20 research outputs found
The best fitting multi-Bernoulli filter
Recent derivations have shown that the full Bayes random finite set filter incorporates a linear combination of multi- Bernoulli distributions. The full filter is intractable as the number of terms in the linear combination grows exponentially with the number of targets; this is the problem of data association. A highly desirable approximation would be to find the multi-Bernoulli distribution that is closest to the full distribution in some sense, such as the set Kullback-Leibler divergence. This paper proposes an approximate method for achieving this, which can be interpreted as an application of the well-known expectation-maximisation (EM) algorithm.Jason L. William
A track-before-detect labelled multi-Bernoulli particle filter with label switching
This paper presents a multitarget tracking particle filter (PF) for general
track-before-detect measurement models. The PF is presented in the random
finite set framework and uses a labelled multi-Bernoulli approximation. We also
present a label switching improvement algorithm based on Markov chain Monte
Carlo that is expected to increase filter performance if targets get in close
proximity for a sufficiently long time. The PF is tested in two challenging
numerical examples.Comment: Accepted for publication in IEEE Transactions on Aerospace and
Electronic System
Poisson multi-Bernoulli conjugate prior for multiple extended object filtering
This paper presents a Poisson multi-Bernoulli mixture (PMBM) conjugate prior
for multiple extended object filtering. A Poisson point process is used to
describe the existence of yet undetected targets, while a multi-Bernoulli
mixture describes the distribution of the targets that have been detected. The
prediction and update equations are presented for the standard transition
density and measurement likelihood. Both the prediction and the update preserve
the PMBM form of the density, and in this sense the PMBM density is a conjugate
prior. However, the unknown data associations lead to an intractably large
number of terms in the PMBM density, and approximations are necessary for
tractability. A gamma Gaussian inverse Wishart implementation is presented,
along with methods to handle the data association problem. A simulation study
shows that the extended target PMBM filter performs well in comparison to the
extended target d-GLMB and LMB filters. An experiment with Lidar data
illustrates the benefit of tracking both detected and undetected targets
A second-order PHD filter with mean and variance in target number
The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters
are popular solutions to the multi-target tracking problem due to their low
complexity and ability to estimate the number and states of targets in
cluttered environments. The PHD filter propagates the first-order moment (i.e.
mean) of the number of targets while the CPHD propagates the cardinality
distribution in the number of targets, albeit for a greater computational cost.
Introducing the Panjer point process, this paper proposes a second-order PHD
filter, propagating the second-order moment (i.e. variance) of the number of
targets alongside its mean. The resulting algorithm is more versatile in the
modelling choices than the PHD filter, and its computational cost is
significantly lower compared to the CPHD filter. The paper compares the three
filters in statistical simulations which demonstrate that the proposed filter
reacts more quickly to changes in the number of targets, i.e., target births
and target deaths, than the CPHD filter. In addition, a new statistic for
multi-object filters is introduced in order to study the correlation between
the estimated number of targets in different regions of the state space, and
propose a quantitative analysis of the spooky effect for the three filters