ENBIS-16 in Sheffield

11 – 15 September 2016; Sheffield Abstract submission: 20 March – 4 July 2016

Accounting for Refractive Index Effects in Multilateration

14 September 2016, 09:20 – 09:40


Submitted by
Alistair Forbes
Alistair Forbes (National Physical Laboratory), Ben Hughes (National Physical Laboratory), Andrew Lewis (National Physical Laboratory)
Laser interferometry is used extensively in length metrology. The operational principle is based on a laser beam sent out from a measuring station and reflected back by a target to interfere with the outgoing beam. Changes in the length of the optical path can be estimated by counting the interferometric fringes. If three or more beams are fixed on a single reflecting target then the location of the target in three dimensions can be estimated, a process known as multilateration. The fringe counts measure the (change in the) optical path length and in order to convert to the (change in the) geometric path length it is necessary to know the average refractive index of the air along the path. The refractive index of air depends primarily on temperature, pressure and humidity, in order of relative importance, and the average refractive index is usually inferred from measurements of temperature and pressure at a small number of locations within the measuring volume. Most multilateration systems assume that the estimated geometric path length derived from the mean refractive index is a sample from a Gaussian distribution centred on the true geometric path and that the measurements of path lengths are statistically independent. However, the refractive index field is likely to be spatially correlated so that mean refractive indices along nearby paths are similar. This paper discusses ways of modelling the refractive index field, the correlating effect of refractive index on the estimates of path lengths and target locations and the evaluation of measurement uncertainty associated with multilateration systems.

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