16-02-2013, 09:47 AM
Modular General-Purpose Data Filtering for Tracking
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ABSTRACT
In nearly all modern tracking systems, signal processing is an important part with state
estimation as the fundamental component. To evaluate and to reassess different tracking
systems in an affordable way, simulations that are in accordance with reality are largely
used. Simulation software that is composed of many different simulating modules, such
as high level architecture (HLA) standardized software, is capable of simulating very
realistic data and scenarios.
A modular and general-purpose state estimation functionality for filtering provides
a profound basis for simulating most modern tracking systems, which in this thesis
work is precisely what is created and implemented in an HLA-framework. Some of
the most widely used estimators, the iterated Schmidt extended Kalman filter, the scaled
unscented Kalman filter, and the particle filter, are chosen to forma toolbox of such functionality.
An indeed expandable toolbox that offers both unique and general features of
each respective filter is designed and implemented, which can be utilized in not only
tracking applications but in any application that is in need of fundamental state estimation.
In order to prepare the user to make full use of this toolbox, the filters’ methods
are described thoroughly, some of which are modified with adjustments that have been
discovered in the process.
INTRODUCTION
Where did it go? To the left ... no, to the right ... no, I’m not sure.
This question and its complex of problems is the main issue in all tracking systems.
Common to all tracking systems is that there is always some kind of information available
about the target which is used by the tracking system in the quest of finding the
target. In old days, Native American hunters—who where very good at tracking—used
the nature and the surrounding wildlife to track down buffaloes. Nowadays tracking
systems are used in a broad variety of applications, some of the typical ones are navigation,
surveillance, and security related applications. These tracking systems have the
same principal procedure as the hunters mentioned, which is to gather and construe
information to extract wanted target position. With the help of advanced sensors and
advanced signal processing, very accurate position estimates can be obtained. In this
report, the focus will be mostly on the signal-processing part.
Presently, there are several available and well known methods for multi-sensor estimation
and they come with different properties. Some of them are better than others,
all depending on the information available and the application to be used in. In some
applications, methods with a high computational cost is accepted to obtain accurate
estimates, whereas in other applications, mostly real-time applications, accuracy is expended
in favor for rapid computations. In some cases a combination of methods is
preferable. To be able to decide which method or what combination that is to be preferred,
some sort of toolbox is desirable. To fulfill this desire, the toolbox should contain
several different methods for estimation and should be designed to offer significant
comparability and flexibility.
Prerequisites
To be able to understand the topics discussed in this report some elementary knowledge
of mathematical statistics, signal processing, and programming is required.
The reader should be familiar with the state-spacemodel representation and discretetime
systems. Although Chapters 2, 3, and 4 give a thorough and profound description
of the theory of the methods that are used, it is appropriate to have some fundamental
state estimation knowledge. It is required to be familiar with stochastic processes and
have a solid knowledge of probability theory. Since a major part of this thesis work is
implementation where some advanced C++ coding is involved, the reader should have
at least moderate knowledge of the C++ language.
Mathematical Models
To simplify and to prepare the reader for what is to come, a collection of mathematical
models, named state-space models, is presented in this section. The following model
representations are different alternatives of representing the real world, mathematically.
To cover a broad range of models, a comprehensive model is presented which is then
decomposed into representations of lower complexity. These models are frequently
used in this report and often referred to.
Filter Methods
As mentioned earlier, there are several different filter1 methods available for estimation.
This report will regard the two most widely used filter algorithms and some of their
extensions: the Kalman filter and the particle filter. A brief introduction is presented
in this section and a thorough discussion can be found in Chapters 2 and 4. Also, the
unscented Kalman filter (UKF), which is an extension of the Kalman filter that slightly
resembles the main idea behind the particle filter, is derived and carefully described in
Chapter 3.
The Kalman filter (KF) has been around for almost six decades and is one of the
most important discoveries in the history of data estimation theory. See Figure 1.1 for
an example of KF estimation in progress. Because of its simplicity and low computer execution
costs, it has been used excessively for quite some time in all kinds of estimation
problems. In a linear and Gaussian domain of mathematical state-space models, the KF
is an optimal linear filter, in terms of minimizing the mean square error (MSE). Thus,
whenever deployed outside this domain, sub-optimal results are acquired. The major
drawback of the KF is the lack of treatment for non-linear mathematical models. This
shortcoming has lead to the development of various extensions, with the aim for better
handling of non-linearities. The estimation properties of these extensions are obviously
approximative and sub-optimal which yield poor results whenever elements of major
non-linearity are involved.
HLA and MOSART
HLA
The high level architecture (HLA) is a general-purpose architecture for simulation reuse
and interoperability; see [5]. It is a standard by which different simulation frameworks
can interact. This standard is very flexible and makes it easy for separate simulation
frameworks to execute large-scale joint simulations. The HLA-based framework requirements
are bound to a set of rules which are specified in the HLA standard. Thus,
the structure of the frameworks can vary substantially under the stipulation that the
set of these rules is obeyed. It was the United States Department of Defense that enforced
the development of HLA and in September 2000 it was approved by the Institute
of Electrical and Electronic Engineers (IEEE) as an open standard, the IEEE Standard
1516.
MOSART
The modeling and simulation for analysis and research testbed (MOSART) is an HLAbased
framework which has been developed as a testbed of mostly security related purposes
for both virtual- and reality-based simulations; see Figure 1.3. MOSART was developed
by the Swedish Defence Research Agency, FOI, during the “MOSART systeminteraction”
project and is currently a well established framework at FOI; see [6]. Development
of MOSART is evidently advancing and a conspicuous need for functionality
described in Section 1.1 has emerged. The contributions from this thesis work aims to
fulfill this need or at least provide a solid foundation for further development in this
area.
Design and Implementation
The main goal is to implement and integrate the modular toolbox described in Section
1.1 intoMOSART so that an HLA-federate, can utilize the provided functionality.
The major implementation parts are related to signal processing and involve programming
in C++. Although the C++ language is an uneasy choice of programming
language when it comes to signal-processing algorithms, Matlab is usually the language
of choice, there are some important design and computational advantages with C++ in
comparison with Matlab. More about this in Section 5.2 on page 44.
Contributions
The contributions from this thesis work are summarized here.
• Amodified IEKF algorithmis presented, which uses an intermediate linearization
process to evaluate the innovation. It is presented in Algorithm 2.6 on page 21.
• A modified scaled UT, which is derived and presented in Section 3.2 on page 29.
One of the weights that is used by the scaled UT is modified.
• A hybrid shell called LALGEBRA that uses BOOST UBLAS as the underlying library.
It has powerful and user-friendly matrix handling features and is presented
in Section 5.3 on page 46.
• A design and an implementation of a toolbox in C++ that is modular, portable,
and user-friendly for general-purpose data filtering. It is named FILTERING and
the main components are the iterated Schmidt extended Kalman filter IEKF, the
scaled unscented Kalman filter SUKF, and the (sampling importance resampling)
particle filter SIRPF. FILTERING is presented in Section 5.4 on page 47.
THE KALMAN FILTER
In this chapter, the Kalman filter and some of its extensions will be presented and derived.
As pointed out before, it is one of the most important discoveries in the history
of data estimation theory. In his twelve pages long paper, see [7], R. E. Kalman presented
his discovery which, after some skepticism, soon became the basis for research
in electrical engineering at numerous universities and research centers. The KF opened
new doors in estimation theory and moreover showed the significance and potential of
the pioneering state-space model representations.
Kalman‘s discovery was indeed motivated by the work of N. Wiener and in particular
by the well-known Wiener filter (WF), which has a convincing resemblance apart
from some requirements, such as the stationarity requirements. The central notion
which lead to the discovery of the KF was Kalman‘s idea of incorporating the statespace
representation into theWF. According to [3], this thought struck his mind in late
November of 1958 on his return trip from a visit to Princeton.
It is worth noting that coinciding with Kalman‘s discovery, the essential abstractions
in the KF had been published by P. Swerling in 1959 and by R. L. Stratonovich in 1960.
Though, it was Kalman who received most of the acknowledgments for the discovery
of the filter, not least the name of the filter.
The Original Kalman Filter
There are several ways of deriving the original KF. However, the most common way
is the algebraic approach using orthogonal projections—this approach was used by
Kalman as well. There is an extensive amount of literature available on the KF, some of
the more deeper discussions can be found in [2] and [3].