Editing True-range multilateration (section)

=== One-time application versus repetitive application ===

This article largely describes 'one-time' application of the true-range multilateration technique, which is the most basic use of the technique. With reference to Fig. 1, the characteristic of 'one-time' situations is that point '''P''' and at least one of '''C1''' and '''C2''' change from one application of the true-range multilateration technique to the next. This is appropriate for surveying, celestial navigation using manual sightings, and some aircraft DME/DME navigation.

However, in other situations, the true-range multilateration technique is applied repetitively (essentially continuously). In those situations, '''C1''' and '''C2''' (and perhaps '''Cn, n = 3,4,...''') remain constant and '''P''' is the same vehicle. Example applications (and selected intervals between measurements) are: multiple radar aircraft surveillance (5 and 12 seconds, depending upon radar coverage range), aerial surveying, Loran-C navigation with a high-accuracy user clock (roughly 0.1 seconds), and some aircraft DME/DME navigation (roughly 0.1 seconds). Generally, implementations for repetitive use: (a) employ a 'tracker' algorithm<ref name="Bar-Shalom">''Tracking and Data Fusion: A Handbook of Algorithms''; Y. Bar-Shalom, P.K. Willett, X. Tian; 2011</ref> (in addition to the multilateration solution algorithm), which enables measurements collected at different times to be compared and averaged in some manner; and (b) utilize an iterative solution algorithm, as they (b1) admit varying numbers of measurements (including redundant measurements) and (b2) inherently have an initial guess each time the solution algorithm is invoked.