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Bayesian Smoothing Filters in Particle Tracking Velocimetry
Smoothing is an integral part of particle tracking velocimetry. Bayesian methods, although promising and common in many other engineering fields, did not receive much attention for PTV processing.
To investigate the use and potential of Bayesian smoothing for PTV, a corresponding implementation is to be developed and compared to widespread smoothing methods.
Keywords: particle image velocimetry, signal processing, system modeling, trajectory smoothing, Bayesian filters, Kalman filter, Rauch-Tung-Striebel smoothing
Particle tracking velocimetry is a mature image analysis technique which is widely used for velocity and acceleration measurements of particles in particle-laden flows. The derivative calculation requires a smoothing step to suppress the detection noise. Currently, either Gaussian or Savitzky-Golay filters are used for this purpose. In contrast to those two filters, Bayesian filters received very little attention in this context so far. Specific Bayesian filter and smoothing topologies, such as the Kalman Filter and the Rauch-Tung-Striebel smoother, are mature, well understood and widely used in other research fields and can even be shown to perform optimal smoothing under certain conditions. In addition, Bayesian filters offer intrinsic uncertainty estimation and a systematic way to incorporate prior information.
The aim of this project is to develop a Bayesian filter for trajectory smoothing in particle tracking velocimetry, and to compare it to other state-of-the-art filter designs. The filter design process includes theoretical work, a thorough literature review and dynamic system analysis, as well as programming an efficient software implementation.
The filter benchmark will be conducted on model signals, existing simulation and experimental data. Important questions to answer include: How are Bayesian filter designs similar or different to Gaussian and Savitzky-Golay filters? Is Bayesian smoothing capable of improving the estimation performance of kinematic quantities? How does the filter perform for different underlying flows? What are the input parameters and how can they be reliably estimated?
This project gives the opportunity to investigate and gain experience in the characteristics, design and use of some of the most important and widespread data analysis tools in engineering.
Requirements:
- High motivation and independent working ability
- Basic knowledge of fluid dynamics and probability theory
- Knowledge in signal processing and dynamic system modelling
- Fluency with basic python programming
Location: Institute of Fluid Dynamics (IFD), ML building, ETH Zentrum
Particle tracking velocimetry is a mature image analysis technique which is widely used for velocity and acceleration measurements of particles in particle-laden flows. The derivative calculation requires a smoothing step to suppress the detection noise. Currently, either Gaussian or Savitzky-Golay filters are used for this purpose. In contrast to those two filters, Bayesian filters received very little attention in this context so far. Specific Bayesian filter and smoothing topologies, such as the Kalman Filter and the Rauch-Tung-Striebel smoother, are mature, well understood and widely used in other research fields and can even be shown to perform optimal smoothing under certain conditions. In addition, Bayesian filters offer intrinsic uncertainty estimation and a systematic way to incorporate prior information.
The aim of this project is to develop a Bayesian filter for trajectory smoothing in particle tracking velocimetry, and to compare it to other state-of-the-art filter designs. The filter design process includes theoretical work, a thorough literature review and dynamic system analysis, as well as programming an efficient software implementation.
The filter benchmark will be conducted on model signals, existing simulation and experimental data. Important questions to answer include: How are Bayesian filter designs similar or different to Gaussian and Savitzky-Golay filters? Is Bayesian smoothing capable of improving the estimation performance of kinematic quantities? How does the filter perform for different underlying flows? What are the input parameters and how can they be reliably estimated?
This project gives the opportunity to investigate and gain experience in the characteristics, design and use of some of the most important and widespread data analysis tools in engineering.
Requirements: - High motivation and independent working ability - Basic knowledge of fluid dynamics and probability theory - Knowledge in signal processing and dynamic system modelling - Fluency with basic python programming
Location: Institute of Fluid Dynamics (IFD), ML building, ETH Zentrum
Develop a Bayesian smoother design and a corresponding simplified dynamic model of particles in turbulence.
- Implement the filter efficiently in python
- Establish guidelines and algorithms for noise level estimation and prior distribution selection
- Select a set of test cases and performance metrics
- Assess the filter performance, robustness and input parameter sensitivity
- Compare the filter with state-of-the-art Gaussian and Savitzky-Golay filters
Develop a Bayesian smoother design and a corresponding simplified dynamic model of particles in turbulence.
- Implement the filter efficiently in python - Establish guidelines and algorithms for noise level estimation and prior distribution selection - Select a set of test cases and performance metrics - Assess the filter performance, robustness and input parameter sensitivity - Compare the filter with state-of-the-art Gaussian and Savitzky-Golay filters