These are challenges 6-10 identified by EPSRC and DSTL as part of their Signal Processing Call. The closing date is 29th October 2008.

CHALLENGE #6: To detect and identify signals within a short observation time frame and low observation duty cycles.

A problem exists to detect and classify multiple signal types, but with a very low duty cycle for the receiver. In certain circumstances, very short windows of opportunity exist where the local signal environment can be sampled and the duty cycle of observation opportunities can be as low as 10%. The signals to be detected may be continuous or intermittent (bursted) transmissions. Within these short windows, it is desirable to detect and classify multiple transmissions in terms of signal type (eg analogue or digital comms, navigation etc.) and location of transmitters. The low duty cycle of observations for the receiver makes this a challenging prospect.

CHALLENGE #7: To classify a noisy signal into known constituent parts.

A set of measurements made by a sensor placed in a noisy environment contains information from the noisy background as well as the signal to be detected. Techniques are required to try to classify the measurements into groups or classes to remove some of the background effects. Detecting the true signal in one class within the time history of the measurements depends on successful classification and minimising overlap between classes. For example, if an innocuous measurement is misclassified as hazardous (say) a small fraction of the time, but occurs in great numbers, then it may trigger a false response in the hazardous class.

This challenge could also link with work “to extract a weak signal from non-stationary, spatially and temporally correlated noise”.

CHALLENGE #8: To detect and track aerosol cloud signals from spectroscopic aerosol lidar data.

Aerosol lidar systems can detect and monitor aerosol clouds across an area of several square kilometres. Automatic cloud detection, even for relatively strong signals, is difficult to implement due to a variety of artefacts that can be present within the data.

• Objects other than aerosol clouds can generate non-stationary signals of similar spatial frequencies and extended signal envelopes.
• Signal Amplifier systems will distort observed signals as a function of signal intensity and frequency.
• Atmospheric conditions can change on a spatial and temporal basis, giving rise to localised or general change in signal bias levels.
• Changing ambient light levels can affect the spectroscopic signal to noise ratio as a unique function for each spectral band.

The challenge would be to autonomously detect and track the extent of a moving aerosol cloud in the presence of these above events whilst still maintaining integrity of the spectral aerosol information.

CHALLENGE #9: To develop a partially supervised learning algorithm to detect and classify anomalies in real time streaming spectroscopic data.

To provide the artificial dog’s brain to go with the artificial dog’s nose. Develop a learning algorithm that will accept streaming spectroscopic data (mass, mobility or optical) and detect anomalies in real time. Further, it should then attempt to classify these anomalies as safe (normal), dangerous (previously identified as dangerous) or unknown, based on previous experience. Finally, if appropriate and possible, it should then proceed to attempt to classify the danger. Where possible, the algorithm should attempt to remain biomimetic in as much as different components should attempt to mimic the different layers of olfactory processing in mammals.

CHALLENGE #10: To develop a general theory to guide the processing of signals from Synthetic Aperture Radar systems with more than two beams.

Future (and at least one current) Synthetic Aperture Radar systems have active array antennas which have panels which can be divided into sub-panels to give multiple beams. There may be significant benefit in utilising multiple beams to detect moving targets in difficult clutter (eg urban, sea etc) at high resolution. The problem is that there is no general theory to guide the best way of processing the signals from such systems for more than two beams when there are many different types and classes of scatterer. There is an elementary result relating to the greatest eigenvalue and corresponding eigenvector of the covariance matrix for the signals received by the N beams but this is only useful for a single class of target in white noise. In the real life situation where there are complicated and difficult types of clutter and targets more general results are required. One approach to this problem is via the covariance matrix for the N channels. For example, in the case of two beams the joint probability density function of the four parameters of the complex, Hermitian, covariance matrix (a Wishart distribution) can be transformed into a joint p.d.f of the two eigenvalues and two angles, one of which is the phase shift between the signals received by the two beams. This is accomplished by means of a special unitary transformation in SU(2). The resulting transformed p.d.f. then gives useful insights into how detection algorithms can be constructed for a two beam system. It is expected that a similar approach for N beams would yield similar insight. However, this is a challenging programme because the required theory needs to be based on the algebra and geometry of the special unitary group SU(N). Even attacking this problem for three beams would be a useful step forward. Much has been learned about SU(3) in the past few decades. For example, SU(3) is central to the ‘eight fold way’ developed by Gell-Mann and Ne’eman. Other applications have included SU(3) nuclear physics models based on the symmetry group of the 3D harmonic oscillator. In the case of more beams, SU(4) and SU(5) also have both been studied in relation to particle physics.