Article
Developing a RealTime Track Display That Operators Do Not Hate
Dept. of Electr. & Comput. Eng., Univ. of Connecticut, Storrs, CT, USA
IEEE Transactions on Signal Processing (Impact Factor: 2.79). 08/2011; 59(7):3441  3447. DOI: 10.1109/TSP.2011.2135346 Source: IEEE Xplore
ABSTRACT
We formulate a method of estimating target states that minimizes the mean optimal subpattern assignment (MOSPA) metric, applied suboptimally to a multihypothesis tracker (MHT) and optimally to a particle filter. This gives the operator a display of the targets with reduced jitter and track switching.

 "We have derived both Wasserstein barycenters and MMOSPA estimators from fundamental mathematical concepts, i.e., the Fréchet mean and the Wasserstein distance, and pointed out recent algorithms, variations, applications, and further developments. In particular, we revealed that the empirical MMOSPA estimate is equivalent to the Wasserstein barycenter for point clouds, which both have been recently independently discussed in [15], [17], [18], [21], [25] and [33]. The two research areas might benefit from the discovered equivalence, e.g., algorithms and insights for solving the underlying optimization problem can be shared. "
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ABSTRACT: The two title concepts have been evolving rather rapidly, but independent of each other. The Wasserstein barycenter, on one hand, has mostly made its appearance in image processing as it can describe a measure of similarity between images. Its minimization might, for example, suggest the best match in image alignment. On the other hand, MMOSPA estimation has been applied largely to multitarget tracking. The Optimal SubPattern Assignment (OSPA) measures the distance between two sets and the Mean OSPA (MOSPA) can be minimized to give the Minimum MOPSA (MMOSPA), which improves MMSE estimation of the target locations when the labeling of the targets in the set is not important. Approximate and exact algorithms have evolved for both Wasserstein barycenters and MMOSPA estimation. Here, we draw connections between the two perspectives and elaborate how they can benefit from each other. 
 "for Gaussian mixtures. In [10] "
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ABSTRACT: In multiobject estimation, the traditional minimum mean squared error (MMSE) objective is unsuitable: a simple permutation of object identities can turn a very good estimate into what is apparently a very bad one. Fortunately, a criterion tailored to sets—minimization of the mean optimal subpattern assignment (MMOSPA)—has recently evolved. Aside from special cases, exact MMOSPA estimates have seemed difficult to compute. But in this work we present the first exact polynomialtime algorithms for calculating the MMOSPA estimate for probability densities that are represented by particles. The key insight is that the MMOSPA estimate can be found by means of enumerating the cells of a hyperplane arrangement, which is a traditional problem from computational geometry. Although the runtime complexity is still high for the general case, efficient algorithms are obtained for two special cases, i.e., (i) two targets with arbitrary state dimensions and (ii) an arbitrary number of onedimensional targets. 
 "For example, the modes of a Gaussian mixture consisting of two onedimensional Gaussians collapse when the absolute distance between their means is less than 2σ, where σ is the standard deviation of both Gaussians [10]. A further general disadvantage of the MAP estimate is that it tends to jitter because the MAP estimate ignores everything around the maximum of the posterior, which may change frequently (see [3] for a more detailed discussion). "
Conference Paper: MMOSPAbased DirectionofArrival Estimation for Planar Antenna Arrays (to appear)
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ABSTRACT: This work is concerned with directionofarrival (DOA) estimation of narrowband signals from multiple targets using a planar antenna array. We illustrate the shortcomings of Maximum Likelihood (ML), Maximum a Posteriori (MAP), and Minimum Mean Squared Error (MMSE) estimation, issues that can be attributed to the symmetry in the likelihood function that must exist when there is no information about labeling of targets. We proffer the recently introduced concept of Minimum Mean OSPA (MMOSPA) estimation that is based on the optimal subpattern assignment (OSPA) metric for sets and hence inherently incorporates symmetric likelihood functions.
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