Surveying-error theory and the basis of measurement adjustment

Introduction Observation Error Research object of surveying adjustment discipline A brief history and development of measurement adjustment The tasks and contents of this course error distribution and precision index Normal Distribution

One dimensional normal distribution

The probability density of one-dimensional random variable X which obeys normal distribution is

F (x) =12π−−√σ∗e− (x−μ) 22σ2 f (x) =\frac{1}{\sqrt{2π}\sigma}*e^{\frac{-(x-μ) ^2}{2\sigma^2}}

Recorded as x~ N (μ,σ).
Mathematical expectation E (x) =μ of normal random variable x;
Variance D (x) =σ of X

n-dimensional normal distribution

F (x1,x2,..., xn) =1 (2π) n2| Dxx|12∗e− (x−μx) T (x−μx) 2DXX f (X_{1},x_{2},\dots,x_{n}) =\frac{1}{{(2π)}^{\frac{n}{2}}| d_{xx}|^{\frac{1}{2}}}*e^{\frac{-(X-μ_{x}) ^t (X-μ_{x})}{2d_{xx}}}

The mathematical expectation of random vector x μxμ_{x} is:
Μx=μ1μ2