# Study of Urban Unmanned Aerial Vehicle Separation in Free Flight Based on Track Prediction
## 1 Introduction
The gas model was initially proposed in the 1970s. [PERSON] et al. [13] estimated the collision risk for manned aircraft by simplifying assumptions about aircraft behavior, ideally setting and quantifying the collision risk among uniformly distributed aircraft within a region. This model was later expanded by [PERSON] et al. [14], who determined the collision rate at the intersection of two flight paths. [PERSON] [15] and [PERSON] et al. [16] introduced an expanded version of the gas model to assess the collision risk between UAVs and manned aircraft. [PERSON] et al. [17] evaluated the collision risk within a UAV swarm. Joint Authorities for Rulemaking on Unmanned Systems (JARUS) released a revised specific operations risk assessment (SORA) guide [18] in 2019, guiding operators in the qualitative assessment of UAV risk. [PERSON] [19] from DLR compared the traditional civil aviation qualitative risk assessment methods with the SORA method proposed by JARUS. In 2019, [PERSON] et al. [20] conducted a collision risk comparison before and after introducing UAVs into manned aircraft airspace in assumed operational scenarios without considering certain factors, such as controller and pilot operation. [PERSON] et al. [21] reviewed typical collision risk models in the UAV collision risk assessment field, looking forward to these models' application and extension in setting UAV operational lateral separations. [PERSON] et al. [22] improved the classic EVENT model, proposing a collision risk model suitable for UAVs. In 2021, SESAR's [23] European Horizon BUBBLES project conducted separation assessments based on the SORA risk model and Monte Carlo simulation. [PERSON] et al. [24], based on the EVENT model, assessed the lateral collision risk between military and civilian aircraft and military UAVs and civilian aircraft. [PERSON] et al. [25], considering the potential safety conflicts caused by multiple logistics UAVs' flying routes in the future, proposed planning safe separations between UAVs to avoid operational risk and, based on the TLS, calculated the minimum safe separation for some logistics routes. It is known that using machine learning models for track prediction based on historical aircraft tracks has become the mainstream approach. Existing research focuses on similar track data or specific flight phases to construct track prediction models, where balancing prediction length and accuracy is challenging and mostly used for short-term predictions. For air collision risk assessment and separation settings for urban logistics UAV flight activities, existing studies can mostly be divided into two schemes. One uses gas models and Monte Carlo methods for collision risk assessment and separation setting, and the other introduces manned aircraft collision risk assessment and separation formulating methods, thus decomposing UAV movement into longitudinal, lateral, and vertical dimensions for formulating separation individually. Neither scheme fully reflects the free flight mode or inherent capability of UAVs. This study is divided into two parts. Firstly, based on historical data, the issue of track prediction is studied. Using a machine learning model, a two-stage track prediction method of classification followed by prediction is proposed for urban logistics UAV track data in a certain area. First, K-means is applied for track identification and categorizing tracks based on UAV speed, flight altitude, latitude, and longitude. Then, the Adam-LSTM deep learning model is designed for detailed prediction of each type of track. Through a large number of predictions, the distribution function of prediction errors can be organized. Afterwards, based on track prediction error distribution, by designing the gas model and position error probability model, a separation calculation model for urban logistics UAVs is proposed.