Regional TEC dynamic modeling based on Slepian functions

Sharifi, Mohammad Ali; Farzaneh, Saeed

doi:10.1016/j.asr.2015.05.024

Cited by 9 publications

(3 citation statements)

References 18 publications

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“…Based on the polynomial and triangular models, a few expanded models have also been proposed [12–14]. By contrast, the spherical harmonic model attracts more interests due to taking the ionospheric spatial characteristic of spherical distribution into account [8, 15–17]. Generally, the low‐order spherical harmonic model has been able to represent the spatial distribution of the regional ionosphere well [18, 19].…”

Section: Introductionmentioning

confidence: 99%

Least‐squares collocation modelling of regional ionospheric TEC for accelerating real‐time single‐frequency PPP convergence

Gong

Cai

Dai

et al. 2019

IET Radar, Sonar & Navigation

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Section: Introductionmentioning

confidence: 99%

Least‐squares collocation modelling of regional ionospheric TEC for accelerating real‐time single‐frequency PPP convergence

Gong

Cai

Dai

et al. 2019

IET Radar, Sonar & Navigation

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“…Slepian functions are also optimally concentrated within the region of the sphere on which they are defined [1], [13]. Consequently, Slepian functions on the sphere have been used for localized spectral and spatial analysis [14]- [16], and signal estimation from incomplete measurements [17], [18], and sparse and efficient representations of spherical in signals in a wide range of applications found in geophysics [16], [19], [20], cosmology and planetary studies [21], [22], optics [18] and computer graphics [23], to name a few.…”

Section: Introductionmentioning

confidence: 99%

Slepian Spatial-Spectral Concentration Problem on the Sphere: Analytical Formulation for Limited Colatitude–Longitude Spatial Region

Bates

Khalid

Kennedy

2017

IEEE Trans. Signal Process.

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In this paper, we develop an analytical formulation for the Slepian spatial-spectral concentration problem on the sphere for a limited colatitude-longitude spatial region on the sphere, defined as the Cartesian product of a range of positive colatitudes and longitudes. The solution of the Slepian problem is a set of functions that are optimally concentrated and orthogonal within a spatial or spectral region. These properties make them useful for applications where measurements are taken within a spatially limited region of the sphere and/or a signal is only to be analyzed within a region of the sphere. To support localized spectral/spatial analysis, and estimation and sparse representation of localized data in these applications, we exploit the expansion of spherical harmonics in the complex exponential basis to develop an analytical formulation for the Slepian concentration problem for a limited colatitudelongitude spatial region. We also extend the analytical formulation for spatial regions that are comprised of a union of rotated limited colatitude-longitude subregions. By exploiting various symmetries of the proposed formulation, we design a computationally efficient algorithm for the implementation of the proposed analytical formulation. Such a reduction in computation time is demonstrated through numerical experiments. We present illustrations of our results with the help of numerical examples and show that the representation of a spatially concentrated signal is indeed sparse in the Slepian basis.Index Terms-Spatial-spectral concentration problem, Slepian functions, 2-sphere (unit sphere), spherical harmonics. 1053-587X

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“…However, it is common for signals to be measured, reconstructed and/or analyzed within a region of the sphere in many fields including medical imaging [20], signal processing [21], [22], geological studies [9], [10], acoustics [7] and cosmological studies [23], [24], to name a few. For example, the samples are unavailable (or unreliable) at the North and South pole for satellite measurements of the Earth's magnetic or gravitational field [25].…”

mentioning

confidence: 99%

Efficient Computation of Slepian Functions for Arbitrary Regions on the Sphere

Bates¹,

Khalid²,

Kennedy³

2017

IEEE Trans. Signal Process.

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Abstract-In this paper, we develop a new method for the fast and memory-efficient computation of Slepian functions on the sphere. Slepian functions, which arise as the solution of the Slepian concentration problem on the sphere, have desirable properties for applications where measurements are only available within a spatially limited region on the sphere and/or a function is required to be analyzed over the spatially limited region. Slepian functions are currently not easily computed for large band-limits for an arbitrary spatial region due to high computational and large memory storage requirements. For the special case of a polar cap, the symmetry of the region enables the decomposition of the Slepian concentration problem into smaller subproblems and consequently the efficient computation of Slepian functions for large band-limits. By exploiting the efficient computation of Slepian functions for the polar cap region on the sphere, we develop a formulation, supported by a fast algorithm, for the approximate computation of Slepian functions for an arbitrary spatial region to enable the analysis of modern datasets that support large band-limits. For the proposed algorithm, we carry out accuracy analysis of the approximation, computational complexity analysis, and review of memory storage requirements. We illustrate, through numerical experiments, that the proposed method enables faster computation, and has smaller storage requirements, while allowing for sufficiently accurate computation of the Slepian functions.

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Regional TEC dynamic modeling based on Slepian functions

Cited by 9 publications

References 18 publications

Least‐squares collocation modelling of regional ionospheric TEC for accelerating real‐time single‐frequency PPP convergence

Least‐squares collocation modelling of regional ionospheric TEC for accelerating real‐time single‐frequency PPP convergence

Slepian Spatial-Spectral Concentration Problem on the Sphere: Analytical Formulation for Limited Colatitude–Longitude Spatial Region

Efficient Computation of Slepian Functions for Arbitrary Regions on the Sphere

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