Measurements are drawn from a Gaussian distribution with variance \sigma^2σ 2 . Which of the estimators below will provide the best estimate of the true value of a parameter

Module 1: Graded Quiz >>> Measurements are drawn from a Gaussian distribution with variance \sigma^2σ 2 . Which of the estimators below will provide the best estimate of the true value of a parameter >>> State Estimation and Localization for Self-Driving Cars

 

 

Correct! By definition, a maximum likelihood estimator will find the parameter value with the greatest likelihood of being the ‘true’ value. ML and LS estimators are equivalent in this case.

Correct! Since all of the variances are identical, ordinary least squares can be used.

Correct! Even when all variances are identical, weighted least squares can be applied.

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Correct! Even if the measured value is static, a disturbance affecting the sensor (e.g., unmodeled vibrations or someone moving the sensor) might cause significantly different measurements to be produced.

Correct! If the measured value is changing (e.g., perhaps switching between two discrete values), the histogram will have multiple peaks.

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Correct! Outliers are not well handled by least squares estimators, since these estimators minimize the sum of squared errors.

Correct! The Central Limit Theorem states that when a noise comes from a large number of independent sources, the noise distribution will tend towards a Gaussian distribution.

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Correct! The distribution of the measurements is clearly not Gaussian, which suggests that least squares will do a poor job.

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