4219-28972:EECS 965 Detection and Estimation Theory LEC

4219-28972:EECS 965 Detection and Estimation Theory LEC

Course Modules

1. Introduction to Detection and Estimation

1. Introduction to Detection and Estimation
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1. Introduction to Detection and Estimation 96426  
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    Operators and Mappings Operators and Mappings
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    Inverse Operators Inverse Operators
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    Linear Operators Linear Operators
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    The Observation Model The Observation Model
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    Statistical Mapping Statistical Mapping
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    Apriori and Likelihood Densities Apriori and Likelihood Densities
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    Detection Detection
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2 Statistical Decision Theory

2 Statistical Decision Theory
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2 Statistical Decision Theory 96774  
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    MAP Detection and Probability of Error MAP Detection and Probability of Error
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    The Sufficient Statistic The Sufficient Statistic
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    The Detection Statistic and Decision Regions The Detection Statistic and Decision Regions
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    Maximum Likelihood Detection Maximum Likelihood Detection
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    Example: A Simple Communications System Example: A Simple Communications System
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    Probability of Detection Error Probability of Detection Error
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    Example: Probability of Error Example: Probability of Error
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    The Confusion Matrix The Confusion Matrix
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    Calculating the Confusion Matrix Calculating the Confusion Matrix
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    Bayesian Risk Bayesian Risk
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3 Detection Theory

3 Detection Theory
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3 Detection Theory 96907  
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    The Likelihood Ratio Test (LRT) The Likelihood Ratio Test (LRT)
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    The LRT and Decision Regions The LRT and Decision Regions
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    Example: The Measurement Vector Example: The Measurement Vector
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    Example: Earthquake Detection Example: Earthquake Detection
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    Detection, Miss, and False Alarm Detection, Miss, and False Alarm
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    Example: Determining Pd and Pfa Example: Determining Pd and Pfa
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    The Neyman-Pearson Criterion The Neyman-Pearson Criterion
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    The Receiver Operating Curve (ROC) The Receiver Operating Curve (ROC)
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4 Deterministic Signal Detection

4 Deterministic Signal Detection
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4 Deterministic Signal Detection 96908  
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    Discrete Signal Representations Discrete Signal Representations
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    A Known Signal in Noise A Known Signal in Noise
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    A Known Signal in Correlated Noise A Known Signal in Correlated Noise
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    Generalized Matched Filter Performance Generalized Matched Filter Performance
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    Optimal Signals for Detection Optimal Signals for Detection
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    Multiple Known Signals Multiple Known Signals
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5 Random Signal Detection

5 Random Signal Detection
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5 Random Signal Detection 96909  
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    Detection of Non Deterministic Signals Detection of Non Deterministic Signals
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6. Introduction to Estimation Theory

6. Introduction to Estimation Theory
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6. Introduction to Estimation Theory 96919  
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    Estimation Estimation
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    Introduction to Estimation Theory Introduction to Estimation Theory
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    Unknown but not Random Unknown but not Random
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    The a priori Controversy The a priori Controversy
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7. Bayesian Estimation

7. Bayesian Estimation
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7. Bayesian Estimation 96920  
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    Bayesian Estimation Theory Bayesian Estimation Theory
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    Bayesian Risk Estimators Bayesian Risk Estimators
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    The Minimum Mean Squared-Error Estimate The Minimum Mean Squared-Error Estimate
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    The MAP Estimate The MAP Estimate
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    When p=1 When p=1
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    Nuisance Parameters Nuisance Parameters
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    Example: The MAP Estimator Example: The MAP Estimator
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    Example: The MMSE Estimator Example: The MMSE Estimator
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    A Comparison of MAP and MMSE Estimators A Comparison of MAP and MMSE Estimators
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8. "Classical" Estimation Theory

8. "Classical" Estimation Theory
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8. "Classical" Estimation Theory 96921  
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    Classical Estimation Theory Classical Estimation Theory
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    The Maximum Likelihood Estimator The Maximum Likelihood Estimator
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9. Information Theoretic Measures of Observations

9. Information Theoretic Measures of Observations
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9. Information Theoretic Measures of Observations 96922  
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    MVU and the Cramer Rao Lower Bound (CRLB) MVU and the Cramer Rao Lower Bound (CRLB)
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    Example: The CRLB Example: The CRLB
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    The CRLB Theorem The CRLB Theorem
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    Transformation of Parameters Transformation of Parameters
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    The Fisher's Information Matrix The Fisher's Information Matrix
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    Properties of the MLE Properties of the MLE
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    Bayesian Information Bayesian Information
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    Van Trees' Information Van Trees' Information
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    Marginal Fisher's Information Marginal Fisher's Information
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10. Maximum Likelihood and the Linear Model

10. Maximum Likelihood and the Linear Model
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10. Maximum Likelihood and the Linear Model 96925  
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    The Linear Model The Linear Model
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    The MLE Estimator and the Linear Model The MLE Estimator and the Linear Model
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    The CRLB of the Linear Model MLE Estimator The CRLB of the Linear Model MLE Estimator
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    The General Linear Model The General Linear Model
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    Geometrical Interpretations Geometrical Interpretations
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    The Matched Filter The Matched Filter
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    A geometrical interpretation of The Matched Filter and the MLE A geometrical interpretation of The Matched Filter and the MLE
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11. Bayesian Estimation and the Linear Model

11. Bayesian Estimation and the Linear Model
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11. Bayesian Estimation and the Linear Model 96923  
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    The MMSE of the Linear Model The MMSE of the Linear Model
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    The MAP estimate of the Linear Model The MAP estimate of the Linear Model
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    MMSE, MAP, MLE, and the Matched Filter MMSE, MAP, MLE, and the Matched Filter
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12. Iterative MMSE and the Kalman Filter

12. Iterative MMSE and the Kalman Filter
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12. Iterative MMSE and the Kalman Filter 96927  
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    Sequential MMSE Sequential MMSE
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    The Kalman Filter The Kalman Filter
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13. Least-Squared Estimators

13. Least-Squared Estimators
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13. Least-Squared Estimators 96926  
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    Linear Least Squares Linear Least Squares
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14. Estimation of Random Variables and Processes

14. Estimation of Random Variables and Processes
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14. Estimation of Random Variables and Processes 96928  
 
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