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Recent years have seen a steady convergence of Radar and Communications band Radio Frequency (RF) transceiver systems. Not only have Communications systems colonised large swathes of previously allocated Radar bands but there is also a convergence of technologies driven by the relatively low cost of software‐defined transceivers and solid‐sate RF sources. Thus, where conventional radar transmissions are characterised by short narrowband pulses with high peak power, new classes of 'pulse‐compression' radar are being developed to exploit this new technology. The resulting Low Probability of Intercept waveforms are designed to spread energy in both time and frequency, yielding a very low instantaneous power spectral density. Methods to detect, analyse and distinguish such sources require longer acquisition periods to collect more energy from the sources. Here, a novel solution is provided for detection and separation based on direction‐finding utilising polynomial matrix methods in conjunction with sparse array geometries. This approach provides enhanced detection, separation and direction finding while using relatively few antenna elements. [ABSTRACT FROM AUTHOR]

The k-means method is an iterative clustering algorithm which associates each observation with one of k clusters. It traditionally employs cluster centers in the same space as the observed data. By relaxing this requirement, it is possible to apply the k-means method to infinite dimensional problems, for example, multiple target tracking and smoothing problems in the presence of unknown data association. Via a Г-convergence argument, the associated optimization problem is shown to converge in the sense that both the k-means minimum and minimizers converge in the large data limit to quantities which depend upon the observed data only through its distribution. The theory is supplemented with two examples to demonstrate the range of problems now accessible by the k-means method. The first example combines a nonparametric smoothing problem with unknown data association. The second addresses tracking using sparse data from a network of passive sensors. [ABSTRACT FROM AUTHOR]