1 Fundamentals of Parameter Estimation
1.1 Introduction
1.2 Maximum Likelihood Estimation
1.3 Bayesian Estimation
1.3.1 Random Parameter Estimation Model
1.3.2 Common Cost Functions
1.3.3 Risk Assessment
1.4 Linear Minimum Mean Squared Error Estimation
1.4.1 Estimation Criterion
1.4.2 Orthogonality Principle
1.5 Performance Measure of Estimators
1.6 Cramer-Rao Bound
1.7 Comparisons of Several Estimation Methods
1.8 Bayesian Revolution in Big Data Era
1.9 Summary
Appendix 1.1: CRB for Vector Parameter Estimation Under the Conditions of General Distribution
Appendix 1.2: CRB for Vector Parameter Estimation Under the Conditions of Gaussian Distribution
References
2 Basic Principles of the RELAX Estimation Algorithm
2.1 Introduction
2.2 Linear Least Squares Estimation
2.2.1 Ordinary Least Squares Solution
2.2.2 Total Least Squares Solution
2.3 Nonlinear Least Squares Estimation
2.3.1 Problems that Can Be Simplified
2.3.2 Conventional Iterative Algorithm
2.3.3 Cyclic Minimizer
2.4 RELAX Estimation Method
2.4.1 RELAX Algorithm for Multiple Sinusoidal Parameter Estimation
2.4.2 RELAX Algorithm for Multiple General Signal Parameter Estimation
2.5 Summary
References
3 Application of RELAX in Line Spectrum Estimation
3.1 Introduction
3.2 Sinusoidal Signal Parameter Estimation
3.2.1 Hybrid Spectral Estimation of One-Dimensional Sinusoidal Signals
3.2.2 Hybrid Spectral Estimation of Two-Dimensional Sinusoidal Signals
3.2.3 Experimental Results
3.3 Exponential Decay Sinusoidal Signal Parameter Estimation
3.3.1 Data Model
3.3.2 DRELAX Algorithm
3.3.3 Experimental Results
3.4 Arbitrary Envelope Sinusoidal Signal Parameter Estimation
3.4.1 Data Model
3.4.2 Parameter Estimation of a Single Signal
3.4.3 Ambiguous Problem of Multiple Signals
3.4.4 Experimental Results
3.5 Chapter Summary
Appendix 3.1: CRB for Sinusoidal Signal Parameter Estimation
Appendix 3.2: CRB for Exponentially Decaying Sinusoidal Signal Parameter Estimation
Appendix 3.3: CRB for Arbitrary Envelope Sinusoidal Signal Parameter Estimation
References
4 Application of RELAX in Time Delay Estimation
4.1 Introduction
4.2 Data Model
4.3 WRELAX Algorithm
4.3.1 Basic Principle
4.3.2 Experimental Results
4.4 Time Delay Estimation for Highly Oscillatory Cost Functions
4.4.1 Hybrid-WRELAX Algorithm
4.4.2 EXIP-WRELAX Algorithm
4.4.3 Experiment Results
4.5 Super Resolution Time Delay Estimation
4.5.1 MODE-WRELAX Algorithm for Complex-Valued Signals
4.5.2 MODE-WRELAX for Real-Valued Signals
4.5.3 Efficient Implementation of MODE-WRELAX
4.5.4 Experimental Results
4.6 Time Delay Estimation with Multiple Look in Colored Gaussian Noise
4.6.1 Data Model
4.6.2 Basic Principle of TWRELAX
4.6.3 Experimental Results
4.7 Chapter Summary
Appendix 4.1: CRB for Time Delay Estimation of Complex-Valued Signals
Appendix 4.2: CRB for Time Delay Estimation of Real-Valued Signals
Appendix 4.3: CRB for Time Delay Estimation with Multiple Look in Colored Gaussian Noise
References
5 Application of RELAX in Direction of Arrival Estimation
5.1 Introduction
5.2 DOA Estimation of Narrowband Signals
5.2.1 Basic Array Processing Concepts
5.2.2 Data Model
5.2.3 Statistic Characteristics of Array Data
5.2.4 NB-RELAX Algorithm
5.2.5 Experimental Results
5.3 DOA Estimation of Wideband Signals
5.3.1 Data Model
5.3.2 WB-RELAX Algorithm
5.3.3 Experimental Results
5.4 Chapter Summary
Appendix 5.1: CRB for DOA Estimation of Narrowband Signals
Appendix 5.2: CRB for DOA Estimation of Wideband Signals
References
6 Application of RELAX in Radar Target Imaging
6.1 Introduction
6.2 Synthetic Aperture R

Signal demixing and parameter estimation for multiple overlapped signals in noise and interference background is a problem often encountered in radar, sonar, communication, navigation, and other fields. Improving parameter estimation performance under low signal-to-noise ratio conditions and robustness in the presence of model errors has always been the focus of research in the field of signal pro cessing and control. Aiming at the above problems, this book presents a general and robust relaxation based estimation method (RELAX) and introduces its basic principles and applications in many aspects.
This book has seven chapters. Chapter 1 introduces fundamentals of parameter estimation. Chapter 2 introduces the basic principle of RELAX. Chapters 3-5 introduces the application of RELAX in classical line spectrum estimation, time delay estimation, and direction of arrival estimation. Chapter 6 introduces the application of RELAX in radar target imaging. Chapter 7 briefly introduces the typical application of RELAX in other aspects.
This book is rich in content. It can be used as a reference reading for a vast number of scientists and technicians in the field of signal processing and control, as well as a teaching material for graduate students in the related fields.