sensor coverage model & data interpolation filefaculty of informatics | internet of things...

faculty of informatics | internet of things

Bayu Erfianto1

Sensor Coverage Model & Data Interpolation

Internet of Things

faculty of informatics | internet of things 2

Schedule & Syllabus


Definition: Sensor coverage models are abstraction models trying to quantify how well sensors can sense physical phenomena at some locations in the Region of Interest (RoI), or in other words, how well sensors can cover such locations

Coverage model can reflect to reflect sensors sensing capability and quality by capturing the geometric relation between a space point and sensors.

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Sensor Coverage Model


Let us consider a space point z and a set of sensors S = {s1,s2,...,sn}. We use d(s, z) to denote the Euclidean distance between a sensor sand a space point z, such that:

Space point covered by 3 sensor

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Sensor Coverage model


Boolean Disk Model

The function is modeled as

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Some researchers argue that the sensing qualityof a sensor reduces with the increase of the distance away from the sensor

Attenuated Disk Coverage Model

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Multi Sensor

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In the attenuated disk coverage model, the coverage measure becomes very small when the distance between a space point and a sensor becomes very large. In such cases, the coverage measure might be neglected, and some approximations can be made.

Truncated Attenuation

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Comparison of Disk Coverage

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Sectorized Coverage

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Assume that Rs is the same. Problem: how to obtain value that weakly covered by two sensing coverage ?

Solution: Interpolation Methods

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Interpolation


What is Interpolation

Given (x0,y0), (x1,y1), …… (xn,yn), find the value of ‘y’ at a value of ‘x’ that is not given.


Direct InterpolationGiven ‘n+1’ data points (x0,y0), (x1,y1),…………..

(xn,yn),

pass a polynomial of order ‘n’ through the data as given below:

where a0, a1,………………. an are real constants.

Set up ‘n+1’ equations to find ‘n+1’ constants.

To find the value ‘y’ at a given value of ‘x’, simply substitute the value of ‘x’ in the above polynomial.

.....................10n

nxaxaay +++=


Find

We have

We can write in matrix

Solve

By knowing a0 and a1, you can find yn with known xn

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Linear Interpolation

( )00, yx( )xf1

( )11, yx

x

y


Quadratic Interpolation

( )00 , yx

( )11, yx( )22, yx

( )xf2

y

x

Find

We have

We can write in matrix

Solve a0, a1,a2

By knowing a0 and a1, you can find yn with known xn


Find

in matrix form

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Bilinear Interpolation


Equation

Comparison

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Bicubic Interpolation


Comparison (with Python)

A: Nearest B: Linear C: Bicubic

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Interpolasi


Temperature measurement

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Example of Interpolation Data


Temperature Map

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Distribusi Polutan

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Scanning Suhu Mobil

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Creating Heatmap with GoogleMap API

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Spatial Interpolation


Tugas UTS (dibawa dan dikumpulkan saat UTS)– Bagaimana caranya melakukan geotagging di Googlemap– Bagaimana caranya menampilkan Heatmap / Variogram di

Googlemap– Interpolasi apa saja yang disediakan oleh GoogleMap

untuk membuat Heatmap berdasarkan data interpolasi

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Spatial Interpolation

THANK YOU

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sensor coverage model & data interpolation filefaculty of informatics | internet of things...

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