Surveying-Error theory and measurement adjustment basis

Introduction Observation Error the research object of surveying adjustment subject A brief history and development of measurement adjustment tasks and content of this course error distribution and accuracy index Normal Distribution

One-dimensional normal distribution

The probability density of a one-dimensional random variable X that obeys a 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).
The mathematical expectation of the normal random variable x is E (x) =μ;
Variance of x D (x) =σ

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