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 Position often refers to: * Position (geometry), the spatial location (rather than orientation) of an entity * Position, a job or occupation Position may also refer to: Games and recreation * Position (poker), location relative to the dealer * ...

coordinates, three

velocity Velocity is a measurement of speed in a certain direction of motion. It is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of physical objects. Velocity is a vector (geometry), vector Physical q ...

terms, and the

time Time is the continuous progression of existence that occurs in an apparently irreversible process, irreversible succession from the past, through the present, and into the future. It is a component quantity of various measurements used to sequ ...

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 system In geometry, a coordinate system is a system that uses one or more numbers, or coordinates, to uniquely determine and standardize the position of the points or other geometric elements on a manifold such as Euclidean space. The coordinates are ...

s (e.g. the North east down coordinate system).

Mathematical representation

See also