Hyperbolic navigation

The term hyperbolic or Hyperbelortung geometric- physical methods of localization are summarized in which either

• Distances between discrete points are measured. This exploits that the received energy E is approximately inversely proportional to the distance d decreases ( d ~ 1 / E)
• Or by utilizing the Doppler effect velocity measurements over time are integrated.

Each tuple several measurements provides a locus for the position of the observer (i.e., its receiver ), when the locations of the transmitters (or the transponder be answered ) are known. The M number of necessary measurements is at least 1 greater than the dimension n of the model ().

Geometry of the transmitter and receiver positions

Usually, these transmitters or transponders are

• Fixed beacon on the earth's surface - whose coordinates are known so -
• Or installed on artificial earth satellite radios - whose position can be determined from the orbital elements of the satellite orbit or directly from on-line Rail Regulations of solid ground stations.

The geometric location of each measured distance difference ( on defined areas known as state lines ) are:

• Hyperbolas, when the geometric location of all transmitter and receiver can be given by a plane or approximated by them (ie on limited parts of the earth's surface ). The foci of this hyperbola coincide with the positions of the transmitters.
• Rotationshyperboloide when the geometric problem can not be solved at the level, but in 3D space. In the two focal points of each hyperboloid again contains one each of the transmitter or transponder (code - responders ).

Solution on the surface of the earth or in space

In the planar problem (eg in the near- and medium-range navigation with HIFIX or DECCA ) satisfy 3 transmitters - which just two hyperbolas results - and the clear reception of their encoded signals. The location of the receiver is derived from the intersection of the two hyperbolic position lines. The third locus is generally the earth's surface or ( in navigation) the leaf ( leaves ) of a chart or an appropriate aeronautical chart (see ICAO and Decca cards).

When spatial average are 4 stations (that is, 4 satellite positions ) is required, must be calculable with sufficient accuracy. Is a location to only about ± 1 km, one finds with current as possible ( " osculating " ) orbital elements the Auslangen (5 geometric elements, a time stamp and a previous two rotational speeds due to the Earth flattening ). If the accuracy be higher, one must take into account up to some 100 orbital parameters and the small irregularities of the earth's rotation.

Relevant methods with inaccurate tracks

• Simultaneous measurements ( on-line measurement campaigns ) on multiple ground stations; more closely with
• Strongly over-determined geometric network ( more than about eight simultaneously measured ground stations )
• Complement the Doppler by runtime measurements (LASER, SLR)
• Short arc methods ( adjustment of the calculated path shape toward a path that satisfies the requirements of celestial mechanics )
• DOI orbit determination programs, such as the software of the Geodesy Institute in Hanover or the Bernese software in the global GPS system. Doppler radar (two measuring principles ) in the navigation (speed over ground) and traffic monitoring ( precision radar)
• Doppler satellite - see also NNSS and NOVA and DORIS
• Doppler sonography in medicine and technology
• Doppler measurement