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Parameter Estimation using Least Squares

Parameter Estimation using Least Squares. u nknown parameters. Least Squares. s calar variables. m easured value. Least squares identification. attempts to find values for theta for which the left- and the right-hand-sides of differ by the smallest possible error. More precisely,

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Parameter Estimation using Least Squares

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  1. Parameter Estimation using Least Squares

  2. unknown parameters Least Squares scalar variables measured value

  3. Least squares identification • attempts to find values fortheta for which the left- and the right-hand-sides of • differ by the smallest possible error. More precisely, • the values of theta leading to the smallest possible sum of squares for the errors over the N experiments.

  4. Least squares model fitting observation error Linear regression observed variable unknown coef. The aim is to find the value of which minimizes the cost function

  5. Least squares model fitting • Example: consider a temperature measuring device with a voltage output, u. It is known that the temperature, y, is a function of the output voltage, the model is given by

  6. Least squares model fitting For N samples The value that minimisesV makes the gradient of V with respect to zero

  7. Least squares model fitting

  8. Using Least squares for Parameter of Plant model G(s)

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