State vector (geographical)
Encyclopedia
A geographical state vector
is a set of data describing exactly where an object is located in space, and how it is moving. From a state vector, the object's current and future position can be determined.
A geographical state vector typically will contain seven elements: three position coordinates, three velocity
terms, and the time
at which these values were valid.
A state vector may be expressed in a variety of coordinate system
s. Selection of a coordinate system depends on what makes sense for the problem being solved. In aviation
, a state vector may be expressed in the North, East, Down coordinate system, where North position is expressed as a latitude
, East position as a longitude
, and Down represents the negative of altitude
. (Down is used instead of Up to conform to the right-hand rule
. The velocity components of the state vector would be North velocity, East velocity, and vertical speed.
State vector
*A state vector in general control systems describes the observed states of an object in state space, e.g. in variables of the degrees of freedom for motion *A state vector in general control systems describes the observed states of an object in state space, e.g. in variables of the degrees of...
is a set of data describing exactly where an object is located in space, and how it is moving. From a state vector, the object's current and future position can be determined.
A geographical state vector typically will contain seven elements: three position coordinates, three velocity
Velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...
terms, and the time
Time
Time is a part of the measuring system used to sequence events, to compare the durations of events and the intervals between them, and to quantify rates of change such as the motions of objects....
at which these values were valid.
A state vector may be expressed in a variety of coordinate system
Coordinate system
In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by...
s. Selection of a coordinate system depends on what makes sense for the problem being solved. In aviation
Aviation
Aviation is the design, development, production, operation, and use of aircraft, especially heavier-than-air aircraft. Aviation is derived from avis, the Latin word for bird.-History:...
, a state vector may be expressed in the North, East, Down coordinate system, where North position is expressed as a latitude
Latitude
In geography, the latitude of a location on the Earth is the angular distance of that location south or north of the Equator. The latitude is an angle, and is usually measured in degrees . The equator has a latitude of 0°, the North pole has a latitude of 90° north , and the South pole has a...
, East position as a longitude
Longitude
Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. It is an angular measurement, usually expressed in degrees, minutes and seconds, and denoted by the Greek letter lambda ....
, and Down represents the negative of altitude
Altitude
Altitude or height is defined based on the context in which it is used . As a general definition, altitude is a distance measurement, usually in the vertical or "up" direction, between a reference datum and a point or object. The reference datum also often varies according to the context...
. (Down is used instead of Up to conform to the right-hand rule
Right-hand rule
In mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicist John Ambrose Fleming in the late 19th century....
. The velocity components of the state vector would be North velocity, East velocity, and vertical speed.