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

⊙

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.