Developing a Real-Time 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: 3.2). 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 multi-hypothesis tracker (MHT) and optimally to a particle filter. This gives the operator a display of the targets with reduced jitter and track switching.

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    ABSTRACT: Displaying tracks is an essential part of a multi- target tracking system. Recently, it was proposed to extract tracks with respect to the Optimal Sub-Pattern Assignment (OSPA) metric, i.e., the traditionally used squared error loss is replaced with an OSPA loss, which leads to the so-called Minimum Mean OSPA (MMOSPA) estimate. So far, work concentrated on traditional trackers that maintain probability densities for the targets. In this paper, we aim at extracting the MMOSPA estimate from a Probability Hypothesis Density (PHD) as used within the PHD filter. We elaborate that the PHD in general does not contain enough information to determine the exact MMOSPA estimate. However, we then show that if the loss function has a specific form, it is indeed possible to extract point estimates from a PHD that are optimal w.r.t. the underlying unknown random finite set. We discuss two specific loss functions that fulfill this condition and are potentially close to the OSPA loss, a nearest neighbor loss and a kernel distance loss. It turns out that track extraction based on the nearest neighbor loss can be performed with the well-known k-means algorithm. Simulations show when the estimates based on the nearest neighbor and the kernel loss are close to the MMOSPA estimate.
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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 multi-target tracking. The Optimal Sub-Pattern 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.
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    ABSTRACT: In multi-object 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 sub-pattern 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 polynomial-time 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 one-dimensional targets.
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