Thales UK are seeking an academic partner and a PhD student for an Industrial Mathematics Internship as part of the UDM Programme.

Description of proposed work plan

A radar, as well as detecting targets of interest, will also generally produce unwanted detections (‘clutter’), due e.g. to reflection from the ground. It is important to estimate the density of the clutter, so that the probability of outputting false radar tracks can be controlled.

For example, consider a radar which measures discrete detections in 2D (range and azimuth). As well as a background of clutter with a continuous density in this 2D space, there may also be:

- discontinuities in the density, i.e. boundaries between regions with different clutter characteristics;

- features which are essentially 1D (compared to length scales of the 2D background) e.g. roads, cliff edges, footpaths;

- features which are essentially 0D, e.g. pylons.

If these features are not identified, then there is a risk that false tracks will be more frequent than desired. Ultimately we need to be able to estimate the probability of making a clutter detection at a given point in space.

The aim of this internship is to perform a more rigorous analysis of the problem, and for each potential solution, to consider efficient strategies for computation on real systems.

The proposed work plan is as follows:

• Perform a review of similar problems in other fields.
• Consider the simplified domain of mapping 1D measurements – essentially adaptive histogramming.
• Extend the analysis to 2D measurements. Based on examples of real data, create a representative synthetic dataset where the underlying clutter density is known. Define a method to assess the performance of candidate solutions.
• Consider how best to include a priori knowledge such as land-use or terrain maps.
• Extend the analysis to the case where the density can change slowly over time.

Ideally the output should be a recommended algorithm to perform clutter mapping, that:

i) Is implementable in real time (e.g. recursive).

ii) Gives answers where the effect of any mapping grid that might be used in the calculation is negligible.

The key skills required

• Making connections to the existing literature - can results elsewhere be applied?

• Imagination for the sort of topological structures that may be present. Mathematical skills, but also approximation, picking out the important things to give a practical algorithm.

• Basic programming - scientific programming, but not software engineering.

• Skills in analysing performance, not just the accuracy of the output but also a rough idea of the likely speed of execution.

Which parts of the company will the Intern become familiar with?

The Thales Aerospace business is organised into a number of business units, which look after our electronic warfare, information systems and other product areas. The internship will take place within the Research, Engineering and Technology directorate which provides scientific and technical support to all the products. As well as becoming familiar with the working of a scientific department in a large aerospace company, the intern will become aware of the principles of the company's range of products, to which the results of the research will in the end be applied.

Duration of the project:
6 months

Company location
Crawley, West Sussex

Security clearance
Please note that an intern will be required to undertake a basic security clearance at the beginning of this project

For more details and to apply for this internship, please email Vera Hazelwood at the Industrial Mathematics KTN.

[Find other open Internships Expressions of Interest]