A spatiotemporal estimation framework for real-world LIDAR wind speed measurements

Despite significant advances in the remote sensing of fluid flows, light detection and ranging (LIDAR) measurement equipment still presents the problems of having only radial (line-of-sight) wind speed measurements (Cyclops' dilemma). Substantial expanses of unmeasured flow still remain and range weighting errors have a considerable influence on LIDAR measurements. Clearly, more information needs to be extracted from LIDAR data. With this motivation in mind, this brief shows that it is possible to estimate the wind velocity, wind direction, and absolute pressure over the entire spatial region of interest. A key challenge is that most established estimation techniques cater for systems that are finite-dimensional and described by ordinary differential equations (ODEs). By contrast, many fluid flows are governed by the Navier-Stokes equations, which are partial differential-algebraic equations (PDAEs). We show how a basis function decomposition method in conjunction with a pressure Poisson equation (PPE) formulation yields a spatially continuous, strangeness-free, reduced-order dynamic model for which a modified DAE form of the unscented Kalman filter (UKF) algorithm is used to estimate unmeasured velocities and pressure using sparse measurements from wind turbine-mounted LIDAR instruments. The approach is validated for both synthetic data generated from large eddy simulations of the atmospheric boundary layer and real-world LIDAR measurement data. Results show that a reconstruction of the flow field is achievable, thus presenting a validated estimation framework for potential applications including wind gust prediction systems and the preview control of wind turbines.