Modeling, Estimation and Optimal Filtration in Signal Processing

Table of Contents

Preface

Chapter 1. Parametric Models

1.1. Introduction

1.2. Discrete linear models

1.2.1. The moving average (MA) model

1.2.2. The autoregressive (AR) model

1.3. Observations on stability, stationarity and invertibility

1.3.1. AR model case

1.3.2. ARMA model case

1.4. The AR model or the ARMA model?

1.5. Sinusoidal models

1.5.1. The relevance of the sinusoidal model

1.5.2. Sinusoidal models

1.6. State space representations

1.6.1. Definitions

1.6.2. State space representations based on differential equation representation

1.6.3. Resolution of the state equations

1.6.4. State equations for a discrete-time system

1.6.5. Some properties of systems described in the state space

1.6.5.1. Introduction

1.6.5.2. Observability

1.6.5.3. Controllability

1.6.5.4. Plurality of the state space representation of the system

1.6.6. Case 1: state space representation of AR processes

1.6.7. Case 2: state space representation of MA processes

1.6.8. Case 3: state space representation of ARMA processes

1.6.9. Case 4: state space representation of a noisy process

1.6.9.1. An AR process disturbed by a white noise

1.6.9.2. AR process disturbed by colored noise itself modeled by another AR process

1.6.9.3. AR process disturbed by colored noise itself modeled by a MA process

1.7. Conclusion

1.8. References

Chapter 2. Least Squares Estimation of Parameters of Linear Models

2.1. Introduction

2.2. Least squares estimation of AR parameters

2.2.1. Determination or estimation of parameters?

2.2.2. ...