State vector (navigation) explained

In navigation, a state vector is a set of data describing exactly where an object is located in space, and how it is moving.

Mathematical representation

A state vector typically will contain seven elements: three position coordinates, three velocity terms, and the time at which these values were valid. Mathematically, in order to describe positions in a N-dimensional space (

R ^{N} ) then a state vector bf{x} belongs to R ^{2N} :

$$\backslash mathbf(t)\; =\; \backslash begin\; x\_1(t)\backslash \backslash \; x\_2\; (t)\backslash \backslash \; x\_3(t)\; \backslash \backslash \; v\_1(t)\; \backslash \backslash \; v\_2\; (t)\; \backslash \backslash \; v\_3\; (t)\; \backslash end$$

or simply

$$\backslash mathbf(t)\; =\; \backslash begin\; \backslash mathbf(t)\; \backslash \backslash \; \backslash mathbf(t)\backslash end$$

where

r = \begin{bmatrix} x _{1} & x _{2} & x _{3} \end{bmatrix} ^{T} is the position vector and v = • r = \begin{bmatrix} v _{1} & v _{2} & v _{3} \end{bmatrix} ^{T} is the velocity vector.

Since there is freedom to choose coordinate systems for position, a state vector may also be expressed in a variety of coordinate systems (e.g. the North east down coordinate system).

See also

• Orbital state vectors