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# lec3 - EE 5243 ESTIMATION THEORY Lesson 3 Prof Daniel Pack...

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EE 5243 ESTIMATION THEORY Lesson 3 Prof. Daniel Pack

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Overview Last time Kalman filter tasks Disciplines required Matrix Linear Algebra Primer with MATLA Today Matrix Linear Algebra Primer with MATLAB State dynamic systems
Linear function ? with n-vector input and m-vector output Scaling: for any scalar value α and input vector x, ? ( α x) = α ? (x) Superposition: for any input vectors x and y, ? (x+ y) = ? (x) + ? (y) EX] y = Ax ? ? = ? ?? ? ?=1 ? ? = ? ?1 ? 1 + ⋯ + ? ?? ? ? , i = 1, … . , ? ? ?? are coefficients by which ?? depends on ? ? A set of m linear equations with n variables ? 1 , ? 2 , .., ? ? can be represented as Ax = b where A is _______ matrix and b is ___ vector. EX] 4? 1 2? 2 + ? 3 = 2 ? 2 + ? 3 = −1 Given Ax = b, if A is invertable, we can find x = ? −1 ? When is A not invertable? In MATLAB: x = A\b; Matrix Linear Algebra Review

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Interpreting y = Ax Suppose a system of linear equations ? 1 = ? 11 ? 1 + ? 12 ? 2 + … + ? 1? ? ? ? 2 = ? 21 ? 1 + ? 22 ? 2 + … + ? 2? ? ? : ? ? = ? ?1 ? 1 + ? ?2 ? 2 + … + ? ?? ? ? which we rewrite as ? = [? 1 ? 2 … . . ? ? ] 𝑇 , ? = ? 11 ? 1? ? ?1 ? ?? , and x = ? 1 ? ? and y = Ax y is measurement or observation and x is unknown Matrix Linear Algebra Review