FUNDAMENTALS OF STATISTICAL SIGNAL PROCESSING ESTIMATION THEORYpdf电子书版本下载

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1 Introduction 1

1.1 Estimation in Signal Processing 1

1.2 The Mathematical Estimation Problem 7

1.3 Assessing Estimator Performance 9

1.4 Some Notes to the Reader 12

2 Minimum Variance Unbiased Estimation 15

2.1 Introduction 15

2.2 Summary 15

2.3 Unbiased Estimators 16

2.4 Minimum Variance Criterion 19

2.5 Existence of the Minimum Variance Unbiased Estimator 20

2.6 Finding the Minimum Variance Unbiased Estimator 21

2.7 Extension to a Vector Parameter 22

3 Cramer-Rao Lower Bound 27

3.1 Introduction 27

3.2 Summary 27

3.3 Estimator Accuracy Considerations 28

3.4 Cramer-Rao Lower Bound 30

3.5 General CRLB for Signals in White Gaussian Noise 35

3.6 Transformation of Parameters 37

3.7 Extension to a Vector Parameter 39

3.8 Vector Parameter CRLB for Transformations 45

3.9 CRLB for the General Gaussian Case 47

3.10 Asymptotic CRLB for WSS Gaussian Random Processes 50

3.11 Signal Processing Examples 53

3A Derivation of Scalar Parameter CRLB 67

3B Derivation of Vector Parameter CRLB 70

3C Derivation of General Gaussian CRLB 73

3D Derivation of Asymptotic CRLB 77

4 Linear Models 83

4.1 Introduction 83

4.2 Summary 83

4.3 Definition and Properties 83

4.4 Linear Model Examples 86

4.5 Extension to the Linear Model 94

5 General Minimum Variance Unbiased Estimation 101

5.1 Introduction 101

5.2 Summary 101

5.3 Sufficient Statistics 102

5.4 Finding Sufficient Statistics 104

5.5 Using Sufficiency to Find the MVU Estimator 107

5.6 Extension to a Vector Parameter 116

5A Proof of Neyman-Fisher Factorization Theorem （Scalar Parameter） 127

5B Proof of Rao-Blackwell-Lehmann-Scheffe Theorem （Scalar Parameter） 130

6 Best Linear Unbiased Estimators 133

6.1 Introduction 133

6.2 Summary 133

6.3 Definition of the BLUE 134

6.4 Finding the BLUE 136

6.5 Extension to a Vector Parameter 139

6.6 Signal Processing Example 141

6A Derivation of Scalar BLUE 151

6B Derivation of Vector BLUE 153

7 Maximum Likelihood Estimation 157

7.1 Introduction 157

7.2 Summary 157

7.3 An Example 158

7.4 Finding the MLE 162

7.5 Properties of the MLE 164

7.6 MLE for Transformed Parameters 173

7.7 Numerical Determination of the MLE 177

7.8 Extension to a Vector Parameter 182

7.9 Asymptotic MLE 190

7.10 Signal Processing Examples 191

7A Monte Carlo Methods 205

7B Asymptotic PDF of MLE for a Scalar Parameter 211

7C Derivation of Conditional Log-Likelihood for EM Algorithm Example 214

8 Least Squares 219

8.1 Introduction 219

8.2 Summary 219

8.3 The Least Squares Approach 220

8.4 Linear Least Squares 223

8.5 Geometrical Interpretations 226

8.6 Order-Recursive Least Squares 232

8.7 Sequential Least Squares 242

8.8 Constrained Least Squares 251

8.9 Nonlinear Least Squares 254

8.10 Signal Processing Examples 260

8A Derivation of Order-Recursive Least Squares 282

8B Derivation of Recursive Projection Matrix 285

8C Derivation of Sequential Least Squares 286

9 Method of Moments 289

9.1 Introduction 289

9.2 Summary 289

9.3 Method of Moments 289

9.4 Extension to a Vector Parameter 292

9.5 Statistical Evaluation of Estimators 294

9.6 Signal Processing Example 299

10 The Bayesian Philosophy 309

10.1 Introduction 309

10.2 Summary 309

10.3 Prior Knowledge and Estimation 310

10.4 Choosing a Prior PDF 316

10.5 Properties of the Gaussian PDF 321

10.6 Bayesian Linear Model 325

10.7 Nuisance Parameters 328

10.8 Bayesian Estimation for Deterministic Parameters 330

10A Derivation of Conditional Gaussian PDF 337

11 General Bayesian Estimators 341

11.1 Introduction 341

11.2 Summary 341

11.3 Risk Functions 342

11.4 Minimum Mean Square Error Estimators 344

11.5 Maximum A Posteriori Estimators 350

11.6 Performance Description 359

11.7 Signal Processing Example 365

11A Conversion of Continuous-Time System to Discrete-Time System 375

12 Linear Bayesian Estimators 379

12.1 Introduction 379

12.2 Summary 379

12.3 Linear MMSE Estimation 380

12.4 Geometrical Interpretations 384

12.5 The Vector LMMSE Estimator 389

12.6 Sequential LMMSE Estimation 392

12.7 Signal Processing Examples - Wiener Filtering 400

12A Derivation of Sequential LMMSE Estimator 415

13 Kalman Filters 419

13.1 Introduction 419

13.2 Summary 419

13.3 Dynamical Signal Models 420

13.4 Scalar Kalman Filter 431

13.5 Kalman Versus Wiener Filters 442

13.6 Vector Kalman Filter 446

13.7 Extended Kalman Filter 449

13.8 Signal Processing Examples 452

13A Vector Kalman Filter Derivation 471

13B Extended Kalman Filter Derivation 476

14 Summary of Estimators 479

14.1 Introduction 479

14.2 Estimation Approaches 479

14.3 Linear Model 486

14.4 Choosing an Estimator 489

15 Extensions for Complex Data and Parameters 493

15.1 Introduction 493

15.2 Summary 493

15.3 Complex Data and Parameters 494

15.4 Complex Random Variables and PDFs 500

15.5 Complex WSS Random Processes 513

15.6 Derivatives，Gradients，and Optimization 517

15.7 Classical Estimation with Complex Data 524

15.8 Bayesian Estimation 532

15.9 Asymptotic Complex Gaussian PDF 535

15.10Signal Processing Examples 539

15A Derivation of Properties of Complex Covariance Matrices 555

15B Derivation of Properties of Complex Gaussian PDF 558

15C Derivation of CRLB and MLE Formulas 563

A1 Review of Important Concepts 567

A1.1 Linear and Matrix Algebra 567

A1.2 Probability，Random Processes，and Time Series Models 574

A2 Glossary of Symbols and Abbreviations 583

INDEX 589