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Introduction to Random Signals and Applied Kalman Filtering with Matlab Exercises, 4th Edition

Book Description

The Fourth Edition to the Introduction of Random Signals and Applied Kalman Filtering is updated to cover innovations in the Kalman filter algorithm and the proliferation of Kalman filtering applications from the past decade. The text updates both the research advances in variations on the Kalman filter algorithm and adds a wide range of new application examples. Several chapters include a significant amount of new material on applications such as simultaneous localization and mapping for autonomous vehicles, inertial navigation systems and global satellite navigation systems.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Preface To The Fourth Edition
  5. Brief Contents
  6. Contents
  7. PART 1: Random Signals Background
    1. Chapter 1: Probability and Random Variables: A Review
      1. 1.1 RANDOM SIGNALS
      2. 1.2 INTUITIVE NOTION OF PROBABILITY
      3. 1.3 AXIOMATIC PROBABILITY
      4. 1.4 RANDOM VARIABLES
      5. 1.5 JOINT AND CONDITIONAL PROBABILITY, BAYES RULE, AND INDEPENDENCE
      6. 1.6 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DENSITY FUNCTION
      7. 1.7 EXPECTATION, AVERAGES, AND CHARACTERISTIC FUNCTION
      8. 1.8 NORMAL OR GAUSSIAN RANDOM VARIABLES
      9. 1.9 IMPULSIVE PROBABILITY DENSITY FUNCTIONS
      10. 1.10 JOINT CONTINUOUS RANDOM VARIABLES
      11. 1.11 CORRELATION, COVARIANCE, AND ORTHOGONALITY
      12. 1.12 SUM OF INDEPENDENT RANDOM VARIABLES AND TENDENCY TOWARD NORMAL DISTRIBUTION
      13. 1.13 TRANSFORMATION OF RANDOM VARIABLES
      14. 1.14 MULTIVARIATE NORMAL DENSITY FUNCTION
      15. 1.15 LINEAR TRANSFORMATION AND GENERAL PROPERTIES OF NORMAL RANDOM VARIABLES
      16. 1.16 LIMITS, CONVERGENCE, AND UNBIASED ESTIMATORS
      17. 1.17 A NOTE ON STATISTICAL ESTIMATORS
    2. Chapter 2: Mathematical Description of Random Signals
      1. 2.1 CONCEPT OF A RANDOM PROCESS
      2. 2.2 PROBABILISTIC DESCRIPTION OF A RANDOM PROCESS
      3. 2.3 GAUSSIAN RANDOM PROCESS
      4. 2.4 STATIONARITY, ERGODICITY, AND CLASSIFICATION OF PROCESSES
      5. 2.5 AUTOCORRELATION FUNCTION
      6. 2.6 CROSSCORRELATION FUNCTION
      7. 2.7 POWER SPECTRAL DENSITY FUNCTION
      8. 2.8 WHITE NOISE
      9. 2.9 GAUSS–MARKOV PROCESSES
      10. 2.10 NARROWBAND GAUSSIAN PROCESS
      11. 2.11 WIENER OR BROWNIAN-MOTION PROCESS
      12. 2.12 PSEUDORANDOM SIGNALS
      13. 2.13 DETERMINATION OF AUTOCORRELATION AND SPECTRAL DENSITY FUNCTIONS FROM EXPERIMENTAL DATA
      14. 2.14 SAMPLING THEOREM
    3. Chapter 3: Linear Systems Response, State-Space Modeling, and Monte Carlo Simulation
      1. 3.1 INTRODUCTION: THE ANALYSIS PROBLEM
      2. 3.2 STATIONARY (STEADY-STATE) ANALYSIS
      3. 3.3 INTEGRAL TABLES FOR COMPUTING MEAN-SQUARE VALUE
      4. 3.4 PURE WHITE NOISE AND BANDLIMITED SYSTEMS
      5. 3.5 NOISE EQUIVALENT BANDWIDTH
      6. 3.6 SHAPING FILTER
      7. 3.7 NONSTATIONARY (TRANSIENT) ANALYSIS
      8. 3.8 NOTE ON UNITS AND UNITY WHITE NOISE
      9. 3.9 VECTOR DESCRIPTION OF RANDOM PROCESSES
      10. 3.10 MONTE CARLO SIMULATION OF DISCRETE-TIME PROCESSES
  8. PART 2: Kalman Filtering And Applications
    1. Chapter 4: Discrete Kalman Filter Basics
      1. 4.1 A SIMPLE RECURSIVE EXAMPLE
      2. 4.2 THE DISCRETE KALMAN FILTER
      3. 4.3 SIMPLE KALMAN FILTER EXAMPLES AND AUGMENTING THE STATE VECTOR
      4. 4.4 MARINE NAVIGATION APPLICATION WITH MULTIPLE-INPUTS/MULTIPLE-OUTPUTS
      5. 4.5 GAUSSIAN MONTE CARLO EXAMPLES
      6. 4.6 PREDICTION
      7. 4.7 THE CONDITIONAL DENSITY VIEWPOINT
      8. 4.8 RE-CAP AND SPECIAL NOTE ON UPDATING THE ERROR COVARIANCE MATRIX
    2. Chapter 5: Intermediate Topics on Kalman Filtering
      1. 5.1 ALTERNATIVE FORM OF THE DISCRETE KALMAN FILTER–THE INFORMATION FILTER
      2. 5.2 PROCESSING THE MEASUREMENTS ONE AT A TIME
      3. 5.3 ORTHOGONALITY PRINCIPLE
      4. 5.4 DIVERGENCE PROBLEMS
      5. 5.5 SUBOPTIMAL ERROR ANALYSIS
      6. 5.6 REDUCED-ORDER SUBOPTIMALITY
      7. 5.7 SQUARE-ROOT FILTERING AND U-D FACTORIZATION
      8. 5.8 KALMAN FILTER STABILITY
      9. 5.9 RELATIONSHIP TO DETERMINISTIC LEAST SQUARES ESTIMATION
      10. 5.10 DETERMINISTIC INPUTS
    3. Chapter 6: Smoothing and Further Intermediate Topics
      1. 6.1 CLASSIFICATION OF SMOOTHING PROBLEMS
      2. 6.2 DISCRETE FIXED-INTERVAL SMOOTHING
      3. 6.3 DISCRETE FIXED-POINT SMOOTHING
      4. 6.4 DISCRETE FIXED-LAG SMOOTHING
      5. 6.5 ADAPTIVE KALMAN FILTER (MULTIPLE MODEL ADAPTIVE ESTIMATOR)
      6. 6.6 CORRELATED PROCESS AND MEASUREMENT NOISE FOR THE DISCRETE FILTER—DELAYED-STATE FILTER ALGORITHM
      7. 6.7 DECENTRALIZED KALMAN FILTERING
      8. 6.8 DIFFICULTY WITH HARD-BANDLIMITED PROCESSES
      9. 6.9 THE RECURSIVE BAYESIAN FILTER
    4. Chapter 7: Linearization, Nonlinear Filtering, and Sampling Bayesian Filters
      1. 7.1 LINEARIZATION
      2. 7.2 THE EXTENDED KALMAN FILTER
      3. 7.3 “BEYOND THE KALMAN FILTER”
      4. 7.4 THE ENSEMBLE KALMAN FILTER
      5. 7.5 THE UNSCENTED KALMAN FILTER
      6. 7.6 THE PARTICLE FILTER
    5. Chapter 8: The “Go-Free” Concept, Complementary Filter, and Aided Inertial Examples
      1. 8.1 INTRODUCTION: WHY GO FREE OF ANYTHING?
      2. 8.2 SIMPLE GPS CLOCK BIAS MODEL
      3. 8.3 EULER/GOAD EXPERIMENT
      4. 8.4 REPRISE: GPS CLOCK-BIAS MODEL REVISITED
      5. 8.5 THE COMPLEMENTARY FILTER
      6. 8.6 SIMPLE COMPLEMENTARY FILTER: INTUITIVE METHOD
      7. 8.7 KALMAN FILTER APPROACH—ERROR MODEL
      8. 8.8 KALMAN FILTER APPROACH—TOTAL MODEL
      9. 8.9 GO-FREE MONTE CARLO SIMULATION
      10. 8.10 INS ERROR MODELS
      11. 8.11 AIDING WITH POSITIONING MEASUREMENTS—INS/DME MEASUREMENT MODEL
      12. 8.12 OTHER INTEGRATION CONSIDERATIONS AND CONCLUDING REMARKS
    6. Chapter 9: Kalman Filter Applications To The GPS And Other Navigation Systems
      1. 9.1 POSITION DETERMINATION WITH GPS
      2. 9.2 THE OBSERVABLES
      3. 9.3 BASIC POSITION AND TIME PROCESS MODELS
      4. 9.4 MODELING OF DIFFERENT CARRIER PHASE MEASUREMENTS AND RANGING ERRORS
      5. 9.5 GPS-AIDED INERTIAL ERROR MODELS
      6. 9.6 COMMUNICATION LINK RANGING AND TIMING
      7. 9.7 SIMULTANEOUS LOCALIZATION AND MAPPING (SLAM)
      8. 9.8 CLOSING REMARKS
  9. APPENDIX A: Laplace and Fourier Transforms
    1. A.1 THE LAPLACE TRANSFORM
    2. A.2 THE FOURIER TRANSFORM
  10. APPENDIX B: The Continuous Kalman Filter
    1. B.1 TRANSITION FROM THE DISCRETE TO CONTINUOUS FILTER EQUATIONS
    2. B.2 SOLUTION OF THE MATRIX RICCATI EQUATION
  11. Index