Includes bibliographical references and indexes.

Part I Background

Chapter 1 System Models and Random Variables 3

Chapter 2 Multiple Random Sequences

Chapter 3 Conditional Probability, Bayes' Rule and Bayesian Estimation 45

Part II Where Does Kalman Filtering Apply and What Does It Intend to Do?

Chapter 4 A Simple Scenario Where Kalman

Chapter 5 General Scenario Addressed by Kalman Filtering and Specific Cases 61

Chapter 6 Arriving at the Kalman Filter Algorithm 75

Chapter 7 Reflecting on the Meaning and Evolution of the Entities in the Kalman Filter Algorithm 87

Part III Examples in MATLAB®

Chapter 8 MATLAB® Function to Implement and Exemplify the Kalman Filter 103

Chapter 9 Univariate Example of Kalman Filter in MATLAB® 113

Chapter 10 Multivariate Example of Kalman Filter in MATLAB® 131

Part IV Kalman Filtering Application to IMUs

Chapter 11 Kalman Filtering Applied to 2-Axis Attitude Estimation from Real IMU Signals 153

Chapter 12 Real-Time Kalman Filtering Application to Attitude Estimation from IMU Signals 179

The emergence of affordable micro sensors, such as MEMS Inertial Measurement Systems, which are being applied in embedded systems and Internet-of-Things devices, has brought techniques such as Kalman Filtering, capable of combining information from multiple sensors or sources, to the interest of students and hobbyists.