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首页slam经典书籍 STATE ESTIMATION FOR ROBOTICS
国外大学slam领域经典教材。 “In this book, we introduce the classic estimation results for linear systems corrupted by Gaussian measurement noise. We then exam- ine some of the extensions to nonlinear systems with non-Gaussian noise. In a departure from typical estimation texts, we take a detailed look at how to tailor general estimation results to robots operating in three-dimensional space, advocating a particular approach to handling rotations.”
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STATE ESTIMATION FOR
ROBOTICS
Timothy D. Barfoot
Copyright
c
2018
Cambridge University Press is the Official Publisher
This Unofficial Version Compiled on November 28, 2018
Send errata to <tim.barfoot@utoronto.ca>


Revision History
13 May 2017 Version best matching published first edition
12 Aug 2017 Equation (4.47a): Σ
x
changed to Σ
xx
12 Aug 2017 Page 111, bullet 4: Σ
y
changed to Σ
yy
12 Aug 2017 Page 117, bullet (ii): changed 4(a) to 3
12 Aug 2017 Equation (4.87):
ˆ
P
−
changed to
ˇ
P
k
12 Aug 2017 Equation (4.89):
ˆ
P
k
changed to
ˇ
P
k
12 Aug 2017 Equation (4.102d): x
op,k,0
changed to x
op,k,i
12 Aug 2017 Equation (7.102): removed negative sign
22 Nov 2017 Fixed typo in Jacobi identity (page 218)
10 Dec 2017 Equation (2.52): Σ
−1
yy
Σ
yx
changed to Σ
xy
Σ
−1
yy
10 Dec 2017 Inline above (8.2): r
vi
i
changed to r
v
k
i
i
10 Dec 2017 Equation (6.26): 0 changed to 0
T
10 Dec 2017 Inline below (4.132): e(x
op
) = Lu(x
op
) changed to
e(x
op
) = L
−1
u(x
op
)
10 Dec 2017 Angular acceleration: ω
◦
−→
21
changed to ω
◦
−→
21
10 Dec 2017 Equation (4.31): corrected a double comma
10 Dec 2017 Equation (4.92a): n
k,j
changed to
ˇ
y
k,j
5 Jan 2018 Page 227, definition of Ad(SE(3)): removed extra
comma before final bracket
5 Jan 2018 Equation (9.55): changed ζ
?
j
to ζ
?
j
5 Jan 2018 Equation (8.47): added missing V
T
in an intermediate
step
5 Jan 2018 Equation (4.207): changed ? to ∗
5 Jan 2018 Equation (4.165a): changed subscript ` to j
5 Jan 2018 Equation (4.166): changed G
k`
to G
jk
16 Feb 2018 Pages 267-8: corrected J
−1
`
and J
−1
r
to J
`
and J
r
25 Mar 2018 Page 108: corrected ‘mean of output is’ to be ‘mean
of input is’
25 Mar 2018 Equation (6.129): corrected r
ba
b
to be r
ab
b
13 Apr 2018 Equation (8.105): corrected j − 1 to j = 1
22 Apr 2018 Equation (2.20): added missing −1 in definition of η
iii

iv Revision History
12 May 2018 Equations (7.234) and (7.239): fixed two negative
signs each to repair proof
12 May 2018 Identity page: fixed summation on series definitions of
T, T , and their inverses to start at n = 0 not n = 1
27 May 2018 Started an appendix with new material since first edi-
tion
13 Jul 2018 Equation (7.150): changed T
21
= T
1
T
−1
2
to T
21
=
T
2
T
−1
1
just below this equation in the text
13 July 2018 Equation (3.99a): removed H
T
22
from front of both
terms to match (3.98)
13 July 2018 Equation (3.99b): removed H
T
32
from front of both
terms to match (3.98), make second term negative
13 Aug 2018 Equation (10.18): corrected J
u
to J
v
13 Aug 2018 Exercise 6.6.6: adjusted wording to due to poor use
of the term ‘affine’
22 Nov 2018 Equation (4.85): corrected n
0
i
to be n
0
k,i
26 Nov 2018 Exercise 2.5.6: corrected N to K in upper limit of
mean summation
28 Nov 2018 Added Appendix A.3 on the posterior covariance re-
cursion for the Cholesky and RTS smoothers.

Contents
Acronyms and Abbreviations xi
Notation xiii
Foreword xv
1 Introduction 1
1.1 A Little History 1
1.2 Sensors, Measurements, and Problem Definition 3
1.3 How This Book Is Organized 4
1.4 Relationship to Other Books 5
Part I Estimation Machinery 7
2 Primer on Probability Theory 9
2.1 Probability Density Functions 9
2.1.1 Definitions 9
2.1.2 Bayes’ Rule and Inference 10
2.1.3 Moments 11
2.1.4 Sample Mean and Covariance 12
2.1.5 Statistically Independent, Uncorrelated 12
2.1.6 Normalized Product 13
2.1.7 Shannon and Mutual Information 14
2.1.8 Cram´er-Rao Lower Bound and Fisher Information 14
2.2 Gaussian Probability Density Functions 15
2.2.1 Definitions 15
2.2.2 Isserlis’ Theorem 16
2.2.3 Joint Gaussian PDFs, Their Factors, and Inference 18
2.2.4 Statistically Independent, Uncorrelated 20
2.2.5 Linear Change of Variables 20
2.2.6 Normalized Product of Gaussians 22
2.2.7 Sherman-Morrison-Woodbury Identity 23
2.2.8 Passing a Gaussian through a Nonlinearity 24
2.2.9 Shannon Information of a Gaussian 28
2.2.10 Mutual Information of a Joint Gaussian PDF 30
2.2.11 Cram´er-Rao Lower Bound Applied to Gaussian PDFs 30
2.3 Gaussian Processes 32
2.4 Summary 33
2.5 Exercises 33
v
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