Conference Paper

Adaptive Aircraft Trajectory Prediction using Particle Filters

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... However, in the case of the airspace capacity reduction probability in relation with available slots linked to the Met, statistical information about weather forecasts are needed (see CATS report D1.1 [12]). To take into account this Met uncertainty, a proposed solution was to use statistical errors on weather forecast [6]. Some research works use Gaussian assumptions and prescribed correlation functions [6] for the Met uncertainties. ...
... To take into account this Met uncertainty, a proposed solution was to use statistical errors on weather forecast [6]. Some research works use Gaussian assumptions and prescribed correlation functions [6] for the Met uncertainties. European programs have investigated this type of uncertainty modelling: HYBRIDGE [11], ERASMUS [13]. ...
... Based on the classical parametric prediction method, a variety of improved target trajectory prediction models are constructed. For example, the basic flight model is proposed to predict the track [4]; the track of the moving target is predicted by combining the prediction model of target acceleration, the track deflection angle and the historical track [5]; the continuous prediction of track position is realized by using the dynamic Kalman filter [6]; an improved adaptive particle filter algorithm is proposed to predict the trajectory of civil aviation aircraft [7]. Because the prediction accuracy of single model estimation is poor and the complexity of the multiple model algorithm is high, in order to modify the deficiency, an interactive multiple model algorithm was proposed in [8]. ...
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Target maneuver trajectory prediction plays an important role in air combat situation awareness and threat assessment. To solve the problem of low prediction accuracy of the traditional prediction method and model, a target maneuver trajectory prediction model based on phase space reconstruction-radial basis function (PSR-RBF) neural network is established by combining the characteristics of trajectory with time continuity. In order to further improve the prediction performance of the model, the rival penalized competitive learning (RPCL) algorithm is introduced to determine the structure of RBF, the Levenberg-Marquardt (LM) and the hybrid algorithm of the improved particle swarm optimization (IPSO) algorithm and the k-means are introduced to optimize the parameter of RBF, and a PSR-RBF neural network is constructed. An independent method of 3D coordinates of the target maneuver trajectory is proposed, and the target manuver trajectory sample data is constructed by using the training data selected in the air combat maneuver instrument (ACMI), and the maneuver trajectory prediction model based on the PSR-RBF neural network is established. In order to verify the precision and real-time performance of the trajectory prediction model, the simulation experiment of target maneuver trajectory is performed. The results show that the prediction performance of the independent method is better, and the accuracy of the PSR-RBF prediction model proposed is better. The prediction confirms the effectiveness and applicability of the proposed method and model.
... Current trajectory prediction methods usually adopt the traditional Markov model [2][3][4][5], particle filter algorithm [6,7], simulated annealing algorithm [8] and Kalman filter algorithm [9]. These methods often have the following shortcomings: First, the ship kinematic equations must be established and consideration of hydrological environmental factors such as wind and current greatly increases the modeling complexity and difficulty; Second, according to the needs of marine collision avoidance decision-making, trajectory prediction must often occur in real time. ...
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There are difficulties in obtaining accurate modeling of ship trajectories with traditional prediction methods. For example, neural networks are prone to falling into local optima and there are a small number of Automatic Identification System (AIS) information samples regarding target ships acquired in real time at sea. In order to improve the accuracy of ship trajectory predictions and solve these problems, a trajectory prediction model based on support vector regression (SVR) is proposed. Ship speed, course, time stamp, longitude and latitude from AIS data were selected as sample features and the wavelet threshold de-noising method was used to process the ship position data. The adaptive chaos differential evolution (ACDE) algorithm was used to optimize the internal model parameters to improve convergence speed and prediction accuracy. AIS sensor data corresponding to a certain section of the Tianjin Port ships were selected, on which SVR, Recurrent Neural Network (RNN) and Back Propagation (BP) neural network model trajectory prediction simulations were carried out. A comparison of the results shows that the trajectory prediction model based on ACDE-SVR has higher and more stable prediction accuracy, requires less time and is simple, feasible and efficient.
... For the conflict detection to be accurate, one should be able to compute a reliable prediction of the trajectory of an aircraft [7]. Increasing levels of traffic require systems that can accurately predict conflicts earlier, in order to accommodate the extra traffic demand. ...
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Enhanced accuracy in aircraft conflict detection allows for more efficient use of the airspace and increased safety levels. Trajectory prediction lies at the heart of most conflict detection algorithms. By comparing the predicted trajectories of different aircraft against each other, we can detect real threats while avoiding false alarms. We show how trajectory prediction tools that account for weather forecast errors can improve the performance of a conflict detection scheme. Using information from multiple aircraft at different locations and time instants, wind forecast uncertainties are reduced increasing trajectory prediction accuracy. We present a particle filtering algorithm that can efficiently cope with the high dimensionality and the non-linearity of the problem and show how using this algorithm can improve considerably conflict detection rates in mid and short term horizon encounters.
... A closely related idea to SCPF, for multi-body visual tracking, is the hybrid joint-separable multi-target filter, which also handles targets in an independent way [14]. Related ideas for improving TP by reducing wind uncertainty are explored in15161718. The impact of wind uncertainty on the TP along-track error and the effect of initial conditions is investigated in [15, 19] . ...
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Accurate prediction of aircraft trajectories is an important part of decision support and automated tools in air traffic management. We demonstrate that by combining information from multiple aircraft at different locations and time instants, one can provide improved trajectory prediction (TP) accuracy. To perform multi-aircraft TP, we have at our disposal abundant data. We show how this multi-aircraft sensor fusion problem can be formulated as a high-dimensional state estimation problem. The high dimensionality of the problem and nonlinearities in aircraft dynamics and control prohibit the use of common filtering methods. We demonstrate the inefficiency of several sequential Monte Carlo algorithms on feasibility studies involving multiple aircraft. We then develop a novel particle filtering algorithm to exploit the structure of the problem and solve it in realistic scale situations. In all studies we assume that aircraft fly level (possibly at different altitudes) with known, constant, aircraft-dependent airspeeds and estimate the wind forecast errors based only on ground radar measurements. Current work concentrates on extending the algorithms to non-level flights, the joint estimation of wind forecast errors and the airspeed and mass of the different aircraft and the simultaneous fusion of airborne and ground radar measurements. Copyright © 2010 John Wiley & Sons, Ltd.
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Trajectory prediction plays an important role in modern air combat. Aiming at the large degree of modern simplification, low prediction accuracy, poor authenticity and reliability of data sample in traditional methods, a trajectory prediction method based on HPSO-TPFENN neural network is established by combining with the characteristics of trajectory with time continuity. The time profit factor was introduced into the target function of Elman neural network, and the parameters of improved Elman neural network are optimized by using the hybrid particle swarm optimization algorithm (HPSO), and the HPSO-TPFENN neural network was constructed. An independent prediction method of three-dimensional coordinates is firstly proposed, and the trajectory prediction data sample including course angle and pitch angle is constructed by using true combat data selected in the air combat maneuvering instrument (ACMI), and the trajectory prediction model based on HPSO-TPFENN neural network is established. The precision and real-time performance of trajectory prediction model are analyzed through the simulation experiment, and the results show that the relative error in different direction is below 1%, and it takes about 42ms approximately to complete 595 consecutive prediction, indicating that the present model can accurately and quickly predict the trajectory of the target aircraft.
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Monte Carlo methods are revolutionizing the on-line analysis of data in fields as diverse as financial modeling, target tracking and computer vision. These methods, appearing under the names of bootstrap filters, condensation, optimal Monte Carlo filters, particle filters and survival of the fittest, have made it possible to solve numerically many complex, non-standard problems that were previously intractable. This book presents the first comprehensive treatment of these techniques, including convergence results and applications to tracking, guidance, automated target recognition, aircraft navigation, robot navigation, econometrics, financial modeling, neural networks, optimal control, optimal filtering, communications, reinforcement learning, signal enhancement, model averaging and selection, computer vision, semiconductor design, population biology, dynamic Bayesian networks, and time series analysis. This will be of great value to students, researchers and practitioners, who have some basic knowledge of probability. Arnaud Doucet received the Ph. D. degree from the University of Paris-XI Orsay in 1997. From 1998 to 2000, he conducted research at the Signal Processing Group of Cambridge University, UK. He is currently an assistant professor at the Department of Electrical Engineering of Melbourne University, Australia. His research interests include Bayesian statistics, dynamic models and Monte Carlo methods. Nando de Freitas obtained a Ph.D. degree in information engineering from Cambridge University in 1999. He is presently a research associate with the artificial intelligence group of the University of California at Berkeley. His main research interests are in Bayesian statistics and the application of on-line and batch Monte Carlo methods to machine learning. Neil Gordon obtained a Ph.D. in Statistics from Imperial College, University of London in 1993. He is with the Pattern and Information Processing group at the Defence Evaluation and Research Agency in the United Kingdom. His research interests are in time series, statistical data analysis, and pattern recognition with a particular emphasis on target tracking and missile guidance.
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Book on stochastic processes and filtering theory covering probability theory, Markov processes, linear and nonlinear filters, etc
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Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference are developed. Conditions under which the numerical approximation converges almost surely to the true value with the number of Monte Carlo replications, and its numerical accuracy may be assessed reliably, are given. Importance sampling densities are derived from multivariate normal or student approximations to the posterior density. These densities are modified by automatic rescaling along each axis. The concept of relative numerical efficiency is introduced to evaluate the adequacy of a chosen importance sampling density. Applications in two illustrative models are presented. Copyright 1989 by The Econometric Society.
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An algorithm, the bootstrap filter, is proposed for implementing recursive Bayesian filters. The required density of the state vector is represented as a set of random samples, which are updated and propagated by the algorithm. The method is not restricted by assumptions of linearity or Gaussian noise: it may be applied to any state transition or measurement model. A simulation example of the bearings only tracking problem is presented. This simulation includes schemes for improving the efficiency of the basic algorithm. For this example, the performance of the bootstrap filter is greatly superior to the standard extended Kalman filter
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We present a method to design controllers for safety specifications in hybrid systems. The hybrid system combines discrete event dynamics with nonlinear continuous dynamics: the discrete event dynamics model linguistic and qualitative information and naturally accommodate mode switching logic, and the continuous dynamics model the physical processes themselves, such as the continuous response of an aircraft to the forces of aileron and throttle. Input variables model both continuous and discrete control and disturbance parameters. We translate safety specifications into restrictions on the system's reachable sets of states. Then, using analysis based on optimal control and game theory for automata and continuous dynamical systems, we derive Hamilton-Jacobi equations whose solutions describe the boundaries of reachable sets. These equations are the heart of our general controller synthesis technique for hybrid systems, in which we calculate feedback control laws for the continuous and discrete variables, which guarantee that the hybrid system remains in the “safe subset” of the reachable set. We discuss issues related to computing solutions to Hamilton-Jacobi equations. Throughout, we demonstrate out techniques on examples of hybrid automata modeling aircraft conflict resolution, autopilot flight mode switching, and vehicle collision avoidance
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The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which simply linearises all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterise mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet general...
Sequential Monte Carlo Methods in Practice Rule Optimization for Airborne Aircraft Separation Trajectory synthesis for air traffic automation A game theoretic approach to controller design for hybrid systems
  • A Doucet
  • J F G De Freitas
  • N Gordon
  • R S Schild
  • R Slattery
  • Y Zhao
  • C Tomlin
  • J Lygeros
  • S Sastry
A. Doucet, J. F. G. De Freitas and N. Gordon. Sequential Monte Carlo Methods in Practice. Statistics for Engineering 17 R. S. Schild. Rule Optimization for Airborne Aircraft Separation. PhD thesis, Vienna Technical University, 1998. 18 R. Slattery and Y. Zhao. Trajectory synthesis for air traffic automation. Journal of Guidance, Control and Dynamics, 20:232–238, 1997. 19 C. Tomlin, J. Lygeros, and S. Sastry. A game theoretic approach to controller design for hybrid systems. Proceeding of the IEEE, 88(7):949–969, 2000.
Sequential Monte Carlo Methods in Practice. Statistics for Engineering and Information Science
  • A Doucet
  • J F G De Freitas
  • N Gordon
A. Doucet, J. F. G. De Freitas and N. Gordon. Sequential Monte Carlo Methods in Practice. Statistics for Engineering and Information Science. Springer Verlag, New York, 2001.
User manual for the base of aircraft data (BADA) revision 3.3
  • Eurocontrol Experimental Centre
Eurocontrol Experimental Centre. User manual for the base of aircraft data (BADA) revision 3.3, 2002.
A stochastic hybrid model for air traffic management processes
  • I Lymperopoulos
  • A Lecchini
  • W Glover
  • J Maciejowski
  • J Lygeros
I. Lymperopoulos, A. Lecchini, W. Glover, J. Maciejowski and J. Lygeros. A stochastic hybrid model for air traffic management processes. Technical Report CUED/F-INFENG/TR.572, University of Cambridge, February 2007.
Combined parameter and state estimation in simulation-based filtering
  • J Liu
  • M West
J. Liu and M. West. Combined parameter and state estimation in simulation-based filtering. In J. F.