ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED)

EE210A: Adaptation and Learning Professor Ali H. Sayed

ELECTRICAL ENGINEERING DEPARTMENT EE210A: ADAPTATION AND LEARNING (A. H. SAYED) 2

MAIN RESULT FROM LAST LECTURE

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MAIN RESULT FROM LAST LECTURE

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LECTURE #03

LINEAR MEAN-SQUARE ERROR ESTIMATION Sections in order: App. C, 3.1, 3.2, 3.3, 3.4, 4.2

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COMPLEX GRADIENTS

A. Cauchy (1789-1857)

G. Riemann (1826-1866)

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CAUCHY RIEMANN CONDITIONS

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SCALAR EXAMPLES

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SCALAR EXAMPLES

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VECTOR EXAMPLES

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VECTOR EXAMPLES

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OPTIMAL MSE ESTIMATOR

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AFFINE ESTIMATOR

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MSE CRITERION

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UNBIASED ESTIMATOR

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MINIMIZING MSE

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MINIMIZING MSE

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MINIMIZING MSE

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COST FUNCTION

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MSE MINIMIZATION

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DIFFERENTIATION ARGUMENT

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COMPLETION OF SQUARES ARGUMENT

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COMPLETION OF SQUARES

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COMPLETION OF SQUARES

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ERROR COVARIANCE MATRIX

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ERROR COVARIANCE MATRIX

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ERROR COVARIANCE MATRIX

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OPTIMAL LINEAR ESTIMATOR

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ORTHOGONALITY CONDITION

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ORTHOGONALITY CONDITION

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DEFINING PROPERTY

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EXAMPLE

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EXAMPLE

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1st DESIGN EXAMPLE

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1st DESIGN EXAMPLE

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1ST DESIGN EXAMPLE

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1ST DESIGN EXAMPLE

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2ND DESIGN EXAMPLE

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2ND DESIGN EXAMPLE

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2ND DESIGN EXAMPLE