trilateration: one construct, many systems

Trilateration fixes an unknown position by measuring distances to points of known position and intersecting the resulting range circles (or spheres), as opposed to triangulation, which intersects measured angles. In geodetic surveying the arrival of electronic distance measurement made whole trilateration networks practical, and Bomford's Geodesy treats their observation and adjustment. The referent is positioning by the intersection of measured ranges.[1]

Unit

The measured ranges to known stations and the coordinates they yield

Recovery means

Not applicable

Measured by

Solved by intersecting range circles or spheres from known control, refined by least-squares adjustment

Satellite navigation is trilateration carried into space: a receiver measures its distance, the pseudorange, to several satellites of known orbital position and solves for its own three coordinates plus a clock offset by intersecting the resulting spheres. Hofmann-Wellenhof, Lichtenegger, and Wasle's GNSS lays out the measurement model and solution. It is the identical range-intersection construct as in ground surveying, realised with radio signals and carrying a fourth unknown for the receiver clock.[2]

Unit

Pseudoranges to satellites and the receiver's solved coordinates and clock bias

Recovery means

Not applicable

Measured by

Computed from pseudoranges to four or more satellites, solving position and clock bias together

In wireless sensor networks and mobile communications, trilateration locates a node from its estimated distances to several anchor nodes of known position, where those distances are inferred from received signal strength, time of arrival, or time difference of arrival. Sayed, Tarighat, and Khajehnouri's review of network-based wireless location surveys these ranging techniques and their error sources. It is the same range-intersection construct as surveying and satellite navigation, differing only in that the ranges are estimated from radio measurements rather than directly observed.[3]

Unit

Estimated node-to-anchor ranges and the inferred node position

Recovery means

Not applicable

Measured by

Estimated from RSS, ToA, or TDoA ranges to anchor nodes, then solved for the node's position