Vertical scaling optimization algorithm for a fractal interpolation model of time offsets prediction in navigation systems

2021 ◽  
Vol 90 ◽  
pp. 862-874
Author(s):  
Tao Han ◽  
Yuanxi Yang ◽  
Guanwen Huang
2012 ◽  
Vol 25 (11) ◽  
pp. 1896-1900 ◽  
Author(s):  
Zhigang Feng ◽  
Yizhuo Feng ◽  
Zhenyou Yuan

2015 ◽  
Vol 91 (3) ◽  
pp. 435-446 ◽  
Author(s):  
HUO-JUN RUAN ◽  
QIANG XU

In this paper, we present a general framework to construct fractal interpolation surfaces (FISs) on rectangular grids. Then we introduce bilinear FISs, which can be defined without any restriction on interpolation points and vertical scaling factors.


Fractals ◽  
2020 ◽  
Vol 28 (06) ◽  
pp. 2050096
Author(s):  
JINMYONG KIM ◽  
HAKMYONG MUN

In this paper, we present a construction of new nonlinear recurrent hidden variable fractal interpolation curves. In order to get new fractal curves, we use Rakotch’s fixed point theorem. We construct recurrent hidden variable iterated function systems with function vertical scaling factors to generate more flexible fractal interpolation curves. We also give an illustrative example to demonstrate the effectiveness of our results.


2006 ◽  
Vol 09 (03) ◽  
pp. 287-293 ◽  
Author(s):  
TONG ZHANG ◽  
JIANLIN LIU ◽  
ZHUO ZHUANG

Iterated Function System (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R2 or R3 (R is the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended from R3 to Rn (n is an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model. This model uses a "mapping partial derivative" and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in Rn. Therefore, the result is very general. Moreover, the multi-dimensional piece-wise self-affine fractal interpolation model in tensor form is more terse than in the usual matrix form.


Fractals ◽  
2019 ◽  
Vol 27 (06) ◽  
pp. 1950103
Author(s):  
JINMYONG KIM ◽  
HYONJIN KIM ◽  
HAKMYONG MUN

This paper presents a method to construct nonlinear hidden variable fractal interpolation functions (FIFs) and their stability results. We ensure that the projections of attractors of vector-valued nonlinear iterated function systems (IFSs) constructed by Rakotch contractions and function vertical scaling factors are graphs of some continuous functions interpolating the given data. We also give an explicit example illustrating obtained results. Then, we get the stability results of the constructed FIFs in the case of the generalized interpolation data having small perturbations.


2019 ◽  
Vol 2019 ◽  
pp. 1-17
Author(s):  
Mingde Gong ◽  
Haohao Wang ◽  
Xin Wang

Road input can be provided for a vehicle in advance by using an optical sensor to preview the front terrain and suspension parameters can be adjusted before a corresponding moment to keep the body as smooth as possible and thus improve ride comfort and handling stability. However, few studies have described this phenomenon in detail. In this study, a LiDAR coupled with global positioning and inertial navigation systems was used to obtain the digital terrain in front of a vehicle in the form of a 3D point cloud, which was processed by a statistical filter in the Point Cloud Library for the acquisition of accurate data. Next, the inverse distance weighting interpolation method and fractal interpolation were adopted to extract the road height profile from the 3D point cloud and improve its accuracy. The roughness grade of the road height profile was utilised as the input of active suspension. Then, the active suspension, which was based on an LQG controller, used the analytic hierarchy process method to select proper weight coefficients of performance indicators according to the previously calculated road grade. Finally, the road experiment verified that reasonable selection of active suspension’s LQG controller weightings based on estimated road profile and road class through fractal interpolation can improve the ride comfort and handling stability of the vehicle more than passive suspension did.


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