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# PA - C8 - DS-télécom-17 : Multi-object estimation and filtering

## Descriptif

1 Overview
Methods for estimating multiple objects from sensor data are in increasing de-
mand and are critically important for national security. For example, the in-
creasing use of space for defence and civil applications makes it imperative
to protect space-based infrastructure. Advanced surveillance capabilities are
needed to be able to identify and monitor activities in earth's orbit from a
variety of di erent sensing platforms and modalities.
There have been a number of important innovations in multitarget tracking
and multisensor fusion in recent years that have had signi cant international
impact across di erent application domains. In particular, the suite of math-
ematical tools, such as point process models, have been developed speci cally
to enable such innovations. Considering systems of multiple objects with point
models to be constructed in a simple way. This course draws together mathemat-
ical concepts from diverse domains to provide a strong grounding for developing
new algorithms for practical applications.
This course will investigate mathematical concepts in multiobject estimation
to enable prospective researchers to better understand and contribute to innova-
tions in this eld. The goal is to develop a broad mathematical perspective for
mathematical modelling for multi-object estimation and explore the literature
in spatial statistics and point processes to aid new advances in sensor fusion for
the development of future technologies for autonomous systems.
2 Course content
The topics have been selected to cover the fundamental topics required for the
development and implementation of practical algorithms for multi-sensor fusion.
The course will cover fundamental mathematical topics, in estimation theory,
information theory, and point process theory as follows.
 Bayesian lters: Kalman lter, extended Kalman lter, unscented Kalman
lter, sequential Monte Carlo (particle) ltering, Gaussian mixture lter-
ing
 Performance bounds and analysis: Fisher information, Cramer-Rao
lower bound, consistency and bias.
 Topics in combinatorics: generating functions, Bell polynomials, par-
titions.
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 Topics in functional calculus: di erentials, functional derivatives, gen-
erating functionals
 Point process statistics: the intensity function, covariance and corre-
lation, moments and cumulants
 Point process descriptions: the probability generating functional, the
Laplace functional
 Point process parameterisations: Bernoulli, Poisson, Panjer, i.i.d.
cluster process, Poisson-binomial
 Topics in multi-target tracking: modelling and derivation of point
process lters, application with Gaussian mixture and particle lters,
 Metrics: mean-squared error, Hausdor distance, OSPA metric
 Practical applications: simultaneous localisation and mapping (SLAM),
tracking multiple targets and camera calibration, distributed multi-sensor
multi-target tracking.
 Topics in information: Shannon entropy, Kullback-Leibler divergence,
Renyi entropy, mutual information, channel capacity.
3 Method of delivery
The course will comprise of 15h lectures lectures and 15h tutorial and practical
work. The assessment will be 30% coursework and 70% exam.
4 Industrial engagement
Competency in this domain is in high demand for defence and national security
organisations. A workshop showcasing work in industry is planned and opportu-
nities for collaboration on project with industrial and governmental partners will
be communicated to students. Provisional commitments for opportunities have
been provided by CNES, NATO CMRE, Naval Group, SAFRAN, Fraunhofer
FKIE, Thales, Dstl and AFRL.
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