TWO PARAMETER-RETRIEVAL ALGORITHMS OF AIRCRAFT WAKE VORTEX WITH DOPPLER LIDAR IN CLEAR AIR

Aircraft wake is a pair of strong counter-rotating vortices generated behind an aircraft, which might be very hazardous to a flowing aircraft and the detection of which has attracted much attention in aviation safety field. This conference paper introduces two parameter-retrieval algorithms, i.e., Optimization method and Max-min method. They have been integrated into a toolbox and can retrieve the parameters of wake vortex efficiently and robustly.


INTRODUCTION
Aircraft wake vortex is a strong counter-rotating turbulence generated by a flying aircraft. It might be very dangerous for a following aircraft because it may cause the following aircraft to roll out of control. To avoid this hazard, a special flight separation rule was proposed by ICAO, but it is conservative and has limited the flight capacity of airports. Therefore, it is very important to detect the wake vortex in real time to make a compromise between the flight safety and capacity. The Single European Sky Air Traffic Management Research(SESAR) [1] plan in EU and the Next Generation Air Transportation System(NGATS) [2,3] plan in US have also delivered a lot of projects on this issue. Basically, there are two types of sensors for wake vortex detection: Radar and Lidar [4] . For wake vortex generated in clean air, the proposed sensor is Lidar, and the representative parameter-retrieval algorithms include the TV method [5] and the radial velocity method [6][7][8] . We have been studying on the radar characteristics and detection of wake vortex for many years and we recently proposed two methods to retrieve the parameters of aircraft wake vortex, say the Optimization method and the Max-Min method. In this conference paper, we briefly introduce these two methods, and whose performances are verified with simulated and field detection data.

Optimization Method
For Lidar detection of aircraft wake vortex in clear air, the particles to be sensed are the aerosols, which are generally with weak inertia. In this sense, the obtained Doppler velocity is assumed to be approximately the same to that of the ambient velocity. According to this principle, a movement equation [9] is established to connect the Doppler velocity and the parameters of wake vortex, and an optimization method has been proposed to solve the equation well.
The radial velocity of the th i detection cell (equal to and opposite to the doppler velocity, The equation contains six unknowns (OL, OR respectively represent left vortex-core and right vortex-core position), so when we use M detection cells The strengths of this method include: 1. The ground effect of wake vortex has been considered by introducing two imaging vortices in the velocity model.
2. The wake vortex moves while the Lidar beam scans up and down alternately, which leads to distortion of Doppler velocity on the RHI plane. This distortion has been fixed by taking into account the acceleration of wake vortex.
3. The fitting algorithm has been introduced to predict the vortex core positions, which could be very helpful to get robust and accurate retrieval results.

Max-min Method
The difference between the maximum and minimum doppler velocities at different elevation and the same radial distance k R is called "doppler velocity range" [10] The "velocity range" at the center of the vortexcore should be significantly larger than that at other radial distances. Therefore, the "velocity range" at different radial distances is fitted as a double Gaussian curve, and two peak points corresponding to the left and right vortex cores can be obtained. The radial distance from the peak ).
From the Burnham-Hallock velocity model, the tangential velocity of a single vortex whose core located at ( , ) where R is the distance from the detection cell to the vortex-core, i * is the circulation, c r is the vortex-core radius. , thus the effect of background wind is mitigated by the subtraction of the two velocities: being the separation between the two vortex cores. 1 2 [ , ] * * can be easily solved by equation (8).

Wake-Vortex Parameter-Retrieval System
We have developed a comprehensive wake vortex simulation and parameter-retrieval system as shown in Fig. 3. The system can well simulate the dynamics, scattering, echo signal, Doppler spectra, and etc. It can handle the Lidar detection data from a number of different Lidars, for example the Halo Streamline, Wind Cube 400S, WindTracer, etc. The two algorithms have been integrated into the processing system to retrieve the wake vortex parameters from simulated data or field detection data, and good performances have been well verified.

CONCLUSION
This paper introduces two parameter-retrieval method we recently developed, i.e., the optimization method and the Max-Min velocity method. They have been integrated into a software toolbox and the good performances have been well verified. The two methods can be very helpful for real time detection and prediction of wake vortex in air traffic control.