Normal distribution

The normal (or Gaussian) distribution is a stochastic model commonly used for estimating sensor uncertainty. The law is given by:

 y(x)=\frac{1}{\sigma.\sqrt{2.\pi}} e^ {-\frac{(x-c)^2}{2\sigma^2}  }


  • \sigma is the standard deviation (square root of the variance)
  • c is the center of the gaussian


Here are some examples of normal distributions:

As the sum of probabilities must be equal to one thus the following surface is equal to one:


68, 95 and 99.7% of the surface is included in respectively \sigma, 2.\sigma and 3.\sigma:

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