Principles and Applications of RELAX:A Robust and Universal Estimator

《Principles and Applications of RELAX:A Robust and Universal Estimator》由吴仁彪等著

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
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