Radial Basis Function Interpolation for Signal-Model-Independent Localization

Pino-Povedano, Sara; Bousoño-Calzón, Carlos; Gonzalez-Serrano, F.J.

doi:10.1109/jsen.2015.2511807

Cited by 9 publications

(4 citation statements)

References 36 publications

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“…us, RBF interpolation is commonly used in signal processing, photogrammetry, digital terrain modeling, and so on [25,26]. RBF interpolation for scattered data can be described as follows.…”

Section: Radial Basis Function Interpolationmentioning

confidence: 99%

RBF Interpolation Algorithm for FTS Tool Path Generation

Nie

et al. 2021

Mathematical Problems in Engineering

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Freeform optics are defined as nonrotational symmetric optical surfaces in the manufacturing industry. Freeform optics are extensively applied to many areas in order to improve system performance. Fast tool servo (FTS) assisting single-point diamond turning technology has high application prospects in freeform optics machining. This paper discusses the interpolation algorithm for tool path generation of FTS through the application of a radial basis function (RBF) algorithm. For this purpose, a positive definite RBF with compact support was employed as the interpolant. The existence is mathematically proven. Numerical simulations were performed to compare the performances of the RBF algorithm and commonly used algorithms for satisfying the requirements of existence, smoothness, and accuracy. Machining experiments were also conducted to validate the applicability of the algorithm. The simulation results showed that the RBF interpolation algorithm outperformed other algorithms in terms of smoothness. The RBF algorithm also provided the highest interpolation accuracy. Furthermore, the RBF interpolation algorithm exhibited the highest accuracy for error distribution, with large errors distributed mainly in transition areas. The machining results were also in general agreement with the simulation results although obvious practical errors were observed. Overall, RBF interpolation can provide higher accuracy and better smoothness in the tool path generation of FTS.

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“…us, RBF interpolation is commonly used in signal processing, photogrammetry, digital terrain modeling, and so on [25,26]. RBF interpolation for scattered data can be described as follows.…”

Section: Radial Basis Function Interpolationmentioning

confidence: 99%

RBF Interpolation Algorithm for FTS Tool Path Generation

Nie

et al. 2021

Mathematical Problems in Engineering

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“…RBF-based interpolation is a viable choice for approximating interpolation on irregular geometry because it has high order accuracy and computational stability for large numbers of scattered data points even in high dimension [4]. Previous studies show many implementation of RBF-based interpolation can be found in various fields: reconstruction from scattered data in computer vision and graphics [5], [6] and [7], mesh deformation on electro-magnetic problem [8], and signal localization approximation [9].…”

Section: Introductionmentioning

confidence: 99%

Irregular Grid Interpolation using Radial Basis Function for Large Cylindrical Volume

Iryanto

Muttaqien

Sadikin

2020

Jurnal Ilmu Komputer dan Informasi

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Irregular grid interpolation is one of the numerical functions that often used to approximate value on an arbitrary location in the area closed by non-regular grid pivot points. In this paper, we propose method for achieving efficient computation time of radial basis function-based non-regular grid interpolation on a cylindrical coordinate. Our method consist of two stages. The first stage is the computation of weights from solving linear RBF systems constructed by known pivot points. We divide the volume into many subvolumes. At second stages, interpolation on an arbitrary point could be done using weights calculated on the first stage. At first, we find the nearest point with the query point by structuring pivot points in a K-D tree structure. After that, using the closest pivot point, we could compute the interpolated value with RBF functions. We present the performance of our method based on computation time on two stages and its precision by calculating the mean square error between the interpolated values and analytic functions. Based on the performance evaluation, our method is acceptable.

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“…Radial basis function interpolation is a classical meshless method for scattered data interpolation, which has the advantages of isotropy, high accuracy and high adaptability, hence it is extensively used in the fields of surface reconstruction, image deformation, data modeling and so on [14][15][16]. RBF interpolation is applied in the low-frequency electromagnetic problems solved by finite element method, which is validated to be effective for the mesh deformation [14].…”

mentioning

confidence: 99%

“…RBF interpolation is applied in the low-frequency electromagnetic problems solved by finite element method, which is validated to be effective for the mesh deformation [14]. In [15], RBF interpolation is used to estimate the position of the target by evaluating the measurement function of whole surveillance area, which has good performance in both singletarget and multi-target location. RBF interpolation and geodesic distance method are combined to synthesize more natural facial animation in [16].…”

mentioning

confidence: 99%

High-Dimensional Radial Basis Function Extension Interpolation Nonlinear Post-Distorter in Visible Light Communication Systems

et al. 2022

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The nonlinearity induced by light-emitting diode (LED) affects the normal transmission and reception, which significantly limits the performance of visible light communication (VLC) system. To address the problem induced by the nonlinearity of LED, a post-distorter for orthogonal frequency division multiplexing (OFDM) based VLC is proposed in this paper. Radial basis function (RBF) interpolation, known as an excellent function approximation method, is investigated to implement the nonlinearity mitigations. To further remove the memory effect of LED, which could not be ignored, we propose to extend RBF to a high-dimensional interpolation so that it can eliminate both nonlinearity and memory effect simultaneously. The performance of the proposed RBF extension interpolation is verified by numerical simulations, and a better performance in suppressing nonlinearity is obtained in VLC-OFDM systems as compared with the frequency domain nonlinear compensation method. A signalto-noise ratio gain of 2dB in terms of 0 bEN can be obtained when bit error rate is about 6*10 -7 at 6dB power back-off (PBO), while 6dB gain can be achieved when BER is 2*10 -4 at 4dB PBO.

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Radial Basis Function Interpolation for Signal-Model-Independent Localization

Cited by 9 publications

References 36 publications

RBF Interpolation Algorithm for FTS Tool Path Generation

RBF Interpolation Algorithm for FTS Tool Path Generation

Irregular Grid Interpolation using Radial Basis Function for Large Cylindrical Volume

High-Dimensional Radial Basis Function Extension Interpolation Nonlinear Post-Distorter in Visible Light Communication Systems

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