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

Contents

Preface

PART 1 RANDOM SIGNALS BACKGROUND

1 Probability and Random Variables: A Review

1.1 Random Signals

1.2 Intuitive Notion of Probability

1.3 Axiomatic Probability

1.4 Random Variables

1.5 Joint and Conditional Probability, Bayes Rule and Independence

1.6 Continuous Random Variables and Probability Density Function

1.7 Expectation, Averages, and Characteristic Function

1.8 Normal or Gaussian Random Variables

1.9 Impulsive Probability Density Functions

1.10 Joint Continuous Random Variables

1.11 Correlation, Covariance, and Orthogonality

1.12 Sum of Independent Random Variables and Tendency Toward Normal Distribution

1.13 Transformation of Random Variables

1.14 Multivariate Normal Density Function

1.15 Linear Transformation and General Properties of Normal Random Variables

1.16 Limits, Convergence, and Unbiased Estimators

1.17 A Note on Statistical Estimators

2 Mathematical Description of Random Signals

2.1 Concept of a Random Process

2.2 Probabilistic Description of a Random Process

2.3 Gaussian Random Process

2.4 Stationarity, Ergodicity, and Classification of Processes

2.5 Autocorrelation Function

2.6 Crosscorrelation Function

2.7 Power Spectral Density Function

2.8 White Noise

2.9 Gauss–Markov Processes

2.10 Narrowband Gaussian Process

2.11 Wiener or Brownian-Motion Process

2.12 Pseudorandom Signals

2.13 Determination of Autocorrelation and Spectral Density Functions from Experimental Data

2.14 Sampling Theorem

3 Linear Systems Response, State-Space Modeling, and ...