Error propagation analysis for a static convergent beam triple LIDAR

• Published in: Applied numerical mathematics 2020-04, Vol.150, p.1-17
• Main Authors: Holtom, Theodore C., Brooms, Anthony C.
• Format: Article
• Language: English
• Subjects: Converging beam LIDAR; Doppler LIDAR; Doppler vectors; Error propagation formula; Forward error propagation; Measurement error; Velocity reconstruction; Wind turbines; Wind velocity field
• ISSN: 0168-9274; 1873-5460
• DOI: 10.1016/j.apnum.2019.08.020

We consider the matter of how to assess uncertainty propagation for the converging beam triple LIDAR technology, which is used for measuring wind velocity passing through a fixed point in space. Converging beam triple LIDAR employs the use of three non-parallel, non-coplanar, laser beams which are directed from a fixed platform, typically at ground level, that extend to meet at the point at which measurement of velocity is sought. Coordinate values of the velocity are ascertained with respect to unit vectors along the lines of sight of the laser beams (Doppler vectors), which are then resolved in order to determine the velocity in terms of Cartesian coordinates (i.e. with respect to the standard basis). However, if there is any discrepancy between the recorded values of the coordinates with respect to the Doppler unit vectors and/or the perceived angle settings for such vectors with what they really should be, however small, then this will lead to errors in the reconstructed Cartesian coordinates. One aim of this paper is to present the detailed formulae that would be required for the computation of the estimated variances of the reconstructed velocities, calculated on the basis of the error propagation formulae (and to highlight to the practitioner the conditions under which such estimated variances could be relied upon). The other main aim of this paper is to demonstrate that for (various wind profiles and, in particular) certain LIDAR configurations, which can be characterized by an associated parallelepiped with unit edge length, the estimated variances have the potential to be unsuitably large, thus indicating that the reconstructed velocity may be unreliable for gauging the value of the true wind velocity and that the practitioner should avoid such configurations in the measurement campaign.