39,342 research outputs found
Trajectory probability hypothesis density filter
This paper presents the probability hypothesis density (PHD) filter for sets of trajectories: the trajectory probability density (TPHD) filter. The TPHD filter is capable of estimating trajectories in a principled way without requiring to evaluate all measurement-to-target association hypotheses. The TPHD filter is based on recursively obtaining the best Poisson approximation to the multitrajectory filtering density in the sense of minimising the Kullback-Leibler divergence. We also propose a Gaussian mixture implementation of the TPHD recursion. Finally, we include simulation results to show the performance of the proposed algorithm
Implementation of the Gamma Gaussian Inverse Wishart Trajectory Probability Hypothesis Density Filter
This report contains equations used in the Gamma Gaussian Inverse Wishart Trajectory Probability Hypothesis Density (GGIWTPHD) filter
The Trajectory PHD Filter for Coexisting Point and Extended Target Tracking
This paper develops a general trajectory probability hypothesis density
(TPHD) filter, which uses a general density for target-generated measurements
and is able to estimate trajectories of coexisting point and extended targets.
First, we provide a derivation of this general TPHD filter based on finding the
best Poisson posterior approximation by minimizing the Kullback-Leibler
divergence, without using probability generating functionals. Second, we adopt
an efficient implementation of this filter, where Gaussian densities correspond
to point targets and Gamma Gaussian Inverse Wishart densities for extended
targets. The L-scan approximation is also proposed as a simplified version to
mitigate the huge computational cost. Simulation and experimental results show
that the proposed filter is able to classify targets correctly and obtain
accurate trajectory estimation
Trajectory PHD and CPHD Filters
This paper presents the probability hypothesis density filter (PHD) and the cardinality PHD (CPHD) filter for sets of trajectories, which are referred to as the trajectory PHD (TPHD) and trajectory CPHD (TCPHD) filters. Contrary to the PHD/CPHD filters, the TPHD/TCPHD filters are able to produce trajectory estimates from first principles. The TPHD filter is derived by recursively obtaining the best Poisson multitrajectory density approximation to the posterior density over the alive trajectories by minimising the Kullback-Leibler divergence. The TCPHD is derived in the same way but propagating an independent identically distributed (IID) cluster multitrajectory density approximation. We also propose the Gaussian mixture implementations of the TPHD and TCPHD recursions, the Gaussian mixture TPHD (GMTPHD) and the Gaussian mixture TCPHD (GMTCPHD), and the L-scan computationally efficient implementations, which only update the density of the trajectory states of the last L time steps
Poisson multi-Bernoulli mixture trackers: continuity through random finite sets of trajectories
The Poisson multi-Bernoulli mixture (PMBM) is an unlabelled multi-target
distribution for which the prediction and update are closed. It has a Poisson
birth process, and new Bernoulli components are generated on each new
measurement as a part of the Bayesian measurement update. The PMBM filter is
similar to the multiple hypothesis tracker (MHT), but seemingly does not
provide explicit continuity between time steps. This paper considers a recently
developed formulation of the multi-target tracking problem as a random finite
set (RFS) of trajectories, and derives two trajectory RFS filters, called PMBM
trackers. The PMBM trackers efficiently estimate the set of trajectories, and
share hypothesis structure with the PMBM filter. By showing that the prediction
and update in the PMBM filter can be viewed as an efficient method for
calculating the time marginals of the RFS of trajectories, continuity in the
same sense as MHT is established for the PMBM filter
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