C9.2 Towards the Assessment of the Accuracy of Measuring the Integral Characteristics of Physical Quantities Using the Sensors of Discrete Values of these Quantities

Using the average air temperature along the trace for atmospheric correction in laser ranging: accuracy analysis

“…with extremum T L/2 = T(x=L/2) at the middle point of the trace x =L/2 and the same air temperature values at the end points T(x=0) = T(x=L) = T 0 . The conditions, under which a similar non-monotonic profile is realized in practice, are typical for measurements on an inhomogeneous underlying surface with landwater-land areas, but in some cases, it is also possible for traces passing only over land [4,7,8]. Formula (8), accounting for dependence T(x) assumed according to (11), takes the form The estimation by formula (12) was performed for T 0 = 293.15 K, P = 1013.25 hPa, e = 13.33 hPa, T L/2 = 291.15 K, i.e.…”

On the accuracy of the gradient method for determining the mean integral refractive index of air for large-scale dimensional measurements

“…The main issues that are considered within this method are formulated in publications [5][6][7]: a) what models justify the possibility of using the sensors of meteorological parameters of the atmosphere to determine the mean integral index of the air refraction, b) what are the requirements for the number of discrete points of the trace on which the sensors should be placed, c) what are the requirements for the accuracy characteristics of the sensors.…”

“…The approach developed in [5][6][7] is rigorous from a metrological point of view. This approach can be considered an addition to the examples set out in the Guide [8] in terms of measurement models for integral (averaged over the spatial coordinate) quantities, for example, temperature, refractive index of air, etc.…”

“…In equation (1), σ is a ray coordinate counted along the signal trajectory of length L. In general, this trajectory is curved due to the refraction effect. However, in the case of lengths up to 5 km long, the refractive curvature of the trajectory is negligibly small (the trajectory virtually coincides with a straight line passing through the end points of the trace), so the coordinate counted along a straight line of length L connecting the end points (σ 0 = 0, σ L = L) of this trace can be considered a ray coordinate σ [6].…”

“…According to [6], the expanded uncertainty of length measurements less than 1 mm for traces of up to 5 km long will be provided if the value is determined with an uncertainty not exceeding ~10 -7 . Further, we will discuss possible variants to realise this requirement by the considered method.…”