State vector (navigation)

Template:Unreferenced 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.Template:Citation needed Mathematically, in order to describe positions in a N-dimensional space (${ℝ}^N$) then a state vector $\mathbf{\text{x}}$ belongs to ${ℝ}^{2N}$:

$$𝐱(t)=\left[\begin{array}{c}{x}_1(t)\\ x_2(t)\\ x_3(t)\\ v_1(t)\\ v_2(t)\\ v_3(t)\end{array}\right]$$

or simply

$$𝐱(t)=\left[\begin{array}{c}𝐫(t)\\ 𝐯(t)\end{array}\right]$$

where $𝐫={\left[\begin{array}{ccc}{x}_1& x_2& x_3\end{array}\right]}^{𝖳}$ is the position vector and $𝐯=\dot{𝐫}={\left[\begin{array}{ccc}{v}_1& v_2& v_3\end{array}\right]}^{𝖳}$ 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