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Probabilistic Conflict Detection for Piecewise Straight Paths
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2008 (English)In: Automatica, ISSN 0005-1098Article in journal (Refereed) Submitted
Abstract [en]

We consider probabilistic methods for detecting conflicts as a function of predicted trajectory. A conflict is an event representing collision or imminent collision between vehicles or objects. The computations use state estimate and covariance from a target tracking filter based on sensor readings. Existing work is primarily concerned with risk estimation at a certain time instant, while the focus here is to compute the integrated risk over the critical time horizon. This novel formulation leads to evaluating the probability for level-crossing. The analytic expression involves a multi-dimensional integral which is hardly tractable in practice. Further, a huge number of Monte Carlo simulations would be needed to get sufficient reliability for the small risks that the applications often require. Instead, we propose a sound numerical approximation that leads to evaluating a one-dimensional integral which is suitable for real-time implementations.

Place, publisher, year, edition, pages
Elsevier, 2008.
Keyword [en]
Probability, Conflict, Detection, Level-crossing
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-15830OAI: diva2:127532
Available from: 2008-12-08 Created: 2008-12-08 Last updated: 2013-07-23Bibliographically approved
In thesis
1. Efficient Estimation and Detection Methods for Airborne Applications
Open this publication in new window or tab >>Efficient Estimation and Detection Methods for Airborne Applications
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The overall purpose with this thesis is to investigate and provide computationally efficient methods for estimation and detection. The focus is on airborne applications, and we seek estimation and detection methods which are accurate and reliable yet effective with respect to computational load. In particular, the methods shall be optimized for terrain-aided navigation andcollision avoidance respectively. The estimation part focuses on particle filtering and the in general much more efficient marginalized particle filter. The detection part focuses on finding efficient methods for evaluating the probability of extreme values. This is achieved by considering the, in general, much easier task to compute the probability of level-crossings.

The concept of aircraft navigation using terrain height information is attractive because of the independence of external information sources. Typicallyterrain-aided navigation consists of an inertial navigation unit supported by position estimates from a terrain-aided positioning (TAP) system. TAP integrated with an inertial navigation system is challenging due to its highly nonlinear nature. Today, the particle filter is an accepted method for estimation of more or less nonlinear systems. At least when the requirements on computational load are not rigorous. In many on-line processing applications the requirements are such that they prevent the use of theparticle filter. We need more efficient estimation methods to overcome this issue, and the marginalized particle filter constitutes a possible solution. The basic principle for the marginalized particle filter is to utilize linear and discrete substructures within the overall nonlinear system. These substructures are used for efficient estimation by applying optimal filters such as the Kalman filter. The computationally demanding particle filter can then be concentrated on a smaller part of the estimation problem.

The concept of an aircraft collision avoidance system is to assist or ultimately replace the pilot in order to to minimize the resulting collision risk. Detection is needed in aircraft collision avoidance because of the stochastic nature of thesensor readings, here we use information from video cameras. Conflict is declared if the minimum distance between two aircraft is less than a level. The level is given by the radius of a safety sphere surrounding the aircraft.We use the fact that the probability of conflict, for the process studied here, is identical to the probability for a down-crossing of the surface of the sphere. In general, it is easier to compute the probability of down-crossings compared to extremes. The Monte Carlo method provides a way forward to compute the probability of conflict. However, to provide a computationally tractable solution we approximate the crossing of the safety sphere with the crossing of a circular disc. The approximate method yields a result which is as accurate as the Monte Carlo method but the computational load is decreased significantly.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2009. 66 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1231
National Category
Signal Processing
urn:nbn:se:liu:diva-15826 (URN)978-91-7393-720-7 (ISBN)
Public defence
2009-01-30, Visionen, Hus B, Campus Valla, Linköping universitet, Linköping, 10:15 (English)
Available from: 2009-01-13 Created: 2008-12-08 Last updated: 2009-03-02Bibliographically approved

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Nordlund, Per-JohanGustafsson, Fredrik
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