Polar Gaussian Processes and Experimental Designs in Circular Domains

Padonou, Espéran; Roustant, Olivier

doi:10.1137/15m1032740

Cited by 20 publications

(29 citation statements)

References 21 publications

(34 reference statements)

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“…For

, as we deal with angles, we cannot use a simple euclidean distance. When choosing the metric to use, we have to ensure that the resulting kernel is positive definite [ 34 , 35 ]. We can define two distance

and

based respectively on the chordal distance and the geodesic distance on

…”

Section: Msis Scan Mergingmentioning

confidence: 99%

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Elevation Angle Estimations of Wide-Beam Acoustic Sonar Measurements for Autonomous Underwater Karst Exploration

Breux

Lapierre

2020

Sensors

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This paper proposes a solution for merging the measurements from two perpendicular profiling sonars with different beam-widths, in the context of underwater karst (cave) exploration and mapping. This work is a key step towards the development of a full 6D pose SLAM framework adapted to karst aquifer, where potential water turbidity disqualifies vision-based methods, hence relying on acoustic sonar measurements. Those environments have complex geometries which require 3D sensing. Wide-beam sonars are mandatory to cover previously seen surfaces but do not provide 3D measurements as the elevation angles are unknown. The approach proposed in this paper leverages the narrow-beam sonar measurements to estimate local karst surface with Gaussian process regression. The estimated surface is then further exploited to infer scaled-beta distributions of elevation angles from a wide-beam sonar. The pertinence of the method was validated through experiments on simulated environments. As a result, this approach allows one to benefit from the high coverage provided by wide-beam sonars without the drawback of loosing 3D information.

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“…For

and

based respectively on the chordal distance and the geodesic distance on

…”

Section: Msis Scan Mergingmentioning

confidence: 99%

“…In [ 35 ], it is shown that for geodesic distance

-Wendland function [ 36 ] can be used to define a valid kernel

…”

Section: Msis Scan Mergingmentioning

confidence: 99%

Elevation Angle Estimations of Wide-Beam Acoustic Sonar Measurements for Autonomous Underwater Karst Exploration

Breux

Lapierre

2020

Sensors

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“…Two variants of tunnel Gaussian process (TGP) models are developed to elucidate aircraft's approach and landing dynamics, leveraging on the data recorded by advanced surface movement guidance and control system (A-SMGCS), which provides surveillance, routing, guidance for the control of vehicles and aircraft (see Section III.A, for details). TGP is developed by modifying and hybridizing sparse variational Gaussian process (SVGP) [24], which enables Gaussian process to handle big amount of data, and polar Gaussian process [25], which permits cylindrical coordinate modeling. The hybridization allows the proposed TGP to inherit the advantages of the two methods, to characterize and reveal the underlying probabilistic structure of approach and landing trajectory, and to provide interpretable tunnel views of the trajectory.…”

Section: Introductionmentioning

confidence: 99%

Tunnel Gaussian Process Model for Learning Interpretable Flight’s Landing Parameters

Goh

Lim

Alam

et al. 2021

Journal of Guidance, Control, and Dynamics

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Approach and landing accidents have resulted in a significant number of hull losses worldwide. Technologies (e.g., instrument landing system) and procedures (e.g., stabilized approach criteria) have been developed to reduce the risks. In this paper, we propose a data-driven method to learn and interpret flight's approach and landing parameters to facilitate comprehensible and actionable insights into flight dynamics. Specifically, we develop two variants of tunnel Gaussian process (TGP) models to elucidate aircraft's approach and landing dynamics using advanced surface movement guidance and control system (A-SMGCS) data, which then indicates the stability of flight. TGP hybridizes the strengths of sparse variational Gaussian process and polar Gaussian process to learn from a large amount of data in cylindrical coordinates. We examine TGP qualitatively and quantitatively by synthesizing three complex trajectory datasets and compared TGP against existing methods on trajectory learning. Empirically, TGP demonstrates superior modeling performance. When applied to operational A-SMGCS data, TGP provides the generative probabilistic description of landing dynamics and interpretable tunnel views of approach and landing parameters. These probabilistic tunnel models can facilitate the analysis of procedure adherence and augment existing aircrew and air traffic controllers' displays during the approach and landing procedures, enabling necessary corrective actions. Nomenclature 𝐺𝑃 = Gaussian process models 𝐾 = kernel function defined by 𝐺𝑃

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“…For example Paciorek and Schervish (2006) create a new class of covariance functions (kernels) allowing the model to adapt itself to spatial surface whose variability changes with location. Likewise, Padonou and Roustant (2016) in a microelectronic framework define a GP model which inserts the geometry of the wafer in the kernel. That's why they introduce the polar GP defined with respect to polar coordinates: the covariance function is a sum of a product kernel of radius and a product kernel of polar angles.…”

Section: Introductionmentioning

confidence: 99%

Four algorithms to construct a sparse kriging kernel for dimensionality reduction

et al. 2019

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In the context of computer experiments, metamodels are largely used to represent the output of computer codes. Among these models, Gaussian process regression (kriging) is very efficient see e.g Snelson (2008). In high dimension that is with a large number of input variables, but with few observations the estimation of the parameters with a classical anisotropic kriging becomes completely wrong. The number of the parameters to estimate is the same as the number of inputs and it implies that the space of the optimization becomes too big compare to the available informations. One way to overcome this drawback is to use the isotropic kernel which is more robust because it estimates not as many parameters. However this model is too restrictive. The aim of this paper is twofold. Our first objective is to propose a smooth kernel with as few parameters as warranted. We propose a kernel which is a tensor product of few isotropic kernels built on well-chosen subgroup of variables. The main difficulty is to find the number and the composition of groups. Our second objective is to propose algorithmic strategies to overcome the difficulty of finding the number and the composition of the groups. Four forward strategies are proposed. They all start with the simplest isotropic kernel and stop when the best model according to BIC criterion is found. They all show very good accuracy results on simulation test cases. But one of them is the most efficient. Tested on a real data set, our kernel shows very good prediction results.

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Polar Gaussian Processes and Experimental Designs in Circular Domains

Cited by 20 publications

References 21 publications

Elevation Angle Estimations of Wide-Beam Acoustic Sonar Measurements for Autonomous Underwater Karst Exploration

Elevation Angle Estimations of Wide-Beam Acoustic Sonar Measurements for Autonomous Underwater Karst Exploration

Tunnel Gaussian Process Model for Learning Interpretable Flight’s Landing Parameters

Four algorithms to construct a sparse kriging kernel for dimensionality reduction

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