The use of light detection and ranging (LiDAR) instruments offer many potential benefits to the wind energy industry. Although much effort has been invested in developing such instruments, the fact remains that they provide limited spatio-temporal velocity measurements of the wind field. Moreover, LiDAR measurements only provide the radial (line-of-sight) velocity component of the wind, making it difficult to precisely determine wind magnitude and direction, owing to the so-called 'cyclops' dilemma. Motivated by a desire to extract more information from typical LiDAR data, this paper aims to show that it is possible to accurately estimate, in a real-time fashion, the radial and tangential velocity components of the wind field. We show how such reconstructions can be generated through the synthesis of an unscented Kalman filter that employs a low-order dynamic model of the wind to estimate the unmeasured velocities within the wind field, using repeated measurement updates from typical nacelle-mounted LiDAR instruments. This approach is validated upon synthetic data generated from large eddy simulations of the atmospheric boundary layer. The accuracy of the wind field estimates are validated across a variety of beam configurations, look directions, atmospheric stabilities and imperfect measurement conditions. The main outcome of this paper is a technique that offers the potential to accurately reconstruct wind fields from LiDAR data, overcoming the cyclops dilemma in the process. The ultimate aim of this research is to provide reliable gust detection warning systems to offshore construction workers, in addition to accurate wind field estimates for use in preview turbine pitch control systems.

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