Wind field evaluation by using radar data and vector spline interpolation

Accurate wind magnitude and direction estimation is essential for aircraft trajectory prediction. The wind data which are currently available through meteorological service broadcast suffer from small measurement rate with respect to location and time. In this paper, a new wind estimation method based on radar track measures is proposed. When on board true air speed measures are available, a linear model is developed for which a Kalman filter is used to produce high quality wind estimate. When only aircraft position measures are available, an observability analysis shows that wind may be estimated only if trajectories have one or two turns depending of the number of aircraft located in a given area. Based on this observability conditions, closed forms of the wind has been developed for the one and two aircraft cases. By this mean, each aircraft can be seen as a wind sensor when it is turning. After performing these pointwise evaluations in realistic frameworks, our approach is now to estimate the wind vector field at any point. Based on those local wind estimates,a global space-time wind field estimation is derived by vector spline interpolation, or by solving Shallow-Water equations, which assumes geostrophic wind. The accuracy of this wind map is dependent of the number wind estimates in a given zone. Numerical tests show the efficiency of the method.