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Question

Two sensors have measurement errors that are Gaussian distributed with zero means and variances σ21 and σ22, respectively. The two sensor measurements x1 and x2 are combined to form the weighted average x=αx1+(1α)x2, 0α1. Assuming that the measurement errors of the two sensors are uncorrelated, the weighting factor α that yields the smallest error variance of x is

A
σ22σ21+σ22
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B
σ21σ21+σ22
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C
σ2σ1+σ2
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D
0.5
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Solution

The correct option is A σ22σ21+σ22
σ22σ21+σ22

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