Introduction to Sensor Data Fusion - Australian Centre for Field

271 Pages·2002·2.38 MB·English

Introduction to Sensor Data Fusion
http://www.acfr.usyd.edu.au/teaching/graduate/Fusion/index.html
Hugh Durrant-Whyte
Australian Centre for Field Robotics
The University of Sydney
[email protected]
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 1
Introduction
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Data fusion is the process of combing information from a number of different sources to provide a
robust and complete description of an environment or process of interest
•
This course provides an introduction to data fusion methods. The focus is on mathematical
methods in probabilistic and estimation-theoretic data fusion.
•
The course is a cut-down version of a full three day course. The full course includes
computer-based laboratories which provide the opportunity to implement and evaluate
multi-sensor tracking, estimation and identification algorithms
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Course Content
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Reference Material
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 2
Course Content
1. Probabilistic Data Fusion
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Probabilistic Methods
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Information Measures
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Alternatives to Probability
2. Multi-Sensor Estimation
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The Kalman Filter
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The Multi-Sensor Kalman Filter and Track-to-Track Fusion
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Non-linear Data Fusion Methods
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Multi-Sensor Multi-Target Data Association
3. Distributed and Decentralised Data Fusion Systems
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Data Fusion Architectures
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Decentralised Estimation
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 3
Laboratory Sessions (not done here)
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Laboratory 1: Probabilistic and Information Data Fusion Methods
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Laboratory 2: Multi-sensor multi-target tracking
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Laboratory 3: Decentralised Data Fusion
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Code freely available at: http://www.acfr.usyd.edu.au/teaching/graduate/Fusion/index.html
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 4
Recommended Reference Material
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Blackman: probably the most comprehensive book on data fusion methods. covers both level 1-2
multi-target tracking and identification problems as well as level 3-4 methods in situation
assessment and sensor management. Notably, it covers a number of current military systems in
some detail and gives develops a number of specific examples of multi-sensor systems.
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Waltz and Linas: something of a classic in the field. Consists of mainly qualitative descriptions
of various data fusion systems (with an emphasis on military systems).
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BarShalom: a number of books on data fusion and tracking, including his classic book on
tracking and data association, and his two edited volumes on data fusion.
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Artech House series: a specialist publishing house in the radar, data fusion and military
systems area.
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 5
Probabilistic Data Fusion
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 6
Probabilistic Data Fusion
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Uncertainty lies at the heart of all descriptions of the sensing and data fusion process.
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Probabilistic models provide a powerful and consistent means of describing uncertainty and lead
naturally into ideas of information fusion and decision making.
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Alternative uncertainty measurement methods also described.
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A brief review of probabilistic methods
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A focus on probabilistic and information theoretic data fusion methods and architectures
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 7
Probabilistic Models
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Familiarity with essential probability theory is assumed
• ·
A probability density function (pdf ) P ( ) is defined on a random variable y,
y
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generally written as P (y) or simply P(y)
y
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The random variable may be a scalar or vector quantity, and may be either discrete or continuous
in measure.
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The pdf is a (probabilistic) model of the quantity y; observation or state.
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The pdf P(y) is considered valid if;
1. It is positive; P(y) > 0 for all y, and
2. It sums (integrates) to a total probability of 1;
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P(y)dy = 1.
y
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The joint distribution P (x,y) is defined in a similar manner.
xy
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 8
Joint Probabilistic Models
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Integrating the pdf P (x,y) over the variable x gives the marginal pdf P (y) as
xy y
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P (y) = P (x,y)dx,
y xy
x
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and similarly integrating over y gives the marginal pdf P (x).
x
• ···
The joint pdf over n variables, P(x , ,x ), may also be defined with analogous properties to
1 n
the joint pdf of two variables.
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The conditional pdf P(x y) is defined by
P(x,y)
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|
P(x y) =
P(y)
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Has the usual properties of a pdf with x the dependent variable given that y takes on specific fixed
values.
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The conditional pdf P(y x) is similarly defined.
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 9
The Total Probability Theorem
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Chain-rule can be used to expand a joint pdf in terms of conditional and marginal distributions:
|
P(x,y) = P(x y)P(y)
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The chain-rule can be extended to any number of variables
··· | ··· ··· |
P(x , ,x ) = P(x x ,x ) P(x x )P(x )
1 n 1 2 n n−1 n n
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Expansion may be taken in any convenient order.
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The Total Probability Theorem
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P (y) = P (y x)P (x)dx.
y x|y x
x
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The total probability in a state y can be obtained by considering the ways in which y can occur
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given that the state x takes a specific value (this is encoded in P (y x)), weighted by the
x|y
probability that each of these values of x is true (encoded in P (x)).
x
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Introduction to Sensor Data Fusion, c Hugh Durrant-Whyte 2002 Slide 10