Certified Randomised Algorithms for Multi-channel Airborne Radar

Next-generation airborne radars digitise every antenna element. As a result, the adaptive filters used to detect slow-moving ground vehicles (Space-Time Adaptive Processing, STAP) must now handle covariance matrices of dimension close to a million, recomputed every few milliseconds. Classical theory demands roughly twice that many statistically identical training samples, which real, heterogeneous terrain cannot supply. Fortunately, ground clutter is strongly low-rank, which is exactly the regime where randomised numerical linear algebra excels. 

This project develops randomised Nyström STAP algorithms whose key novelty is certification. Instead of matrix-norm error bounds (tail concentration), guarantees will be expressed in radar context terms that are intuitive to radar engineers, e.g. probability of detection at a fixed false-alarm rate, and minimum detectable velocity. These will be delivered in conjunction to randomised sketch size, training budget and latency. 

The student will also use statistical leverage scores and diversity-promoting sampling to screen contaminated training data without the circular need for a covariance inverse. Depending on progress, a further strand could investigate how re-randomising the sketch every processing interval makes the adaptive response unpredictable to a jammer. Methods will be validated on benchmark datasets such as KASSPER/DARPA against established baselines. The outcome is an assurable alternative to learned methods for ISR aircraft operating in cluttered, contested electromagnetic environments.