The nature of error ellipsoids and their application to confidence domain problems

Error ellipsoid;  Confidence domain;  probability distribution;  Multivariate analysis

The properties of the error ellipsoids and the representation of spatial point errors were studied. Using probability theory and multivariate analysis as tools, it is proved that the probability of the spatial point error falling into the ellipsoid can be represented by the distribution function and density function of the standard normal distribution. It is proved that the spatial point error can be decomposed into three independent components along the direction of the error ellipsoid main axis, and the decomposition method and example are given. The probability of proving that the point error falls within one side of the error ellipsoid is a constant, which is independent of the tangent point coordinates and can be represented by the standard normal distribution function; The visual expression of point error is discussed, ellipsoid and cuboid confidence domains are established for spatial points, and the calculation formula of confidence level is given.