Kalman Filtering and Information Fusion

295 Pages·2020·8.459 MB·English

by  Hongbin Ma, Liping Yan, Yuanqing Xia, Mengyin Fu

Hongbin Ma · Liping Yan ·
Yuanqing Xia · Mengyin Fu
Kalman Filtering
and Information
Fusion
Kalman Filtering and Information Fusion
Hongbin Ma Liping Yan Yuanqing Xia
(cid:129) (cid:129) (cid:129)
Mengyin Fu
Kalman Filtering
and Information Fusion
123
Hongbin Ma LipingYan
Schoolof Automation Schoolof Automation
Beijing Institute of Technology Beijing Institute of Technology
Beijing,China Beijing,China
Yuanqing Xia MengyinFu
Schoolof Automation Schoolof Automation
Beijing Institute of Technology Beijing Institute of Technology
Beijing,China Beijing,China
ISBN978-981-15-0805-9 ISBN978-981-15-0806-6 (eBook)
https://doi.org/10.1007/978-981-15-0806-6
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The ultimate value of life
And the awakening of the ability to think,
Rather than just to survive
—Aristotle
This book is dedicated to our families,
for their endless love and support.
This book is also dedicated to our teachers,
who taught us love and wisdom.
Preface
This book will address one key technology, named as Kalman filtering, for digital
informationprocessing,whichwaseverregardedasoneofthegreatestdiscoveries
inthetwentiethcentury.Kalmanfiltering,alsoknownaslinear-quadraticestimation
(LQE),isoneofthemostsuccessfulandwidelyusedestimationmethods.Standard
Kalmanfiltercanbederivedfromleastsquaresalgorithm,whichbridgestheoretical
science and practical world in a large. The application of Kalman filter is the
combination of mathematics and the physical world. It has been used as the key
element of the algorithm for many applications in aircraft/ship/ground vehicle
navigation, spacecraft attitude determination, orbit determination, missile guidance
andcontrol,RFantenna/laserterminaltargetacquisition/tracking,RF/opticalsignal
acquisition and tracking, seismic data processing, medical signal processing, and
other fields in the industry.
StandardKalmanfilterisoptimalinthesense ofminimum meansquarederrors
and maximum likelihood estimation, provided that the system model is linear and
precisely known a priori and the process and measurement noises are zero mean,
completely unrelated and jointly Gaussian with known covariance matrices.
However,inpractice,theserequirementscanseldombecompletelysatisfieddueto
the following reasons:
(a) The practical systems are usually nonlinear although many of them may be
approximated by linear systems. Absolutely linear systems in state-space sel-
dom exist in practical engineering applications.
(b) Even if the practical system in consideration is linear, the system model may
not be exactly known with accurate parameters. In practice, model parameters
may be approximately identified by applying some system identification
methodsofflinethroughthedataobtainedviaextensiveexperiments.However,
this approach is usually expensive and does not guarantee accurate system
identification,whichmakesthatstandardKalmanfiltermaynotworkverywell
for the identified model. Furthermore, if the practical system is in fact
time-varying, then the approach of system identification will usually fail.
ix
x Preface
(c) Standard Kalman filter requires that the process and measurement noises are
zero-mean random noises. However, in some applications, the noise may be
biased and its mean or mathematical expectation may be unknown. In such
cases, further noise modeling is often needed and it is possible to use Kalman
filter by augmenting the mean of the noise as an extra state.
(d) In most cases, we cannot have the covariance matrix of the unknown process
andmeasurementnoisesapriori.Therefore,toapplythestandardKalmanfilter,
we must first try to obtain the statistical properties of the process and mea-
surement noises, which are usually calculated from extensive practical exper-
iments. To deal with this problem, an alternative approach is to simply use
largercovariancematrixtorepresenttheaprioriknowledgeontheprocessand
measurement noises.
(e) In practice, the probability distribution of the process noise or measurement
noise may not be normal distribution, and this case is often termed as
non-Gaussian system, which often results that the performance of standard
Kalman filter may degrade much.
Besides the issues of various uncertainties in a single plant, which will be
addressedindetailandsomecorrespondingsolutionsbasedonadaptiveestimation
willbeintroducedinthisbook,moreissuescouldbenaturallyraisedwhenKalman
filtering technology is applied in multisensor systems and/or multi-agent systems.
Wenoticethatinmodernengineeringsystems,thereisatrendthatsystemstendto
become bigger or more complex with more components. Especially, various sen-
sors are used in systems like intelligent robots, autonomous cars, smart homes,
smart buildings, etc., which call for the techniques of multisensor information
fusion, which will be extensively discussed in this book. Furthermore, when
multiple agents (subsystems) interact with one another, coupling uncertainties
wouldalsobeonechallengingissuetohandlewith,whichisalsoaddressedinthis
book by some novel decentralized adaptive filtering techniques.
To address possible uncertainty in system model or the statistical properties
oftheprocessandobservationnoises,someexistingextensionsandgeneralizations
have been proposed to obtain good denoising and estimating effects when the
modeluncertaintyisrelativelysmallinsensethatonlysmallmodelperturbationor
unknown covariance of the noise is considered. Meanwhile, the filtering and pre-
diction problems when system models have large uncertainty or when the covari-
ance matrices of both the process and measurement noises were completely
unknown are seldom addressed. To address these problems, some novel ideas are
introduced in this book. Since the number of the systems may increase, how to
estimatethestatewithmultiplesetsofdataisanotherimportanttopicinthisbook.
In this book, a novel real-time filter, named as fast minimum norm filtering algo-
rithm,hasbeenproposedtodealwiththecasewhenthecovariancematricesofthe
processandmeasurementnoiseswereunknowninthelineartime-invariantsystems
with state-space model. A general framework of finite-model Kalman filter is
introduced. A new discretized method is introduced to discretize continuous sys-
tems under nonuniformly sampling intervals is discussed. In summary, the
Preface xi
objective of this book is to present an advanced technology used for various
applications by addressing various challenging issues such as nonlinearity, uncer-
tainties, and complexity.
This book contains four main parts. Part I provides preliminaries of Kalman
filtering including brief introduction to Kalman filtering, challenges of Kalman
filtering,andintroductiontoinformationfusion.PartIIfocusesonKalmanfiltering
for uncertain systems, where the uncertainties addressed include noise covariance,
model uncertainty, parameter uncertainty, etc. In Part III, Kalman filtering for
multisensor systems is extensively addressed, and optimal information fusion
techniques are proposed for various multisensor systems. In Part IV, Kalman fil-
teringformulti-agentsystemsisdiscussedbyaddressingseveralchallengingissues
such as coupling uncertainties and communication limits.
This book is featured with a number of attractive and original research studies,
including a general framework offinite-model adaptive Kalman filtering, wireless
sensor network localization, a recursive covariance estimation (RCE) algorithm,
decentralized adaptive filtering,optimalmultisensorinformationfusion,andsoon.
The book is primarily intended for researches and engineers in estimation and
control community. This book will bring fresh new ideas into education and will
benefit students by exposing them to the very forefront offiltering research.
The authors would also like to thank the help from our students and
collaborators.
Beijing, China Hongbin Ma
July 2017 Liping Yan
Yuanqing Xia
Mengyin Fu
Acknowledgements The authors would like to acknowledge support from National Natural
Science Foundation of China (NSFC) grants 61004059, 61473120, 61473038, and 91648117,
BeijingOutstandingTalentsProgramme(2012D009011000003).Thefundershadnoroleinstudy
design, data collection and analysis, decision to publish, or preparation of the manuscript. The
authorswouldalsoliketothankthehelpfromMeiWu,NannanLi,XiaofeiZhang,andShanLi
duringthepreparationofthisbook.
Theauthorswouldalsoliketothankthegenerousandegolesslovesfromourfamilies.Without
theircontinuoussupportandforgiveness,thisbookwouldnotappearinitscurrentform.During
thedaysworkingwithuncertaintiesandchallenges,theirencouragement,enquiries,andenduring
tousalwaysaccompaniedwithus,whichmakeourselvesnotfeellonelyinthosehardtimes.
Contents
Part I Kalman Filtering: Preliminaries
1 Introduction to Kalman Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 What Is Filtering?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Historical Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Wiener Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2 Challenges in Kalman Filtering. . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1 Standard Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2 Requirements of Standard Kalman Filtering . . . . . . . . . . . . . . . 14
2.3 Effects of System Uncertainties . . . . . . . . . . . . . . . . . . . . . . . . 15
2.4 Effects of Multiple Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.5 Effects of System Couplings . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.6 Conclusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Part II Kalman Filtering for Uncertain Systems
3 Kalman Filter with Recursive Process Noise Covariance
Estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.2 Problem Formulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.1 Standard Kalman Filter. . . . . . . . . . . . . . . . . . . . . . . . 23
3.2.2 Problem To Be Resolved . . . . . . . . . . . . . . . . . . . . . . 23
3.3 Basic Idea: Estimating Covariance Matrix . . . . . . . . . . . . . . . . 26
3.4 Kalman Filter Based on Algorithm
RecursiveCovarianceEstimation . . . . . . . . . . . . . . . . 31
3.5 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
xiii