Shiryaev's Bayesian Quickest Change Detection (QCD) problem is to detect a change in the statistical problems of an observed process. This is an important signal processing problem with application in a diverse range of areas including:
- automatic control
- quality control
- target detection and more.
Recently a critical deficiency in Shiryaev's QCD problem has been identified to occur due to the insufficient informativeness of measurement in low signal-to-noise (SNR) to overcome geometric prior assumption on the change event.
Essentially, these deficiencies arise due to the non-ergodic nature of the model underlying Shiryaev’s problem with results in the measurement being ignored.
To side-step this feature of QCD, an alternative intermittent signal detection (ISD) problem has been proposed that avoids these deficiencies by considering an (ergodic) detection problem that allows repeating change events. Moreover, these ISD approaches have been shown to be extremely effective detecting low SNR change events (in vision based detection problems).
The issues arising from non-ergodic signal problems are not limited to the Shiryaev's Bayesian QCD problem and have already been shown to occur in detection and isolation problem and strongly suspected to occur in applications with the left-to-right models such as (historically) those used in natural language processing and in industry equipment condition monitoring.
This PhD project will identify, characterise and then create new solutions to a number of signal processing problems where the non-ergodic signal model is currently used.
This PhD project will identify, characterise and then create new solutions to a number of signal processing problems where non-ergodic signal model are currently used.
This includes looking at:
- The mathematics of statistical processing such as Markov chain
- Probability and mathematical expectation operations
- Dynamic programming/recursion equations.
Some algorithm development and data analysis will take place during this project. Likely MATLAB will be enough for what we are looking to achieve.
An example of the types of mathematics that will be used in this project: On the Informativeness of Measurements in Shiryaev’s Bayesian.
An example of the type of applications that will be used in this project: Quickest detection of intermittent signals with application to vision-based aircraft detection.
We expect the research project to produce:
- new algorithms to better solve a range of change-detection problems
- new mathematics that characterise the deficiencies of a range of detection problems and the properties of newly proposed approaches.
Skills and experience
For this student topic we expect you to have the following skills:
- mathematics or the willingness to learn
- MATLAB programming
- data analysis.
You may be able to apply for a research scholarship in our annual scholarship round.
Contact the supervisor for more information.