handbook of multisensor data fusion phần 5 pot

©2001 CRC Press LLC
measurements are linear and hopefully the measurement errors are Gaussian. In combining all this
information into one tracker, the approximations and the use of disparate coordinate systems become
more problematic and dubious. In contrast, the use of likelihood functions to incorporate all this
information (and any other information that can be put into the form of a likelihood function) is quite
straightforward, no matter how disparate the sensors or their measurement spaces. Section 10.2.4.1
provides a simple example of this process involving a line of bearing measurement and a detection.
10.2.4.1 Line of Bearing Plus Detection Likelihood Functions
Suppose that there is a sensor located in the plane at (70,0) and that it has produced a detection. For
this sensor the probability of detection is a function, P
d
(r), of the range r from the sensor. Take the case
of an underwater sensor such as an array of acoustic hydrophones and a situation where the propagation
conditions produce convergence zones of high detection performance that alternate with ranges of poor
detection performance. The observation (measurement) in this case is Y = 1 for detection and 0 for no
detection. The likelihood function for detection is L
d
(1|x) = P
d
(r(x)), where r(x) is the range from the
state x to the sensor. Figure 10.1 shows the likelihood function for this observation.
Suppose that, in addition to the detection, there is a bearing measurement of 135 degrees (measured
counter-clockwise from the x
1
axis) with a Gaussian measurement error having mean 0 and standard
deviation 15 degrees. Figure 10.2 shows the likelihood function for this observation. Notice that, although
the measurement error is Gaussian in bearing, it does not produce a Gaussian likelihood function on
the target state space. Furthermore, this likelihood function would integrate to infinity over the whole
state space. The information from these two likelihood functions is combined by point-wise multiplica-
tion. Figure 10.3 shows the likelihood function that results from this combination.
10.2.4.2 Combining Information Using Likelihood Functions

Although the example of combining likelihood functions presented in Section 10.2.4.1 is simple, it
illustrates the power of using likelihood functions to represent and combine information. A likelihood
function converts the information in a measurement to a function on the target state space. Since all
information is represented on the same state space, it can easily and correctly be combined, regardless
of how disparate the sources of the information. The only limitation is the ability to compute the
likelihood function corresponding to the measurement or the information to be incorporated. As an
example, subjective information can often be put into the form of a likelihood function and incorporated
into a tracker if desired.
FIGURE 10.1 Detection likelihood function for a sensor at (70,0).
20
40
60
x
1
20
40
60
x
2
0

©2001 CRC Press LLC

11

Data Association Using
Multiple Frame

Assignments

11.1 Introduction

11.2 Problem Background

11.3 Assignment Formulation of Some General Data
Association Problems

11.4 Multiple Frame Track Initiation and Track
Maintenance

Track Initiation • Track Maintenance Using a Sliding Window

11.5 Algorithms

Preprocessing • The Lagrangian Relaxation Algorithm for the
Assignment Problem • Algorithm Complexity • Improvement
Methods

11.6 Future Directions

Other Data Association Problems and Formulations • Frames
of Data • Sliding Windows • Algorithms • Network-
Centric Multiple Frame Assignments

Acknowledgments

References

11.1 Introduction

The ever-increasing demand in surveillance is to produce highly accurate target identification and esti-
mation in real time, even for dense target scenarios and in regions of high track contention. Past
surveillance sensor systems have relied on individual sensors to solve this problem; however, current and
future needs far exceed single sensor capabilities. The use of multiple sensors, through more varied
information, has the potential to greatly improve state estimation and track identification. Fusion of
information from multiple sensors is part of a much broader subject called data or information fusion,
which for surveillance applications is defined as “a multilevel, multifaceted process dealing with the
detection, association, correlation, estimation, and combination of data and information from multiple
sources to achieve refined state and identity estimation, and complete and timely assessments of situation
and threat”.

1

(A comprehensive discussion can be found in Waltz and Llinas.)

2

Level 1 deals with single
and multisource information involving tracking, correlation, alignment, and association by sampling the
external environment with multiple sensors and exploiting other available sources. Numerical processes
thus dominate Level 1. Symbolic reasoning involving various techniques from artificial intelligence
permeates Levels 2 and 3.

Aubrey B. Poore

Colorado State University

Suihua Lu

Colorado State University

Brian J. Suchomel

Numerica, Inc.

©2001 CRC Press LLC

12

General Decentralized
Data Fusion
with Covariance

Intersection (CI)

12.1 Introduction

12.2 Decentralized Data Fusion

12.3 Covariance Intersection

Problem Statement • The Covariance Intersection Algorithm

12.4 Using Covariance Intersection for Distributed Data
Fusion

12.5 Extended Example

12.6 Incorporating Known Independent Information

Example Revisited

12.7 Conclusions

Acknowledgments

Appendix 12.A The Consistency of CI

Appendix 12.B MATLAB Source Code

Conventional CI • Split CI

References

12.1 Introduction

One of the most important areas of research in the field of control and estimation is decentralized (or
distributed) data fusion. The motivation for decentralization is that it can provide a degree of scalability
and robustness that cannot be achieved with traditional centralized architectures. In industrial applica-
tions, decentralization offers the possibility of producing plug-and-play systems in which sensors can be
slotted in and out to optimize a tradeoff between price and performance. This has significant implications
for military systems as well because it can dramatically reduce the time required to incorporate new
computational and sensing components into fighter aircraft, ships, and other types of platforms.
The benefits of decentralization are not limited to sensor fusion onboard a single platform; decentral-
ization also can allow a network of platforms to exchange information and coordinate activities in a
flexible and scalable fashion that would be impractical or impossible to achieve with a single, monolithic
platform. Interplatform information propagation and fusion form the crux of the network centric warfare
(NCW) vision for the U.S. military. The goal of NCW is to equip all battlespace entities — aircraft, ships,
and even individual human combatants — with communication and computing capabilities to allow
each to represent a node in a vast decentralized command and control network. The idea is that each

Simon Julier

IDAK Industries

Jeffrey K. Uhlmann

University of Missouri