Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory
A unified presentation of parameter estimation for those involved in the design and implementation of statistical signal processing algorithms. Covers important approaches to obtaining an optimal estimator and analyzing its performance; and includes numerous examples as well as applications to real- world problems. MARKETS: For practicing engineers and scientists who design and analyze signal processing systems, i.e., to extract information from noisy signals — radar engineer, sonar engineer, geophysicist, oceanographer, biomedical engineer, communications engineer, economist, statistician, physicist, etc.
Why Read This Book
You should read this book because it gives a clear, mathematically rigorous foundation for designing and analyzing estimators you will use in real DSP systems. It balances theory (CRLB, Fisher information, asymptotics) with practical examples so you can both understand estimator performance and apply it to radar, communications, audio, and biomedical problems.
Who Will Benefit
Graduate students and practicing engineers (radar, communications, audio, biomedical) who need a rigorous, application-oriented treatment of parameter estimation and performance analysis.
Level: Advanced — Prerequisites: Probability and random processes (including pdfs and conditional distributions), linear algebra, multivariable calculus, and basic familiarity with inference concepts (bias, variance, likelihood).
Key Takeaways
- Derive and implement maximum-likelihood and method-of-moments estimators for common signal models.
- Use the Cramér–Rao bound and Fisher information to quantify estimator performance and judge efficiency.
- Construct Bayesian estimators and understand the tradeoffs between Bayesian and classical approaches.
- Identify and exploit sufficient statistics and apply Rao–Blackwellization to improve estimators.
- Analyze large-sample (asymptotic) properties: consistency, asymptotic normality, and efficiency.
- Apply estimation principles to practical signal-processing problems (e.g., parameter estimation in noisy radar/communication models).
Topics Covered
- 1. Introduction and Overview of Estimation Problems
- 2. Estimation Criteria and Performance Measures (MSE, Bias, Risk)
- 3. Classical Point-Estimation Methods (Method of Moments, Least Squares)
- 4. Maximum Likelihood Estimation and Properties
- 5. Bayesian Estimation and Minimum Mean-Square Error Estimators
- 6. Fisher Information and the Cramér–Rao Lower Bound
- 7. Sufficiency, Completeness, Rao–Blackwell and MVUE
- 8. Invariance and Transformation-Based Methods
- 9. Asymptotic Theory: Consistency, Efficiency, and Normality
- 10. Linear Models and Linear Estimation (LS, BLUE)
- 11. Examples and Applications in Radar, Communications, and Biomedical Signals
- Appendices: Useful Mathematical Results and Derivations
Languages, Platforms & Tools
How It Compares
More application-focused and accessible than Van Trees' Detection, Estimation, and Modulation Theory (which is broader and more classical); more practically oriented than the purely theoretical treatment in Lehmann & Casella's Theory of Point Estimation.
