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. This will book will develop just 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 wide audience Interactive learning techniques with code examples
Author(s): Armando Barreto; Malek Adjouadi; Francisco Ortega; Nonnarit O-Larnnithipong
Publisher: CRC Press
Year: 2021
Language: English
Pages: 200
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
8.3 RECURSIVE EXECUTION OF THE KALMAN FILTER ALGORITHM
8.4 THE KALMAN FILTER ESTIMATOR AS A “FILTER”
Chapter 9 Univariate Example of Kalman Filter in MATLAB®
9.1 IDENTIFICATION OF THE KALMAN FILTER VARIABLES AND PARAMETERS
9.2 STRUCTURE OF OUR MATLAB® SIMULATIONS
9.3 CREATION OF SIMULATED SIGNALS: CORRESPONDENCE OF PARAMETERS AND SIGNAL CHARACTERISTICS
9.4 THE TIMING LOOP
9.5 EXECUTING THE SIMULATION AND INTERPRETATION OF THE RESULTS
9.6 ISOLATING THE PERFORMANCE OF THE MODEL (BY NULLIFYING THE KALMAN GAIN)
Chapter 10 Multivariate Example of Kalman Filter in MATLAB®
10.1 OVERVIEW OF THE SCENARIO AND SETUP OF THE KALMAN FILTER
10.2 STRUCTURE OF THE MATLAB® SIMULATION FOR THIS CASE
10.3 TESTING THE SIMULATION
10.4 FURTHER ANALYSIS OF THE SIMULATION RESULTS
10.5 ISOLATING THE EFFECT OF THE MODEL
Part IV Kalman Filtering Application to IMUs
Chapter 11 Kalman Filtering Applied to 2-Axis Attitude Estimation from Real IMU Signals
11.1 ADAPTING THE KALMAN FILTER FRAMEWORK TO ATTITUDE ESTIMATION FROM IMU SIGNALS
11.2 REVIEW OF ESSENTIAL ATTITUDE CONCEPTS: FRAMES OF REFERENCE, EULER ANGLES AND QUATERNIONS
11.3 CAN THE SIGNALS FROM A GYROSCOPE BE USED TO INDICATE THE CURRENT ATTITUDE OF THE IMU?
11.4 CAN WE OBTAIN “MEASUREMENTS” OF ATTITUDE WITH THE ACCELEROMETERS?
11.5 SUMMARY OF THE KALMAN FILTER IMPLEMENTATION FOR ATTITUDE ESTIMATION WITH AN IMU
11.6 STRUCTURE OF THE MATLAB® IMPLEMENTATION OF THIS KALMAN FILTER APPLICATION
11.7 TESTING THE IMPLEMENTATION OF KALMAN FILTER FROM PRE-RECORDED IMU SIGNALS
Chapter 12 Real-Time Kalman Filtering Application to Attitude Estimation from IMU Signals
12.1 PLATFORM AND ORGANIZATION OF THE REAL-TIME KALMAN FILTER IMPLEMENTATION FOR ATTITUDE ESTIMATION
12.2 SCOPE OF THE IMPLEMENTATION AND ASSUMPTIONS
12.3 INITIALIZATION AND ASSIGNMENT OF PARAMETERS FOR THE EXECUTION
12.4 BUILDING (COMPILING AND LINKING) THE EXECUTABLE PROGRAM RTATT2IMU.EXE—REQUIRED FILES
12.5 COMMENTS ON THE CUSTOM MATRIX AND VECTOR MANIPULATION FUNCTIONS
12.6 INPUTS AND OUTPUTS OF THE REAL-TIME IMPLEMENTATION
12.7 TRYING THE REAL-TIME IMPLEMENTATION OF THE KALMAN FILTER FOR ATTITUDE ESTIMATION
12.8 VISUALIZING THE RESULTS OF THE REAL-TIME PROGRAM
APPENDIX A LISTINGS OF THE FILES FOR REAL-TIMEIMPLEMENTATION OF THE KALMANFILTER FOR ATTITUDE ESTIMATION WITH ROTATIONS IN 2 AXES
REFERENCES
INDEX
