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25 wents sp 8 b) Theoretically, the relation between eye angle and voltage should be sinusoidal, with a period of 360°. Fit the data with the following sinusoid, using the x-function as the cost function and the Simplex method for function minimization Use the same estimated variance of the measurement error for all eye angles as in a). T voltage = Par1 + Par2 * sin (angleeye - Par3) 180° - Calculate the confidence interval at 68% level for the fit parameters. You'll have to use the grid search method. Plot the x-value on a grid of pairs of parameters using surf. Programming hint: with [C.-] = contour3(..., LevelList',value); you can extract all parameter values for a contour at a certain x²-value. - Calculate the goodness of fit (probability Q that the remaining deviations between model and data are explained by statistical errors). - Plot the data and the resulting fit. Questions: Which model do you think is best? How certain are the models about the estimated parameters? Was the calibration a success? 08 0.76 0.13 0.14 part 0.15 0.16 12 chi square 12 11 10 par3 0.78 0.8 0.82 0.04 par2 25
chi square 25 20 15 0.84 0.82 par2 0.8 0.78 0.13 0.14 par1 0.15 0.16 28 26 24 22 20 18 16 14 12
chi square 35 30 25 20 15 12 11 10 par3 9 0.78 0.8 0.82 0.84 par2 35 30 25 20 15
25 20 15 0.84 TT voltage Par1 + Par2 sin | (angleeye - Par3) 180° - Calculate the confidence interval at 68% level for the fit parameters. You'll have to use the grid search method. Plot the x²-value on a grid of pairs of parameters using surf. Programming hint: with [C,~] = contour3(..., 'LevelList', value); you can extract all parameter values for a contour at a certain x²-value. - Calculate the goodness of fit (probability Q that the remaining deviations between model and data are explained by statistical errors). - Plot the data and the resulting fit. Questions: Which model do you think is best? How certain are the models about the estimated parameters? Was the calibration a success? 0.82 08 par2 0.78 0.13 0.14 part 0.15 0.16 12 auenbe sup 30 25 20 15 e - 10 par3 0.78 0.8 0.82 0.84 par2 25
b) Theoretically, the relation between eye angle and voltage should be sinusoidal, with a period of 360°. Fit the data with the following sinusoid, using the y²-function as the cost function and the Simplex method for function minimization Use the same estimated variance of the measurement error for all eye angles as in a). T 180° (angleeye - Par3) voltage = Parl + Par2 * sin - Calculate the confidence interval at 68% level for the fit parameters. You'll have to use the grid search method. Plot the x²-value on a grid of pairs of parameters using surf. Programming hint: with [C,~] = contour3(..., LevelList,value); you can extract all parameter values for a contour at a certain x²-value. - Calculate the goodness of fit (probability Q that the remaining deviations between model and data are explained by statistical errors). - Plot the data and the resulting fit. Questions: Which model do you think is best? How certain are the models about the estimated