"Intuitive understanding of Kalman filtering with MATLAB" / Armando Barreto [and three others]

Format:

Book

Author/Creator:

Barreto, Armando, 1963- author.

Adjouadi, Malek, 1955- author.

Ortega, Francisco R., author.

O-larnnithipong, Nonnarit, author.

Language:

English

Subjects (All):

MATLAB.

Kalman filtering.

Numerical analysis--Computer programs.

Numerical analysis.

Physical Description:

1 online resource (xviii, 229 pages) : illustrations.

Edition:

1st Edition.

Place of Publication:

Boca Raton, Florida ; London ; New York : CRC Press, [2021]

Summary:

"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"-- Provided by publisher.

Contents:

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.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-429-57545-9

0-429-20065-X

0-429-57756-7

9780429200656

OCLC:

1162374369