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Downsampling01:20

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When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
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Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...
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Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
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Appropriate sampling methods ensure that samples are drawn without bias and accurately represent the population. Because measuring the entire population in a study is not practical, researchers use samples to represent the population of interest.
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MapReduce particle filtering with exact resampling and deterministic runtime.

Jeyarajan Thiyagalingam1, Lykourgos Kekempanos1, Simon Maskell1

  • 1Department of Electrical Engineering and Electronics, University of Liverpool, Liverpool, L69 3GJ UK.

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|February 4, 2020
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Summary

This study introduces a novel MapReduce implementation for particle filters, optimizing the resampling component for Big Data. This scalable approach enhances sequential estimation accuracy with large particle numbers.

Keywords:
Big data samplingMCMC methodsMapReduceParticle filtersResampling

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Area of Science:

  • Computational Statistics
  • Bayesian Inference
  • Big Data Analytics

Background:

  • Particle filters are powerful Bayesian methods for sequential estimation in complex models.
  • Increasing particle count improves accuracy but poses computational challenges for Big Data.
  • Existing particle filter implementations lack efficient MapReduce integration.

Purpose of the Study:

  • To develop an efficient MapReduce implementation of particle filters.
  • To address the resampling component bottleneck in parallel particle filter execution.
  • To enable the use of a significantly larger number of particles for improved estimation.

Main Methods:

  • Implementation of a particle filter using the MapReduce programming model.
  • Development of a novel, approximation-free resampling component for parallel processing.
  • Analysis of the resampling component's spatial and time complexity (O(N) and O((logN)^2)).

Main Results:

  • A functional MapReduce-based particle filter implementation was successfully developed.
  • The new resampling component achieves deterministic O((logN)^2) time complexity.
  • Demonstrated scalability with a particle filter using 2^24 particles across 512 cores.

Conclusions:

  • The proposed MapReduce particle filter implementation effectively handles Big Data challenges.
  • The optimized resampling component significantly improves parallel execution efficiency.
  • This work facilitates more accurate sequential estimation in non-linear, non-Gaussian scenarios using Big Data.