Wavelet based filtering of mobile object fractional trajectory parameters

Amosov, O.S.; Baena, S.G.

doi:10.1109/icca.2017.8003045

Cited by 13 publications

(7 citation statements)

References 11 publications

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“…Recently, interest in the class of non-stationary processes that have a fractal nature has deepened [ 1 , 2 , 3 , 5 , 6 , 7 , 8 , 9 , 10 , 14 , 18 , 19 ].…”

Section: Mathematical Model Of Inertial Sensor Errors In Navigation Systems With Respect To the Chaotic Indicatormentioning

confidence: 99%

“…In both cases, when solving the problem of trajectory tracking, the mathematical models based on the classical Wiener process are widely applicable. At the same time, an aggregation in the form of the FWP is used to model stochastic processes with fractal properties [ 1 , 18 ].…”

Section: Navigation and Motion Controlmentioning

confidence: 99%

“…Let us also consider the object movement models traditionally used to solve orientation tracking problems [ 16 , 18 , 26 , 27 ].…”

Section: Navigation and Motion Controlmentioning

confidence: 99%

“…With this in mind, we propose new models of object motion based on the use of the fractional Wiener process (2) [ 18 , 28 ].…”

Section: Navigation and Motion Controlmentioning

confidence: 99%

“…To obtain a linear model of measurements, the primary measurements of the polar coordinates of an object, range (

), and bearing (

), can be converted into a rectangular coordinate system and are presented in the following form [ 18 , 26 ]

where

and

are random errors of coordinate measurements with the following characteristics

…”

Section: Navigation and Motion Controlmentioning

confidence: 99%

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Peculiarities and Applications of Stochastic Processes with Fractal Properties

Amosov

Amosova

2021

Sensors

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In this paper, the fractal properties of stochastic processes and objects in different areas were specified and investigated. These included: measuring systems and sensors, navigation and motion controls, telecommunication systems and networks, and flaw detection technologies. Additional options that occur through the use of fractality were also indicated and exemplified for each application. Regarding the problems associated with navigation information processing, the following fractal nature processes were identified: errors of inertial sensors based on the microelectromechanical systems called MEMS, in particular gyroscopic drift and accelerometer bias, and; the trajectory movement of mobile objects. With regard to navigation problems specifically, the estimation problem statement and its solution are given by way of the Bayesian approach for processing fractal processes. The modified index of self-similarity for telecommunication series was proposed, and the self-similarity of network traffic based on the R/S method and wavelet analysis was identified. In failure detection, fractality manifested as porosity, wrinkles, surface fractures, and ultrasonic echo signals measured using non-destructive sensors used for rivet compound testing.

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“…Recently, interest in the class of non-stationary processes that have a fractal nature has deepened [ 1 , 2 , 3 , 5 , 6 , 7 , 8 , 9 , 10 , 14 , 18 , 19 ].…”

Section: Mathematical Model Of Inertial Sensor Errors In Navigation Systems With Respect To the Chaotic Indicatormentioning

confidence: 99%

Section: Navigation and Motion Controlmentioning

confidence: 99%

“…Let us also consider the object movement models traditionally used to solve orientation tracking problems [ 16 , 18 , 26 , 27 ].…”

Section: Navigation and Motion Controlmentioning

confidence: 99%

“…With this in mind, we propose new models of object motion based on the use of the fractional Wiener process (2) [ 18 , 28 ].…”

Section: Navigation and Motion Controlmentioning

confidence: 99%

“…To obtain a linear model of measurements, the primary measurements of the polar coordinates of an object, range (

), and bearing (