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

The prediction of the performance limits of radar systems is of great practical importance since it allows the specifications to be set close to those limits and, by identifying the factors which currently limit performance, it determines the direction which should be taken by future developments to improve that performance.

The work of Woodward, epitomised in references [1] and [2] laid the foundations for the information-theoretic based analysis of the performance, but his work was limited to a few particular cases. The aim of this internship is to extend that work to allow the same rigour to be applied to a wider range of practical radar problems. The programme of work needed to perform this is as follows:

a) Extend Woodward's work to pulse-Doppler radars and to scanning radars - this needs to be carried out rigorously to provide a firm foundation for the other activities.

b) Rigorously examine the question of how much extra information detection and the measurement of radar cross section add to the location information discussed by Woodward.

c) Examine how much information loss is inherent in the way radar codes position as a pulse delay, and consider whether any ways exist to improve on this.

d) Find ways of making better use of the information in the range resolution (which is frequently unused in current systems).

e) Examine whether the radar is in fact obtaining other information, which may be of no use to the observer, but which may still be considered to convey potential information.

f) Examine the relationship between these other types of potential information and the information needed to classify targets. This seems to be intrinsically connected with the way the returns differ from those from ideal point targets, but this needs to be examined rigorously.

g) Examine the relationship between the information obtained by the radar about its targets (carried in the convolution of the transmitted waveform with the response of the target to an ideal pulse train) and the information which the transmitted waveform itself can convey to a receiver which tries to intercept those transmissions (an Electronic Support Measures system).

It is expected that this activity would be better suited to a six-month internship than to a shorter period, although it is likely that even so only some aspects are likely to be able to be addressed. The areas to be addressed will be selected as the work progresses, to concentrate on those which seem most likely to provide novel results which will provide useful improvements in the design and analysis of practical systems.

The expected outcomes are a more rigorous understanding of whether information theory shows ways in which radar detection performance can be improved and to provide some upper limits to target recognition capabilities.

[1]: Woodward, P. M., and Davies, I. L., A Theory of Radar Information, Phil. Mag. 41, 1001-17, October 1950

[2] Woodward, P. M., Probability and Information Theory, with Applications to Radar, London, 1953, Pergamon Press

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.

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