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
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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 ? ? = ± ?? ² ?³1 ? ? = ± ?1 ? 1 + ⋯ + ± ? ² , i = ´, … . , µ ± ?? are coefficients by which depends on ? ? A set of m linear equations with n variables ? 1 , ? 2 , . ., ? ² can be represented as Ax = b where A is _______ matrix and b is ___ vector. EX] 4? 1 ·? 2 + ? 3 = · ? 2 + ? 3 = −´ Given Ax = b, if A is invertable, we can find x = ± ¸1 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 … . . ? ± ] ° , ? = ? 11 ? 1? ? ±1 ? ±? , and x = ? 1 ? ? and y = Ax y is measurement or observation and x is unknown Matrix Linear Algebra Review
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Interpreting by rows A is a function that maps ? ∈ ° ? ?±²? ? ∈ ° ³ ´ µ¶ is a gain factor from ·²ℎ input ( ? ) to ?²ℎ output ( ? µ ) i th row of A is associated with i th output j th column of A is associated with j th input ´ 12 = 0 means the first output ( ?
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lec3 - EE 5243 ESTIMATION THEORY Lesson 3 Prof Daniel Pack...

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