Model-Based Trajectory Reconstruction using IMM Smoothing and Motion Pattern Identification 1 Jesús García Computer Science Department-GIAA Universidad Carlos III de Madrid Colmenarejo, Spain jgherrer@inf.uc3m.es José M. Molina Computer Science Department-GIAA Universidad Carlos III de Madrid Colmenarejo, Spain molina@ia.uc3m.es Juan A. Besada Signal Systems and Radio-communications Department-GPDS Universidad Politécnica de Madrid, Spain besada@grpss.ssr.upm.es Gonzalo de Miguel Signal Systems and Radio-communications Department-GPDS Universidad Politécnica de Madrid, Spain gonzalo@grpss.ssr.upm.es 1 Fund e d b y p ro je c ts C IC YT TSI2005-07344, C IC YT TEC 2005-07186 a nd C AM MADRINET S- 0505/ TIC / 0255 Abstract - This work addresses off-line accurate trajectory reconstruction for Air Traffic Control. We propose the use of specific dynamic models after identification of regular motion patterns. Datasets recorded from opportunity traffic are first segmented in motion segments, based on the mode probabilities of an IMM filter. Then, reconstruction is applied with an optimal smoothing filter operating forward and backward. The parameters describing the specific modes are estimated and then used as external input for smoothing filters. The performance of this approach is compared with a method based on interpolation B- splines. Comparative results on simulated and real data are discussed at the end. Keywords: Trajectory reconstruction, data smoothing, air traffic control, real-data validation. 1 Introduction Data-processing systems operating in critical applications such as Air Traffic Control (ATC) [1,2] require from validation with real data. Performance assessment of ATC centres by means of recorded datasets (also named opportunity traffic) requires as a previous step the reconstruction of trajectories. This reconstruction process provides the unknown ground truth to be used as reference in the evaluation. However, both data processing and trajectory reconstruction can be considered as estimation problems. The only difference is that ATC processors operate in real time (data is processed in a single forward sequence as measurements become available), while the reconstruction, or smoothing, is a batch process which makes use of all available data. Therefore, the reconstruction performed off-line over recorded data files can be formulated as a special multi- sensor fusion process. The particular aspect is the advantage of knowledge about both past and future target position reports to improve the performance of classification and estimation algorithms. A theoretically optimal approach consists in a double tracking loop in the forward and backward directions for smoothing [3,4]. The use of multiple-model to this end has been also proposed in [5]. Furthermore, data smoothing has been tackled from others points of view. Basically, one may either choose to create a parametric model or a nonparametric model for fitting trajectory data. In non-parametric models, a free equation such as a polynomial curve or a fixed neural network architecture is selected as basic shape of the model curve. Then the curve is optimized for smoothness, while minimizing error against the sampled data points in both position and velocity. However, if a parametric representation is a priori known for the motion being modelled (parabolic motion for a falling object, coordinated turn for regular flight motion, etc.), then well established estimation methods may be used. Splines are the most used methods for non-parametric data fitting, in cases were accurate models of the motion are not available, particularly when modelling human or terrain robots movement. Following the second formulation, in this work we propose the use of IMM tracking filters to this end, Model-Based Reconstruction (MBR), exploiting physical motion models usually performed by aircraft flying in controlled airspace. It is based on the segmentation of trajectory in regular motion segments : Uniform motion, Transversal manoeuvre, Longitudinal manoeuvre, Combined manoeuvre. Then, an accurate reconstruction can be performed now using trajectory interpolation accordingly to the models identified in the flight. In this study we develop a reconstruction architecture based on this ideas and compare with an nonparameteric method as previously used in ATC [1,2]. Comparative results on simulated and real data are discussed to compare both approaches in this specific domain. Next section reviews basis of spline approximation and section 3 presents the proposed structure to process available data and generate reconstruction. Section 4 presents the results obtained with simulated and real