State Vector (geographical)

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 ($\mathbb^N$) then a state vector $\textbf$ belongs to $\mathbb^$:

$\mathbf(t) = \begin x_1(t)\\ x_2 (t)\\ x_3(t) \\ v_1(t) \\ v_2 (t) \\ v_3 (t) \end$

or simply

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

where $\mathbf = \begin x_1 & x_2 & x_3 \end^\mathsf$ is the position vector and $\mathbf = \dot = \begin v_1 & v_2 & v_3 \end^\mathsf{T}$ 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

Navigation