Kalman Filter from the Ground Up

Table of Contents

I Introduction to Kalman Filter
1 The Necessity of Prediction
2 Essential background I
3 The  – filter
4 Kalman Filter in one dimension
5 Adding process noise
II Multivariate Kalman Filter
6 Foreword
7 Essential background II
8 Kalman Filter Equations Derivation
9 Multivariate KF Examples
III Non-linear Kalman Filters
10 Foreword
11 Essential background III
12 Non-linearity problem
13 Extended Kalman Filter (EKF)
14 Unscented Kalman Filter (UKF)
15 Non-linear filters comparison
16 Conclusion
IV Kalman Filter in practice
17 Sensors Fusion
18 Variable measurement error
19 Treating missing measurements
20 Treating outliers
21 Kalman Filter Initialization
22 KF Development Process
Appendices
V Appendices
A The expectation of variance
B Confidence Interval
C Modeling linear dynamic systems
D Derivative of matrix product trace
E Pendulum motion simulation
F Statistical Linear Regression
G The product of univariate Gaussian PDFs
H Product of multivariate Gaussian PDFs
Bibliography
Index