Lect5 - Stochastic Process 10/27/2006 Lecture 5...

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Stochastic Process 10/27/2006 Lecture 5 Fundamentals of Estimation NCTUEE Summary In this lecture, I will discuss: Estimation Estimator Performance Sample Mean and Sample Variance Gaussian Sample Notation We will use the following notation rules, unless otherwise noted, to represent symbols during this course. Boldface upper case letter to represent MATRIX Boldface lower case letter to represent vector Superscript ( · ) T and ( · ) H to denote transpose and hermitian (conjugate transpose), respectively Upper case italic letter to represent RANDOM VARIABLE 5-1
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1 Estimation Why Estimation? (1) The parameter itself is of interest, such as the distance of an aircraft from the base of a radar system (2) For the purpose of decision making Knowledge of the parameter describes the statistical property, i.e. pdf, of observed (or measured) data y What is an Estimator? An estimator ˆ θ is a function g ( y ) of the observation vector y that estimates θ but is not a function of θ . Example: Let y 1 , ··· ,y n be n observations with y i = θ + ² i , where θ is the unknown parameter we want to estimate, and ² i ’s are measurement noises. A reasonable estimator for θ is the sample mean ˆ θ = 1 n n X i =1 y i . 5-2
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Mathematic Model (1) Model Formulation In determining good estimators the first step is to mathematically model the received data, explicitly establishing the relationship be- tween the unknown quantities and the measured data Example: In the previous example, we have a model y
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Lect5 - Stochastic Process 10/27/2006 Lecture 5...

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