## 2 Background
### Lidar System Optimization for Control Applications
#### 2.4.2 Optimizing Lidars by Assessing the Accuracy of Simulated Lidar Measurements  
Another strategy for optimizing lidar scan patterns is the direct comparison between simulated lidar measurements and the true variables they are intended to represent, thereby removing the controller from the analysis entirely. [PERSON] et al. (2015) examined how accurately different scan patterns are able to measure yaw misalignment (i.e., the relative wind direction) in stochastic turbulent wind fields with a constant yaw error imposed. By modeling a CW lidar with a focus distance of 100 m, the authors compared the accuracy of measurements from a linear scan pattern sweeping left and right at hub height, a circular scan pattern, and a 2D scan pattern that covers more of the rotor disk area, for cone angles of 15\({}^{\circ}\) and 30\({}^{\circ}\). Using a 10-min averaging time, it was found that the circular scan results in the lowest error. For all scan patterns, the larger 30\({}^{\circ}\) cone angle improves accuracy. However, the authors showed that when horizontal shear is introduced to the wind fields, the accuracy of the wind direction estimates becomes worse; horizontal shear appears similar to yaw misalignment when measurements are constrained to LOS velocities. Returning to longitudinal wind speed measurements, [PERSON] et al. (2016) simulated measurements from circularly-scanning CW and pulsed lidars rotating at the same speed as the 126 m-diameter rotor of the NREL 5 MW reference turbine model ([PERSON] et al., 2016) in stochastic turbulent wind fields. The lidar optimization is made relevant for pitch controlled turbines by analyzing root mean square (RMS) measurement error for the \"blade effective wind speed\", approximated by averaging the longitudinal wind speed along a line representing the blade, weighted by the radially-dependent contribution to aerodynamic torque production. A scan radius near 44 m (70% of the rotor radius (\(R\))) produced the most accurate measurements, in part because the aerodynamic torque production is concentrated near this region of the blade. For the CW lidar model, the optimal preview distance was found to be in the range of 150 to 180 m (1.2 to 1.4 \(D\)), depending on the amount of turbulence. Beyond the optimal preview distance, the amount of spatial averaging increases too much (the effective length that is averaged along the beam scales with the square of the focus distance). For shorter preview distances, the cone angle becomes too large and the measured LOS velocities contain too many contributions from the transverse and vertical wind components, instead of the longitudinal component of interest. For the pulsed lidar, however, the measurement error was found to always improve as preview distance increases because the amount of range weighting along the beam remains constant. Whereas the previous two studies rely on stochastic turbulent wind fields, [PERSON] et al. (2016) simulated lidar measurements using a more physically realistic wind field generated using large-eddy simulation (LES), a computational fluid dynamics (CFD) technique. The LES wind field, with 8 m/s mean wind speed, includes the interaction with a model of an operating NREL 5 MW reference turbine, causing reduced velocities upstream of the rotor in the turbine's \"induction zone\". Wind evolution is also inherently included. Note that wind evolution places an additional penalty on long preview distances due to the decorrelation of the wind. By simulating a hub-mounted 3-beam circularly-scanning CW lidar at (a) the location of the operating turbine and (b) far upstream of the turbine, the impact of the induction zone on measurement quality was investigated. A model-based wind speed estimator, which relies on measured turbine variables to estimate the true wind disturbances, was used to determine the rotor effective wind speed as well as horizontal and vertical shear.