2.1 Functional model

When approximate values for all unknowns are given the matrix equation

(2.1/1)

where

l :vector of (shortened) observations

v :vector of residuals

A :model matrix

x :vector of unknown parameters (or corrections to the unknowns)

describes the relations between the unknowns and the observations of the system. If we assume a weight matrix P, which describes the stochastic model of the observations, x can be calculated from the normal equation

(2.1/2)

or

(2.1/3)

where

N :normal-equation matrix

n :right side of the normal equation

The solution of this equation is described in Section 2.4.

The present chapter describes which functions in BINGO may be applied according to equation (2.1/2). In doing so, one has to differentiate between:

• image measurements,
• photogrammetric observations and conditions,
• geodetic measurements including ground control points,
• GPS/IMU data, and
• calibration information for the cameras.

All given data and resulting values are, unless otherwise stated, defined in the object space, which is determined by a global coordinate system.

Fig 2.1-1 Point in the object space. P = Position vector,
X = Easting (abscissa), Y = Northing (ordinate), Z = Height