Extended Object Tracking: Introduction, Overview and Applications

This article provides an elaborate overview of current research in extended object tracking. We provide a clear definition of the extended object tracking problem and discuss its delimitation to other types of object tracking. Next, different aspects of extended object modelling are extensively discussed. Subsequently, we give a tutorial introduction to two basic and well used extended object tracking approaches - the random matrix approach and the Kalman filter-based approach for star-convex shapes. The next part treats the tracking of multiple extended objects and elaborates how the large number of feasible association hypotheses can be tackled using both Random Finite Set (RFS) and Non-RFS multi-object trackers. The article concludes with a summary of current applications, where four example applications involving camera, X-band radar, light detection and ranging (lidar), red-green-blue-depth (RGB-D) sensors are highlighted.Comment: 30 pages, 19 figure

Accurate detection of moving targets via random sensor arrays and Kerdock codes

The detection and parameter estimation of moving targets is one of the most important tasks in radar. Arrays of randomly distributed antennas have been popular for this purpose for about half a century. Yet, surprisingly little rigorous mathematical theory exists for random arrays that addresses fundamental question such as how many targets can be recovered, at what resolution, at which noise level, and with which algorithm. In a different line of research in radar, mathematicians and engineers have invested significant effort into the design of radar transmission waveforms which satisfy various desirable properties. In this paper we bring these two seemingly unrelated areas together. Using tools from compressive sensing we derive a theoretical framework for the recovery of targets in the azimuth-range-Doppler domain via random antennas arrays. In one manifestation of our theory we use Kerdock codes as transmission waveforms and exploit some of their peculiar properties in our analysis. Our paper provides two main contributions: (i) We derive the first rigorous mathematical theory for the detection of moving targets using random sensor arrays. (ii) The transmitted waveforms satisfy a variety of properties that are very desirable and important from a practical viewpoint. Thus our approach does not just lead to useful theoretical insights, but is also of practical importance. Various extensions of our results are derived and numerical simulations confirming our theory are presented

NLTT 41135: a field M-dwarf + brown dwarf eclipsing binary in a triple system, discovered by the MEarth observatory

We report the discovery of an eclipsing companion to NLTT 41135, a nearby M5 dwarf that was already known to have a wider, slightly more massive common proper motion companion, NLTT 41136, at 2.4 arcsec separation. Analysis of combined-light and radial velocity curves of the system indicates that NLTT 41135B is a 31-34 +/- 3 MJup brown dwarf (where the range depends on the unknown metallicity of the host star) on a circular orbit. The visual M-dwarf pair appears to be physically bound, so the system forms a hierarchical triple, with masses approximately in the ratio 8:6:1. The eclipses are grazing, preventing an unambiguous measurement of the secondary radius, but follow-up observations of the secondary eclipse (e.g. with the James Webb Space Telescope) could permit measurements of the surface brightness ratio between the two objects, and thus place constraints on models of brown dwarfs.Comment: 15 pages, 6 figures, 10 tables, emulateapj format. Accepted for publication in Ap

Spatial Compressive Sensing for MIMO Radar

We study compressive sensing in the spatial domain to achieve target localization, specifically direction of arrival (DOA), using multiple-input multiple-output (MIMO) radar. A sparse localization framework is proposed for a MIMO array in which transmit and receive elements are placed at random. This allows for a dramatic reduction in the number of elements needed, while still attaining performance comparable to that of a filled (Nyquist) array. By leveraging properties of structured random matrices, we develop a bound on the coherence of the resulting measurement matrix, and obtain conditions under which the measurement matrix satisfies the so-called isotropy property. The coherence and isotropy concepts are used to establish uniform and non-uniform recovery guarantees within the proposed spatial compressive sensing framework. In particular, we show that non-uniform recovery is guaranteed if the product of the number of transmit and receive elements, MN (which is also the number of degrees of freedom), scales with K(log(G))^2, where K is the number of targets and G is proportional to the array aperture and determines the angle resolution. In contrast with a filled virtual MIMO array where the product MN scales linearly with G, the logarithmic dependence on G in the proposed framework supports the high-resolution provided by the virtual array aperture while using a small number of MIMO radar elements. In the numerical results we show that, in the proposed framework, compressive sensing recovery algorithms are capable of better performance than classical methods, such as beamforming and MUSIC.Comment: To appear in IEEE Transactions on Signal Processin

An Unbiased Survey of 500 Nearby Stars for Debris Disks: A JCMT Legacy Program

We present the scientific motivation and observing plan for an upcoming detection survey for debris disks using the James Clerk Maxwell Telescope. The SCUBA-2 Unbiased Nearby Stars (SUNS) Survey will observe 500 nearby main sequence and sub-giant stars (100 of each of the A, F, G, K and M spectral classes) to the 850 micron extragalactic confusion limit to search for evidence of submillimeter excess, an indication of circumstellar material. The survey distance boundaries are 8.6, 16.5, 22, 25 and 45 pc for M, K, G, F and A stars, respectively, and all targets lie between the declinations of -40 deg to 80 deg. In this survey, no star will be rejected based on its inherent properties: binarity, presence of planetary companions, spectral type or age. This will be the first unbiased survey for debris disks since IRAS. We expect to detect ~125 debris disks, including ~50 cold disks not detectable in current shorter wavelength surveys. A substantial amount of complementary data will be required to constrain the temperatures and masses of discovered disks. High resolution studies will likely be required to resolve many of the disks. Therefore, these systems will be the focus of future observational studies using a variety of observatories to characterize their physical properties. For non-detected systems, this survey will set constraints (upper limits) on the amount of circumstellar dust, of typically 200 times the Kuiper Belt mass, but as low as 10 times the Kuiper Belt mass for the nearest stars in the sample (approximately 2 pc).Comment: 11 pages, 7 figures (3 color), accepted by the Publications of the Astronomical Society of the Pacifi