknown underwater flow fields, the sporadic localization measurements carry information of the underwater flow field. Motion tomography (MT) algorithms have been developed to compute a underwater flow map based on the sporadic localization measurements. This paper extends MT by introducing Laplacian regularization in to the problem formulation and the MT algorithm. Laplacian regularization enforces smoothness in the spatial distribution of the underwater flow field. The resulted Laplacian regularized motion tomography (RMT) algorithm converges to achieve a finite error bounded. The performance of the RMT and other variants of MT are compared through the method of data resolution analysis. The improved performance of RMT is confirmed by experimental data collected from underwater glider ocean sensing experiments.

show abstract

Motion Tomography via Occupation Kernels

Cited by 3 publications

References 6 publications

Laplacian regularized motion tomography for underwater vehicle flow mapping with sporadic localization measurements

Laplacian regularized motion tomography for underwater vehicle flow mapping with sporadic localization measurements

Control Occupation Kernel Regression for Nonlinear Control-Affine Systems

Laplacian Regularized Motion Tomography for Underwater Vehicle Flow Mapping with Sporadic Localization Measurements

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