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The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
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The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...
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The Discrete-Time Fourier Transform (DTFT) is an essential mathematical tool for analyzing discrete-time signals, converting them from the time domain to the frequency domain. This transformation allows for examining the frequency components of discrete signals, providing insights into their spectral characteristics. In the DTFT, the continuous integral used in the continuous-time Fourier transform is replaced by a summation to accommodate the discrete nature of the signal.
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The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
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Unsupervised Learning in RSS-Based DFLT Using an EM Algorithm.

Ossi Kaltiokallio1, Roland Hostettler2, Hüseyin Yiğitler3

  • 1Unit of Electrical Engineering, Tampere University, 33720 Tampere, Finland.

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|August 28, 2021
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Summary
This summary is machine-generated.

This study introduces a new device-free localization and tracking (DFLT) system that eliminates the need for calibration. The Expectation-Maximization algorithm accurately estimates wireless signal parameters for improved tracking.

Keywords:
bayesian filtering and smoothingexpectation-maximization algorithmlocalization and trackingparameter estimationreceived signal strength

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Area of Science:

  • Wireless Sensor Networks
  • Localization and Tracking Technologies
  • Machine Learning for Signal Processing

Background:

  • Received Signal Strength (RSS) changes from static wireless nodes enable device-free localization and tracking (DFLT).
  • Existing RSS-based DFLT systems often require extensive and costly calibration periods, hindering practical deployment.
  • Calibration involves collecting RSS measurements during unoccupied periods or with subjects in known locations.

Purpose of the Study:

  • To develop a novel device-free localization and tracking (DFLT) system that removes the necessity for calibration periods.
  • To estimate arbitrary target trajectories using an advanced algorithm for improved localization accuracy.
  • To enhance the efficiency and performance of RSS-based DFLT systems.

Main Methods:

  • Development of an Expectation-Maximization (EM) algorithm incorporating Gaussian smoothing.
  • The EM algorithm estimates unknown Received Signal Strength (RSS) model parameters without supervised training.
  • Implementation of a novel localization and tracking system designed to estimate target trajectories.

Main Results:

  • The proposed system successfully operates without requiring any calibration period.
  • The EM algorithm demonstrates improved accuracy compared to existing device-free localization and tracking (DFLT) methods.
  • The system exhibits computational efficiency and outperforms a state-of-the-art adaptive DFLT system in tracking accuracy.

Conclusions:

  • The developed EM-based DFLT system offers a practical solution by eliminating calibration requirements.
  • The approach significantly enhances localization and tracking accuracy while maintaining computational efficiency.
  • This method represents a substantial advancement for device-free localization and tracking applications.