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Sensor Fusion with Normally Distributed Noise

​
number of measurements
1
2
3
4
measurement variances
2
σ
1
5
2
σ
2
10
2
σ
3
10
2
σ
4
10
measurement 1
measurement 2
combined estimate
⊙
⊙
Given
n
unbiased sensor measurements of a scalar quantity, each corrupted by independent, normally distributed noise with variance
2
σ
n
, the likelihood function for the true value (purple, dashed) is also a normal density.
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