Mean Optimal Subpattern Assignment Research Articles

Study on multiple targets tracking algorithm based on multiple sensors

For the problem that traditional data association algorithms tend to coalesce neighboring tracks for multiple close targets tracking application in dense clutter, measurements adaptive censor (MAC) method to Set JPDA (SJPDA) algorithm was introduced in this paper, then the proposed the MACSJPDA algorithm of target tracking discards several data associations with small probability and accelerates the convergence speed of the SJPDA algorithm. The algorithm can achieve better effects of multiple targets tracking by multiple sensors in wireless sensor networks. Monte Carlo simulation revealed that estimation effect of the MACSJPDA algorithm is much smoother, and it needs less run time than SJPDA algorithm for handling closely spaced and crossing targets, in the meanwhile the mean optimal sub-pattern assignment (MOSPA) deviation of the MACSJPDA algorithm is also smaller.

A Geometrical Look at MOSPA Estimation Using Transportation Theory

It was shown in [6] that the Wasserstein distance is equivalent to the Mean Optimal Sub-Pattern Assignment (MOSPA) measure for empirical probability density functions. A more recent paper [7], extends on it by drawing new connections between the MOSPA concept, which is getting a foothold in the multi-target tracking community, and the Wasserstein distance, a metric widely used in theoretical statistics. However, the comparison between the two concepts has been overlooked. In this letter we prove that the equivalence of Wasserstein distance with the MOSPA measure holds for general types of probability density function. This non trivial result allows us to leverage one recent finding in the computational geometry literature to show that the Minimum MOPSA (MMOSPA) estimates are the centroids of additive weighted Voronoi regions with a specific choice of the weights.

Reduced palm intensity for track extraction

The pair correlation function is introduced to target tracking filters that use a finite point process target model as a means to investigate interactions in the Bayes posterior target process. It is shown that the Bayes posterior target point process of the probability hypothesis density (PHD) filter—before using the Poisson point process approximation to close the recursion—is a spatially correlated process with weakly repulsive pair interactions. The reduced Palm target point process is introduced to define the conditional target point process given the state of one or more known targets. Using the intensity function of the reduced Palm process, an approximate two-stage pseudomaximum a posteriori track extractor is developed. The proposed track extractor is formulated for the PHD filter and implemented in a numerical study that involves tracking two nearby targets. Numerical results demonstrate improvement in the mean optimal subpattern assignment statistic for the proposed track extractor in comparison to the Gaussian mixture PHD filter’s state extractor.

A Batch Algorithm for Estimating Trajectories of Point Targets Using Expectation Maximization

In this paper, we propose a strategy that is based on expectation maximization for tracking multiple point targets. The algorithm is similar to probabilistic multi-hypothesis tracking (PMHT) but does not relax the point target model assumptions. According to the point target models, a target can generate at most one measurement, and a measurement is generated by at most one target. With this model assumption, we show that the proposed algorithm can be implemented as iterations of Rauch-Tung-Striebel (RTS) smoothing for state estimation, and the loopy belief propagation method for marginal data association probabilities calculation. Using example illustrations with tracks, we compare the proposed algorithm with PMHT and joint probabilistic data association (JPDA) and show that PMHT and JPDA exhibit coalescence when there are closely moving targets whereas the proposed algorithm does not. Furthermore, extensive simulations c comparing the mean optimal subpattern assignment (MOSPA) performance of the algorithm for different scenarios averaged over several Monte Carlo iterations show that the proposed algorithm performs better than JPDA and PMHT. We also compare it to benchmarking algorithm: $N$ -scan pruning based track-oriented multiple hypothesis tracking (TOMHT). The proposed algorithm shows a good tradeoff between computational complexity and the MOSPA performance.

On Wasserstein Barycenters and MMOSPA Estimation

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.

Polynomial-Time Algorithms for the Exact MMOSPA Estimate of a Multi-Object Probability Density Represented by Particles

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.

An Efficient, Variational Approximation of the Best Fitting Multi-Bernoulli Filter

The joint probabilistic data association (JPDA) filter is a popular tracking methodology for problems involving well-spaced targets, but it is rarely applied in problems with closely-spaced targets due to its complexity in these cases, and due to the well-known phenomenon of coalescence. This paper addresses these difficulties using random finite sets (RFSs) and variational inference, deriving a highly tractable, approximate method for obtaining the multi-Bernoulli distribution that minimises the set Kullback-Leibler (KL) divergence from the true posterior, working within the RFS framework to incorporate uncertainty in target existence. The derivation is interpreted as an application of expectation-maximisation (EM), where the missing data is the correspondence of Bernoulli components (i.e., tracks) under each data association hypothesis. The missing data is shown to play an identical role to the selection of an ordered distribution in the same ordered family in the set JPDA algorithm. Subsequently, a special case of the proposed method is utilised to provide an efficient approximation of the minimum mean optimal sub-pattern assignment estimator. The performance of the proposed methods is demonstrated in challenging scenarios in which up to twenty targets come into close proximity.

Set JPDA Filter for Multitarget Tracking

In this article, we show that when targets are closely spaced, traditional tracking algorithms can be adjusted to perform better under a performance measure that disregards identity. More specifically, we propose an adjusted version of the joint probabilistic data association (JPDA) filter, which we call set JPDA (SJPDA). Through examples and theory we motivate the new approach, and show its possibilities. To decrease the computational requirements, we further show that the SJPDA filter can be formulated as a continuous optimization problem which is fairly easy to handle. Optimal approximations are also discussed, and an algorithm, Kullback-Leibler SJPDA (KLSJPDA), which provides optimal Gaussian approximations in the Kullback-Leibler sense is derived. Finally, we evaluate the SJPDA filter on two scenarios with closely spaced targets, and compare the performance in terms of the mean optimal subpattern assignment (MOSPA) measure with the JPDA filter, and also with the Gaussian-mixture cardinalized probability hypothesis density (GM-CPHD) filter. The results show that the SJPDA filter performs substantially better than the JPDA filter, and almost as well as the more complex GM-CPHD filter.

Developing a Real-Time Track Display That Operators Do Not Hate

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.