Fingerprint Database Enhancement by Applying Interpolation and Regression Techniques for IoT-based Indoor Localization

Most applied indoor localization is based on distance and fingerprint techniques. The distance-based technique converts specific parameters to a distance, while the fingerprint technique stores parameters as the fingerprint database. The widely used Internet of Things (IoT) technologies, e.g., Wi-Fi and ZigBee, provide the localization parameters, i.e., received signal strength indicator (RSSI). The fingerprint technique advantages over the distance-based method as it straightforwardly uses the parameter and has better accuracy. However, the burden in database reconstruction in terms of complexity and cost is the disadvantage of this technique. Some solutions, i.e., interpolation, image-based method, machine learning (ML)-based, have been proposed to enhance the fingerprint methods. The limitations are complex and evaluated only in a single environment or simulation. This paper proposes applying classical interpolation and regression to create the synthetic fingerprint database using only a relatively sparse RSSI dataset. We use bilinear and polynomial interpolation and polynomial regression techniques to create the synthetic database and apply our methods to the 2D and 3D environments. We obtain an accuracy improvement of 0.2m for 2D and 0.13m for 3D by applying the synthetic database. Adding the synthetic database can tackle the sparsity issues, and the offline fingerprint database construction will be less burden. Doi: 10.28991/esj-2021-SP1-012 Full Text: PDF

Analysis of calculations when creating a theoretical drawing of a tug by the interpolation method

The development of a theoretical drawing by manual methods is notable for considerable laboriousness, in this regard, the use of methods that significantly reduce the development time and increase its quality is relevant. In this work, a comparative analysis of methods for obtaining ordinates of a theoretical drawing is carried out. The existing methods of computer-aided design and methods of forming a theoretical drawing are considered: classical, interpolation, affine transformation method, modular method. The process of development of the surface of the tug by the interpolation method is shown, the substantiation of its application is carried out. On the basis of the developed model, a program for calculating the ordinates of the theoretical drawing of tugboats was developed. The results of the software package operation are presented, namely, the ordinates of the theoretical drawing of the tugboat and the hull of the theoretical drawing, as well as the analysis of the calculation accuracy. The adopted approach to the development of the ship's surface can significantly reduce the time and cost of design work on the development of the ship's surface, can be used for its further automation and use as scientific, industrial and educational purposes.

On the Raşa Inequality for Higher Order Convex Functions

We study the following $$(q-1)$$ ( q - 1 ) th convex ordering relation for qth convolution power of the difference of probability distributions $$\mu $$ μ and $$\nu $$ ν $$\begin{aligned} (\nu -\mu )^{*q}\ge _{(q-1)cx} 0 , \quad q\ge 2, \end{aligned}$$ ( ν - μ ) ∗ q ≥ ( q - 1 ) c x 0 , q ≥ 2 , and we obtain the theorem providing a useful sufficient condition for its verification. We apply this theorem for various families of probability distributions and we obtain several inequalities related to the classical interpolation operators. In particular, taking binomial distributions, we obtain a new, very short proof of the inequality given recently by Abel and Leviatan (2020).

THE PROBLEM OF THE COMBINED USE OF FILTRATION THEORY AND MACHINE LEARNING ELEMENTS FOR SOLVING THE INVERSE PROBLEM OF RESTORING THE HYDRAULIC CONDUCTIVITY OF AN OIL FIELD

This article presents the methodology involving the combined use of machine learning elements and a physically meaningful filtration model. The authors propose using a network of radial basis functions for solving the problem of restoring hydraulic conductivity in the interwell space for an oil field. The advantage of the proposed approach in comparison with classical interpolation methods as applied to the problems of reconstructing the filtration-capacitive properties of the interwell space is shown. The paper considers an algorithm for the interaction of machine learning methods, a filtration model, a mechanism for separating input data, a form of a general objective function, which includes physical and expert constraints. The research was carried out on the example of a symmetrical element of an oil field. The proposed procedure for finding a solution includes solving a direct and an adjoint problem.

On the reconstruction via Urysohn-Chlodovsky operators

The main first goal of this work is to introduce an Urysohn type Chlodovsky operators defined on positive real axis by using the Urysohn type interpolation of the given function f and bounded on every finite subinterval. The basis used in this construction are the Fréchet and Prenter Density Theorems together with Urysohn type operator values instead of the rational sampling values of the function. Afterwards, we will state some convergence results, which are generalization and extension of the theory of classical interpolation of functions to operators.

Valiron’s Interpolation Formula and a Derivative Sampling Formula in the Mellin Setting Acquired via Polar-Analytic Functions

In this paper, we first recall some recent results on polar-analytic functions. Then we establish Mellin analogues of a classical interpolation of Valiron and of a derivative sampling formula. As consequences a new differentiation formula and an identity theorem in Mellin–Bernstein spaces are obtained. The main tool in the proofs is a residue theorem for polar-analytic functions.

A NOTE ON INTERPOLATION OF PERMUTATIONS OF A SUBSET OF A FINITE FIELD

We determine several variants of the classical interpolation formula for finite fields which produce polynomials that induce a desirable mapping on the nonspecified elements, and without increasing the number of terms in the formula. As a corollary, we classify those permutation polynomials over a finite field which are their own compositional inverse, extending work of C. Wells.

Optimization of Interpolation Algorithm in Survey Calculation

The interpolation algorithm in survey calculation is widely used in petroleum engineering, and it is different from the general mathematical interpolation. Along with the development of oil exploitation, various special type of well begin to appear, but the original interpolation method can not meet the needs of the field work. So the paper according to classical interpolation model of the interpolation algorithm, the three optimization intercalation models the curvature radius of curvature, minimum curvature, and natural curve were figured out. Theory analysis and results show that optimized interpolation formula the paper established can meet all kinds of optimization calculation of the inclined interpolation needs.