# Location determination

The determination of position, position determination or localization, also localization , is the determination of the place in relation to a defined fixed point ( reference system ). Location determination in particular is the determination of one's own location , whereas the determination of the position of a distant object is called localization . The mere determination of the presence of an object is called detection.

A location determination usually concerns places in the open air. Such systems are  standardized according to ISO 19762-5 for real-time applications . One of the best-known and most widespread systems is the satellite-based Global Positioning System (GPS), the miniaturization of which enables installation in many smartphones and tablet computers .

Electronic systems (radio-based, optical or acoustic) also enable precise location determination inside buildings . There are some special features of the measurement process between reflective surfaces to be observed .

## geometry

The mathematical methods of location determination are defined by the Euclidean geometry of the plane triangles ( trigonometry ) and the spherical triangles ( spherical trigonometry ). The following mathematical facts exist to determine the location:

• Flat triangles are clearly defined by three sizes, at least one of which is length.
• Ball triangles are clearly defined by four sizes, at least one of which is length.
• Locations on the plane are determined by two variables and a reference variable as well as an orientation variable (angle of rotation).
• Places in space are determined by three sizes and a reference size as well as an orientation.
• Locations on the spherical surface are determined by two quantities and a reference quantity as well as an orientation.
• Locations in the spherical volume are determined by three sizes and a reference size as well as an orientation.

The (ambiguous) determination of a place by a line that goes through this place and that refers to another line, the baseline, is called bearing . For the unambiguous determination of a location by means of bearings, you need exactly two bearings in addition to the baseline known in the direction and two points and the orientation with respect to this baseline. Having more than two bearings can improve accuracy.

The (ambiguous) determination of a place by a line that goes through this place and that includes a metric for the distance is called distance . For the unambiguous determination of a location through distances, in addition to the baseline known in the direction and two points and the orientation with respect to this baseline, exactly two distances are required. More than two distances can improve accuracy.

### Place and location (orientation)

In spatial reference systems , a distinction must be made between location (position in space ) and location ( orientation in space). A body can change its spatial position by twisting it without changing its location and vice versa. The reference system covers both aspects, so that the complete spatial specification of an object requires its location and orientation.

If the location of an object is expanded to include its movement , the times at which the location and position data apply must also be specified.

The use of the terms location (position by specifying the coordinates and their metrics ) and position (orientation of the coordinates and position angle in space) is often blurred, as is the case with descriptions of the calibration. A bearing does not record the location, but only a direction (or an angle) to the targeted location. A distance measurement does not record the position of the object relative to the reference point, but only the distance to this location.

For location purposes, terrestrial navigation mostly only measures positions in a reference system, whereas inertial navigation only measures movement. The necessary integration constants for determining location and position can not be determined directly from measured accelerations and angular velocities in an inertial manner. To do this, you need additional instruments such as gyroscopes looking to the north or, alternatively, magnetic compass and odometer or the determination of the distance covered from the integral of speed measured at certain points over the individual measured times.

• The determination of a place is called location determination or position determination.
• The determination of the location of an object is called positioning or localization.
• The change of an object in place is called a shift or translation .
• The change in the spatial position of an object is called a rotation or rotation .
• Changing an object's location and spatial position is called correct positioning .
• The determination of the movement of an object through several places is called a trace .
• The confirmation of a suspected place by another measuring point using direction finding is confirmed location.

### Local determination and external localization

To specify the term location determination, one denotes

• the determination of the position (location) or path (track) of an object or a signal emanating from an object as an external location,
• the determination of one's own place as determination of one's own location. For example, it defines the location as the intersection of the location lines .

Each location is identified by means of coordinates in a coordinate system or highlighted with other means of description in relation to the environment.

### Methods of location determination

The methods of location determination are as diverse as the subject areas that require them.

• The range goes from the nano range (physics) over a few centimeters (cartometry), 100 km (navigation), 30,000 km (GPS) up to many light years in astronomy.
• The measurement methods are primarily the determination of distances, angles, directions, heights and transit times.
• The coordinates are 1D (as in rail transport or odometry ), 2D (polar, geographic), 3D (spatial), and also 4D for time series .
• The resulting position can be relative or absolute.

### Geodetic location determination

Location determination in the technical sense of geodesy means measuring the position of individual survey points and the course of boundary lines or stratification lines on the earth's surface. The ellipsoid of the earth serves as the global computing surface, and a plane (2D) coordinate system for local tasks . The determination of points is mainly carried out by distance and angle measurement , occasionally also by special base lines . Accordingly, the uniqueness of measurements of further points in a space of the dimension is determined by at least distances . Additional measurements improve the numerical accuracy. ${\ displaystyle n + 1}$${\ displaystyle n}$

## Coordinate systems

Known coordinate systems for location representations can be converted into one another. Previous simplifications in projections or idealizations produce errors in such transformations.

### Planar coordinates (2D)

The use of planar mathematical coordinate systems with a uniform reference point is common:

• Cartesian coordinates for flat surfaces and derived, mostly shifted, grids
• Plane spherical coordinates for the earth's surface and derived, also projected grids

At least three ( ) determining equations are required for a point in a two-dimensional ( ) coordinate network. ${\ displaystyle n = 2}$${\ displaystyle n + 1}$

### Cubic coordinates (3D)

A complete description of a point in space is achieved by a three-dimensional coordinate specification with a radius (or height), latitude ( latitude ) and longitude ( longitude ). For a point in a three-dimensional ( ) coordinate network, at least four ( ) determining equations are required. ${\ displaystyle n = 3}$${\ displaystyle n + 1}$

The technical use of planar coordinate systems on irregularly curved surfaces is not common. Then an approximation for a plane or sphere is used for simplification.

### Polar coordinates

• Direction and distance from a survey point , church , etc.
• Course and distance from / to the next port
• Polar distance only indicates the distance to the reference point, but does not indicate any direction.
• Bearings indicate two directions, but no distance. This is determined using the basic distance between the reference points.

### Mental determination

A mental orientation takes place constantly - unconsciously, intuitively or explicitly, on foot or in a vehicle.

• Position in relation to a known object, such as "3 meters to the right of the entrance gate"
• Position in relation to a known object, such as "facing the entrance gate"
• Position in a grid (geometrical or mental), such as "at the 3rd intersection on the left, 4th house on the right"
• Position in space, such as "100 meters above (uphill) the mountain hut"
• Position in the room, such as "lying on your back, head up the slope, feet pointing towards the mountain hut"
• Position opposite the sun (e.g. "sun behind you")
• Movement next to a neighbor (level)
• Timing like "10 minutes to the beach"

## Important measurement methods for location determination

The type of measurements in question follows automatically from the above .

### Location information in relative coordinates

Relative coordinates are used on bounded areas and in rooms. There one or more reference points are chosen arbitrarily. Individual known points, lines, areas or spaces describe a reference system even without specifying exact coordinates.

### Positioning with index points

In transport logistics, it is often sufficient to register a passage past one place. Then the identity of the object together with the time information of the passage is a validity date for the already known location information of the index point. This applies accordingly to crossing lines, driving on an area or staying in a room.

### Base lines as a reference system and measurement method

In most systems, several measurement methods are used and their results are combined. The following mentions alone do not describe complete measurement methods.

### Distance, angle and height measurement

In general, all known models of measurement technology are used. Because of the large distances and the effect of small angular errors, optical and quasi-optical ( radio ) measurement methods for lengths and angles as well as various time measurement methods for time differences and transit time differences are preferred . In addition, barometric models are used for altitude measurement and dynamic gravimetric and magnetic models are used for north orientation .

Examples of measurement methods used are for the

### Location determination for natural hearing and stereo hearing

The determination of the direction of a heard object is called localization in specialist circles . We localize the sound source through natural hearing and when reproducing the loudspeaker stereophony we localize the phantom sound source , which is called directional localization . This localization heard is not a localization in the usual terminology.

### Geodetic measurement methods

• Lateration, distance of the target object is recorded by optical measurement over a running time and distance networks ( trilateration )
• Angulation: The position of the target object is given by the angle of at least two fixed points to the object and surveying networks ( triangulation )
• Polar method (up to about 500 m)
• Polygon course (about 100 m per measuring point)
• Method of free stationing (using identical, 2 to 3 times measured points)

## Compact solutions

For industrial needs and in service processes, compact solutions are required that deliver sufficient results even under restricted visibility. This includes systems like

• radio frequency identification (RFID) at index points,
• radio-frequency determination of the location within sight.

In connection with the use of passive RFID technology, the possibility is often written that it is suitable for location determination or localization (see search engine results for the word combination “RFID + location determination”). In this respect, each reading device would enable RFID transponders to be located. Basically, however - as the name Radio Frequency Identification suggests - it is only a means of identification using radio signals. Localization can therefore only take place indirectly through the current location of an RFID reader, and even there only in the vicinity of a few meters.

This is in short technical range of the signal and sufficient selectivity of a bulk reading of RFID tags as a bottleneck localization (Engl. Or i-point localization choke point locating ), respectively. Without this brief coincidence of reader and RFID tag (identification), precise statements about identity, time and place would not be possible.

### Dynamic Solutions (RTLS)

With the further development of the RFID technology to the RTLS Real-Time Locating System , approximate localizations would be possible if the distance between the transmitter and receiver (s) can be estimated. Methods of level measurement, error evaluation or runtime measurement come into question . However, the technical applicability is severely restricted by the interference level of other transmitters, multipath propagation, multiple reflections and the attenuation when passing through dielectric masses. Operational applications have so far only been found sporadically, other interests are still few.

### Person tracking systems

There are active RFID transponders (transmitter systems, mostly worn in clothing or sewn in) for people. In connection with the infrastructure of a person tracking system, they serve to protect people at risk or to improve processes carried out by people.

A temporary assignment of a marked object to a person does not yet localize this person due to the lack of identification of the person. Descriptions to the contrary belong in the categories of amateur false statements or intentional misinterpretation. Simply creating a connection between the terms RFID and location does not change the technical possibilities determined by physics. On the other hand, RFID technology is considered to be explosive, which is not justified by its technical performance alone.

Active radio-frequency transmitters, for example, trigger a signal when the person in care leaves care facilities. It is not possible with all monitoring techniques to install transmitters under the skin, as the transmission signal is partially weakened by the water content of the skin. However, passive personal monitoring using subcutaneously implanted RFID chips is possible.

All solutions of this kind require the consent of those involved or affected or their legal representatives. The admissibility of locating people who are under curative or legal supervision is controversial . The balancing of protection and control interests against the right to informational self-determination is easiest to secure through the voluntary consent of the carrier. In all other cases, a neutral or an authorized body should make the appropriate decisions.

The view of the guardianship courts on the admissibility and the need for approval as a measure depriving liberty (§ 1906 BGB) is different. This question was answered in the affirmative by AG Hannover, BtPrax  1992, 113; AG Bielefeld, BtPrax 1996, 232; AG Stuttgart-Bad Cannstatt FamRZ  1997, 704. In a new decision the Higher Regional Court of Brandenburg speaks out against the authorization requirement of the transmitter chip as such: It is subject to authorization if it is clear that freedom-restricting measures are actually being taken in the facility (OLG Brandenburg FamRZ 2006 , 1481).

The open political discussion on this topic in Germany lags far behind the social discourse in neighboring countries. In Austria it is common to use small transponders on all lifts. In the USA, every patient in the hospital is increasingly tagged with a transponder. The safety advantages for operation, treatment and rescue are many.

### Device location systems

There are transponders (transmission systems, mostly hidden) for devices. These work in conjunction with the infrastructure of a device tracking system for theft protection .

The transmitters trigger a signal if, for example, devices are removed from the permitted area of ​​use through improper transport (theft, unauthorized loan, unpaid purchase, unrelated shipment). It is impossible to install transmitters under metal surfaces because the transmission signal is weakened by the metal layer.

## Positioning algorithms

• Proximity Sensing: The method is based on the simple idea of ​​several distributed receivers whose positions are known. The position of the object to be located is then approximately the same as the coordinates of the closest receiving antenna. This procedure forms the basis for the positioning of all cell-based systems that offer location-based services , such as B. Cellular , GSM and UMTS .
• (Circular / hyperbolic) trilateration : Approximation of the coordinates of the target object by comparing the signal transit times at the end device, given several transmitters. In 2D space, three signal transmitters are required to determine the exact position; in 3D space, at least four transmitters are required in order to be able to calculate the position exactly. This method is used by satellite navigation systems such as GPS and Galileo .
• Dead Reckoning ( dead reckoning ): Are initial coordinates of the own vehicle (ship, air) known, with speed and direction ( course ) the position be determined at any time. Use in systems with mobile devices that permanently change their position ( flight monitoring , OBU2 , GIS measuring vehicles)
• Complex geodetic software: