A Deterministic VOR Error Modeling Method—Application to Wind Turbines

Abstract

VOR devices are sensitive to multipath. These perturbations yield an error on the azimuth information received by the aircraft. This article presents a simulation method to estimate the impact of the environment on the received VOR signal. This method uses a two-ray model and a hybridisation between parabolic equation (PE) and physical optics (PO). The direct field between the VOR station and the aircraft is given by a two-ray model, PE is used to compute the propagation between the VOR station and the obstacles, and PO is used to compute the scattered field. Finally, the VOR error is deduced from the direct and the scattered fields. The hybridisation between PE and PO is performed as follows: the obstacles are meshed and the PE incident field is cast as a plane wave on each facet to efficiently compute the scattered field. The simulation method is confronted to in-flight measurements in the presence of a wind farm around a VOR station in Boulogne-sur-Mer, France. The maximum VOR error along the trajectories is retrieved within 1.1 degree and the statistical behaviour is reproduced. The standard deviation is within 0.3 degree, and the skewness and Kurtosis differ of less than 2 between simulations and measurements. Finally, parametric studies performed with this method show that the rotor-blades can be neglected in this scenario. It is also shown that the knowledge of the aircraft trajectory is of major importance to predict or reproduce VOR error measurements.

Probabilistic VOR error due to several scatterers — Application to wind farms

“…All the following numerical simulations are performed using PEPO method (hybridisation parabolic wave equation / physical optics) [4]. The application cases involve wind farms near a CVOR station.…”

“…In the numerical simulations presented in this paper, they are calculated with a deterministic method based on a hybridisation between physical optics and parabolic equation solved by split-step Fourier [4]. However, any method giving the a n (or an overestimation of the a n ) can be used.…”

“…Some of them include a simple model of the CVOR (Conventional VOR) receiver [1] to quantify the VOR error [2], [3], [4]. They suppose the knowledge of the amplitude and phase of each multipath.…”

“…The drawback of these approaches is that the obtained VOR error is deterministic. Therefore, the unavoidable uncertainties on the phases make the VOR error hard to interpret [4].…”

A method for computing the VOR multipath error - comparisons with in-flight measurements

“…The hybridisation method is detailed in Claudepierre et al [12]. The main advantages are to considered the antenna radiation pattern and the relief between the VOR antenna and the wind turbines.…”