Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Acknowledgments -- Authors -- Introduction -- Part I Background -- Chapter 1 System Models and Random Variables -- 1.1 DETERMINISTIC AND RANDOM MODELS AND VARIABLES -- 1.2 HISTOGRAMS AND PROBABILITY FUNCTIONS -- 1.3 THE GAUSSIAN (NORMAL) DISTRIBUTION -- 1.4 MODIFICATION OF A SIGNAL WITH GAUSSIAN DISTRIBUTION THROUGH A FUNCTION REPRESENTED BY A STRAIGHT LINE -- 1.5 EFFECTS OF MULTIPLYING TWO GAUSSIAN DISTRIBUTIONS -- Chapter 2 Multiple Random Sequences Considered Jointly -- 2.1 JOINT DISTRIBUTIONS-BIVARIATE CASE

2.2 BIVARIATE GAUSSIAN DISTRIBUTION-COVARIANCE AND CORRELATION -- 2.3 COVARIANCE MATRIX -- 2.4 PROCESSING A MULTIDIMENSIONAL GAUSSIAN DISTRIBUTION THROUGH A LINEAR TRANSFORMATION -- 2.5 MULTIPLYING TWO MULTIVARIATE GAUSSIAN DISTRIBUTIONS -- Chapter 3 Conditional Probability, Bayes' Rule and Bayesian Estimation -- 3.1 CONDITIONAL PROBABILITY AND THE BAYES' RULE -- 3.2 BAYES' RULE FOR DISTRIBUTIONS -- Part II Where Does Kalman Filtering Apply and What Does It Intend to Do? -- Chapter 4 A Simple Scenario Where Kalman Filtering May Be Applied

4.1 A SIMPLE MODELING SCENARIO: DC MOTOR CONNECTED TO A CAR BATTERY -- 4.2 POSSIBILITY TO ESTIMATE THE STATE VARIABLE BY PREDICTION FROM THE MODEL -- 4.2.1 Internal Model Uncertainty -- 4.2.2 External Uncertainty Impacting the System -- 4.3 POSSIBILITY TO ESTIMATE THE STATE VARIABLE BY MEASUREMENT OF EXPERIMENTAL VARIABLES -- 4.3.1 Uncertainty in the Values Read of the Measured Variable -- Chapter 5 General Scenario Addressed by Kalman Filtering and Specific Cases -- 5.1 ANALYTICAL REPRESENTATION OF A GENERIC KALMAN FILTERING SITUATION

5.2 UNIVARIATE ELECTRICAL CIRCUIT EXAMPLE IN THE GENERIC FRAMEWORK -- 5.3 AN INTUITIVE, MULTIVARIATE SCENARIO WITH ACTUAL DYNAMICS: THE FALLING WAD OF PAPER -- Chapter 6 Arriving at the Kalman Filter Algorithm -- 6.1 GOALS AND ENVIRONMENT FOR EACH ITERATION OF THE KALMAN FILTERING ALGORITHM -- 6.2 THE PREDICTION PHASE -- 6.3 MEASUREMENTS PROVIDE A SECOND SOURCE OF KNOWLEDGE FOR STATE ESTIMATION -- 6.4 ENRICHING THE ESTIMATE THROUGH BAYESIAN ESTIMATION IN THE "CORRECTION PHASE" -- Chapter 7 Reflecting on the Meaning and Evolution of the Entities in the Kalman Filter Algorithm

7.1 SO, WHAT IS THE KALMAN FILTER EXPECTED TO ACHIEVE? -- 7.2 EACH ITERATION OF THE KALMAN FILTER SPANS "TWO TIMES" AND "TWO SPACES" -- 7.3 YET, IN PRACTICE ALL THE COMPUTATIONS ARE PERFORMED IN A SINGLE, "CURRENT" ITERATION-CLARIFICATION -- 7.4 MODEL OR MEASUREMENT? KG DECIDES WHO WE SHOULD TRUST -- Part III Examples in MATLAB® -- Chapter 8 MATLAB® Function to Implement and Exemplify the Kalman Filter -- 8.1 DATA AND COMPUTATIONS NEEDED FOR THE IMPLEMENTATION OF ONE ITERATION OF THE KALMAN FILTER -- 8.2 A BLOCK DIAGRAM AND A MATLAB® FUNCTION FOR IMPLEMENTATION OF ONE KALMAN FILTER ITERATION

The emergence of affordable micro sensors, such as MEMS Inertial Measurement Systems, are applied in embedded systems and Internet-of-Things devices. This has brought techniques such as Kalman Filtering, which are capable of combining information from multiple sensors or sources, to the interest of students and hobbyists. This book will explore the necessary background concepts, helping a much wider audience of readers develop an understanding and intuition that will enable them to follow the explanation for the Kalman Filtering algorithm. Key Features: Provides intuitive understanding of Kalman Filtering approach Succinct overview of concepts to enhance accessibility and appeal to a wide audience Interactive learning techniques with code examples Malek Adjouadi, PhD, is Ware Professor with the Department of Electrical and Computer Engineering at Florida International University, Miami. He received his PhD from the Electrical Engineering Department at the University of Florida, Gainesville. He is the Founding Director of the Center for Advanced Technology and Education funded by the National Science Foundation. His earlier work on computer vision to help persons with blindness led to his testimony to the U.S. Senate on the committee of Veterans Affairs on the subject of technology to help persons with disabilities. His research interests are in imaging, signal processing and machine learning, with applications in brain research and assistive technology. Armando Barreto, PhD, is Professor of the Electrical and Computer Engineering Department at Florida International University, Miami, as well as the Director of FIU's Digital Signal Processing Laboratory, with more than 25 years of experience teaching DSP to undergraduate and graduate students. He earned his PhD in electrical engineering from the University of Florida, Gainesville. His work has focused on applying DSP techniques to the facilitation of human-computer interactions, particularly for the benefit of individuals with disabilities. He has developed human-computer interfaces based on the processing of signals and has developed a system that adds spatialized sounds to the icons in a computer interface to facilitate access by individuals with "low vision." With his research team, he has explored the use of Magnetic, Angular-Rate and Gravity (MARG) sensor modules and Inertial Measurement Units (IMUs) for human-computer interaction applications. He is a senior member of the Institute of Electrical and Electronics Engineers (IEEE) and the Association for Computing Machinery (ACM). Francisco R. Ortega, PhD, is an Assistant Professor at Colorado State University and Director of the Natural User Interaction Lab (NUILAB). Dr. Ortega earned his PhD in Computer Science (CS) in the field of Human-Computer Interaction (HCI) and 3D User Interfaces (3DUI) from Florida International University (FIU). He also held a position of Post-Doc and Visiting Assistant Professor at FIU. His main research area focuses on improving user interaction in 3DUI by (a) eliciting (hand and full-body) gesture and multimodal interactions, (b) developing techniques for multimodal interaction, and (c) developing interactive multimodal recognition systems. His secondary research aims to discover how to increase interest for CS in non-CS entry-level college students via virtual and augmented reality games. His research has resulted in multiple peer-reviewed publications in venues such as ACM ISS, ACM SUI, and IEEE 3DUI, among others. He is the first-author of the CRC Press book Interaction Design for 3D User Interfaces: The World of Modern Input Devices for Research, Applications and Game Development. Nonnarit O-larnnithipong, PhD, is an Instructor at Florida International University. Dr. O-larnnithipong earned his PhD in Electrical Engineering, majoring in Digital Signal Processing from Florida International University (FIU). He also held a position of Post-Doctoral Associate at FIU in 2019. His research has focused on (1) implementing the sensor fusion algorithm to improve orientation measurement using MEMS inertial and magnetic sensors and (2) developing a 3D hand motion tracking system using Inertial Measurement Units (IMUs) and infrared cameras. His research has resulted in multiple peer-reviewed publications in venues such as HCI-International and IEEE Sensors.

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