KalCal: a novel calibration framework for radio interferometry using the Kalman Filter and Smoother
- Authors: Welman, Brian Allister
- Date: 2024-10-11
- Subjects: Radio interferometers , Calibration , Kalman filtering , Bayesian inference , Signal processing , Radio astronomy , MeerKAT
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/467127 , vital:76818
- Description: Calibration in radio interferometry is essential for correcting measurement errors. Traditional methods employ maximum likelihood techniques and non-linear least squares solvers but face challenges due to the data volumes and increased noise sensitivity of contemporary instruments such as MeerKAT. A common approach for mitigating these issues is using “solution intervals”, which helps manage the data volume and reduces overfitting. However, inappropriate interval sizes can degrade calibration quality, and determining optimal sizes is challenging, often relying on brute-force methods. This study introduces Kalman Filtering and Smoothing in Calibration (KalCal), a new framework for calibration that combines the Kalman Filter, Kalman Smoother, and the energy function: the negative logarithm of the Bayesian evidence. KalCal offers Bayesian-optimal solutions as probability densities and models calibration effects with lower computational requirements than iterative approaches. Unlike traditional methods, which require all the data for a particular solution to be in memory simultaneously, KalCal’s recursive computations only need a single pass through the data with appropriate prior information. The energy function provides the means for KalCal to determine this prior information. Theoretical contributions include additions to complex optimisation literature and the “Kalman-Woodbury Identity” that reformulates the traditional Kalman Filter. A Python implementation of the KalCal framework was benchmarked against solution intervals as implemented in the QuartiCal package. Simulations show KalCal matching solution intervals in high Signal-to-Noise Ratio (SNR) scenarios and surpassing them in low SNR conditions. Moreover, the energy function produced minima that coincide with KalCal’s Mean Square Error (MSE) on the true gain signal. This result is significant as the MSE is unavailable in real applications. Further research is needed to assess the computational feasibility and intricacies of KalCal. , Thesis (MSc) -- Faculty of Science, Physics and Electronics, 2024
- Full Text:
- Date Issued: 2024-10-11
- Authors: Welman, Brian Allister
- Date: 2024-10-11
- Subjects: Radio interferometers , Calibration , Kalman filtering , Bayesian inference , Signal processing , Radio astronomy , MeerKAT
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/467127 , vital:76818
- Description: Calibration in radio interferometry is essential for correcting measurement errors. Traditional methods employ maximum likelihood techniques and non-linear least squares solvers but face challenges due to the data volumes and increased noise sensitivity of contemporary instruments such as MeerKAT. A common approach for mitigating these issues is using “solution intervals”, which helps manage the data volume and reduces overfitting. However, inappropriate interval sizes can degrade calibration quality, and determining optimal sizes is challenging, often relying on brute-force methods. This study introduces Kalman Filtering and Smoothing in Calibration (KalCal), a new framework for calibration that combines the Kalman Filter, Kalman Smoother, and the energy function: the negative logarithm of the Bayesian evidence. KalCal offers Bayesian-optimal solutions as probability densities and models calibration effects with lower computational requirements than iterative approaches. Unlike traditional methods, which require all the data for a particular solution to be in memory simultaneously, KalCal’s recursive computations only need a single pass through the data with appropriate prior information. The energy function provides the means for KalCal to determine this prior information. Theoretical contributions include additions to complex optimisation literature and the “Kalman-Woodbury Identity” that reformulates the traditional Kalman Filter. A Python implementation of the KalCal framework was benchmarked against solution intervals as implemented in the QuartiCal package. Simulations show KalCal matching solution intervals in high Signal-to-Noise Ratio (SNR) scenarios and surpassing them in low SNR conditions. Moreover, the energy function produced minima that coincide with KalCal’s Mean Square Error (MSE) on the true gain signal. This result is significant as the MSE is unavailable in real applications. Further research is needed to assess the computational feasibility and intricacies of KalCal. , Thesis (MSc) -- Faculty of Science, Physics and Electronics, 2024
- Full Text:
- Date Issued: 2024-10-11
MeerKAT observations of three high-redshift galaxy clusters
- Authors: Manaka, Sinah Mokatako
- Date: 2023-03-29
- Subjects: MeerKAT , Galaxies Clusters , Calibration , Radio interferometers , Radio halo
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/422367 , vital:71936
- Description: Galaxy clusters are the largest, gravitationally-bound structures in the Universe, formed through the hierarchical merger of smaller structures. The most accepted view is that the merging process injects energy into the intracluster medium (ICM) and re-accelerates pre-existing particles and compresses magnetic fields, generating, eventually, synchrotron emission. Such radio emission appears as radio halos, i.e. central Mpc-size diffuse structures, mostly visible in merging or unrelaxed clusters and with a spatial correspondence with the thermal gas component of the ICM. Observations have probed radio halo properties mostly for clusters withM500 > 6×1014 M⊙ at intermediate redshifts (0.3 < z < 0.4), providing support to their connection between mergers, which provide the necessary energy to re-accelerate particles via turbulence. Probing the redshift evolution of radio halos is an important test of the turbulent re-acceleration scenario, as fewer halos are expected at high redshift, given the same mass interval. In this thesis, we present MeerKAT observations at 1.28 GHz of three high-redshift (PSZ2G254.08- 58.45, PSZ2G255.60-46.18 and PSZ2G277.76-51.74, in the 0.42 ≲ z ≲ 0.46 range) clusters, with masses M500 ≳ 6.2 × 1014 M⊙, selected for their disturbed dynamical state – inferred from existing X-ray observations. Our observations reached rms noise values between 20 and 23.5 μJy beam−1, with ∼ 4′′ angular resolution. No evidence of diffuse emission is found at ii full resolution. Low-resolution (∼ 30′′) images achieved rms noise levels of 30-50 μJy beam−1, amongst the deepest observations of high-redshift targets. One radio halo was detected in the least massive cluster PSZ2G254.08-58.45 extending over ∼ 500 kpc, with a 1.20 } 0.08 mJy integrated flux density. We placed a ∼1 mJy upper limit at 95% confidence level on the radio halo flux density for the other two targets. The radio-halo detection is consistent with the recent P1.4 GHz − M500 correlation from Cuciti et al. (2021b), while the upper limit on PSZ2G255.60-46.18 is consistent with being on the correlation. On the other hand, the upper limit on PSZ2G277.76-51.74 places the radio halo well below the correlation. Recently a 1.5 GHz survey (Giovannini et al., 2020) detected a slightly higher fraction of radio halos in clusters in the same redshift range, with power and size typically higher than what we found in our observations. Both observations are, however, not inconsistent with each other. Our results, although with limited statistics, do not disfavour the current scenario of radiohalo formation based on the turbulent re-acceleration model. , Thesis (MSc) -- Faculty of Science, Physics and Electronics, 2023
- Full Text:
- Date Issued: 2023-03-29
- Authors: Manaka, Sinah Mokatako
- Date: 2023-03-29
- Subjects: MeerKAT , Galaxies Clusters , Calibration , Radio interferometers , Radio halo
- Language: English
- Type: Academic theses , Master's theses , text
- Identifier: http://hdl.handle.net/10962/422367 , vital:71936
- Description: Galaxy clusters are the largest, gravitationally-bound structures in the Universe, formed through the hierarchical merger of smaller structures. The most accepted view is that the merging process injects energy into the intracluster medium (ICM) and re-accelerates pre-existing particles and compresses magnetic fields, generating, eventually, synchrotron emission. Such radio emission appears as radio halos, i.e. central Mpc-size diffuse structures, mostly visible in merging or unrelaxed clusters and with a spatial correspondence with the thermal gas component of the ICM. Observations have probed radio halo properties mostly for clusters withM500 > 6×1014 M⊙ at intermediate redshifts (0.3 < z < 0.4), providing support to their connection between mergers, which provide the necessary energy to re-accelerate particles via turbulence. Probing the redshift evolution of radio halos is an important test of the turbulent re-acceleration scenario, as fewer halos are expected at high redshift, given the same mass interval. In this thesis, we present MeerKAT observations at 1.28 GHz of three high-redshift (PSZ2G254.08- 58.45, PSZ2G255.60-46.18 and PSZ2G277.76-51.74, in the 0.42 ≲ z ≲ 0.46 range) clusters, with masses M500 ≳ 6.2 × 1014 M⊙, selected for their disturbed dynamical state – inferred from existing X-ray observations. Our observations reached rms noise values between 20 and 23.5 μJy beam−1, with ∼ 4′′ angular resolution. No evidence of diffuse emission is found at ii full resolution. Low-resolution (∼ 30′′) images achieved rms noise levels of 30-50 μJy beam−1, amongst the deepest observations of high-redshift targets. One radio halo was detected in the least massive cluster PSZ2G254.08-58.45 extending over ∼ 500 kpc, with a 1.20 } 0.08 mJy integrated flux density. We placed a ∼1 mJy upper limit at 95% confidence level on the radio halo flux density for the other two targets. The radio-halo detection is consistent with the recent P1.4 GHz − M500 correlation from Cuciti et al. (2021b), while the upper limit on PSZ2G255.60-46.18 is consistent with being on the correlation. On the other hand, the upper limit on PSZ2G277.76-51.74 places the radio halo well below the correlation. Recently a 1.5 GHz survey (Giovannini et al., 2020) detected a slightly higher fraction of radio halos in clusters in the same redshift range, with power and size typically higher than what we found in our observations. Both observations are, however, not inconsistent with each other. Our results, although with limited statistics, do not disfavour the current scenario of radiohalo formation based on the turbulent re-acceleration model. , Thesis (MSc) -- Faculty of Science, Physics and Electronics, 2023
- Full Text:
- Date Issued: 2023-03-29
Finite precision arithmetic in Polyphase Filterbank implementations
- Authors: Myburgh, Talon
- Date: 2020
- Subjects: Radio interferometers , Interferometry , Radio telescopes , Gate array circuits , Floating-point arithmetic , Python (Computer program language) , Polyphase Filterbank , Finite precision arithmetic , MeerKAT
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/146187 , vital:38503
- Description: The MeerKAT is the most sensitive radio telescope in its class, and it is important that systematic effects do not limit the dynamic range of the instrument, preventing this sensitivity from being harnessed for deep integrations. During commissioning, spurious artefacts were noted in the MeerKAT passband and the root cause was attributed to systematic errors in the digital signal path. Finite precision arithmetic used by the Polyphase Filterbank (PFB) was one of the main factors contributing to the spurious responses, together with bugs in the firmware. This thesis describes a software PFB simulator that was built to mimic the MeerKAT PFB and allow investigation into the origin and mitigation of the effects seen on the telescope. This simulator was used to investigate the effects in signal integrity of various rounding techniques, overflow strategies and dual polarisation processing in the PFB. Using the simulator to investigate a number of different signal levels, bit-width and algorithmic scenarios, it gave insight into how the periodic dips occurring in the MeerKAT passband were the result of the implementation using an inappropriate rounding strategy. It further indicated how to select the best strategy for preventing overflow while maintaining high quantization effciency in the FFT. This practice of simulating the design behaviour in the PFB independently of the tools used to design the DSP firmware, is a step towards an end-to-end simulation of the MeerKAT system (or any radio telescope using nite precision digital signal processing systems). This would be useful for design, diagnostics, signal analysis and prototyping of the overall instrument.
- Full Text:
- Date Issued: 2020
- Authors: Myburgh, Talon
- Date: 2020
- Subjects: Radio interferometers , Interferometry , Radio telescopes , Gate array circuits , Floating-point arithmetic , Python (Computer program language) , Polyphase Filterbank , Finite precision arithmetic , MeerKAT
- Language: English
- Type: text , Thesis , Masters , MSc
- Identifier: http://hdl.handle.net/10962/146187 , vital:38503
- Description: The MeerKAT is the most sensitive radio telescope in its class, and it is important that systematic effects do not limit the dynamic range of the instrument, preventing this sensitivity from being harnessed for deep integrations. During commissioning, spurious artefacts were noted in the MeerKAT passband and the root cause was attributed to systematic errors in the digital signal path. Finite precision arithmetic used by the Polyphase Filterbank (PFB) was one of the main factors contributing to the spurious responses, together with bugs in the firmware. This thesis describes a software PFB simulator that was built to mimic the MeerKAT PFB and allow investigation into the origin and mitigation of the effects seen on the telescope. This simulator was used to investigate the effects in signal integrity of various rounding techniques, overflow strategies and dual polarisation processing in the PFB. Using the simulator to investigate a number of different signal levels, bit-width and algorithmic scenarios, it gave insight into how the periodic dips occurring in the MeerKAT passband were the result of the implementation using an inappropriate rounding strategy. It further indicated how to select the best strategy for preventing overflow while maintaining high quantization effciency in the FFT. This practice of simulating the design behaviour in the PFB independently of the tools used to design the DSP firmware, is a step towards an end-to-end simulation of the MeerKAT system (or any radio telescope using nite precision digital signal processing systems). This would be useful for design, diagnostics, signal analysis and prototyping of the overall instrument.
- Full Text:
- Date Issued: 2020
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