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Efficient Estimation and Detection Methods for Airborne Applications
Linköping University, Department of Electrical Engineering. Linköping University, The Institute of Technology. (Reglerteknik)
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.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1231
National Category
Signal Processing
Identifiers
URN: urn:nbn:se:liu:diva-15826ISBN: 978-91-7393-720-7 (print)OAI: oai:DiVA.org:liu-15826DiVA: diva2:128131
Public defence
2009-01-30, Visionen, Hus B, Campus Valla, Linköping universitet, Linköping, 10:15 (English)
Opponent
Supervisors
Available from: 2009-01-13 Created: 2008-12-08 Last updated: 2009-03-02Bibliographically approved
List of papers
1. Marginalized Particle Filters for Mixed Linear/Nonlinear State-Space Models
Open this publication in new window or tab >>Marginalized Particle Filters for Mixed Linear/Nonlinear State-Space Models
2005 (English)In: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, no 7, 2279-2289 p.Article in journal (Refereed) Published
Abstract [en]

The particle filter offers a general numerical tool to approximate the posterior density function for the state in nonlinear and non-Gaussian filtering problems. While the particle filter is fairly easy to implement and tune, its main drawback is that it is quite computer intensive, with the computational complexity increasing quickly with the state dimension. One remedy to this problem is to marginalize out the states appearing linearly in the dynamics. The result is that one Kalman filter is associated with each particle. The main contribution in this paper is the derivation of the details for the marginalized particle filter for a general nonlinear state-space model. Several important special cases occurring in typical signal processing applications will also be discussed. The marginalized particle filter is applied to an integrated navigation system for aircraft. It is demonstrated that the complete high-dimensional system can be based on a particle filter using marginalization for all but three states. Excellent performance on real flight data is reported.

Place, publisher, year, edition, pages
IEEE Signal Processing Society, 2005
Keyword
Kalman filter, Marginalization, Navigation systems, Nonlinear systems, Particle filter, State estimation
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-11749 (URN)10.1109/TSP.2005.849151 (DOI)
Available from: 2008-05-07 Created: 2008-05-07 Last updated: 2013-11-27Bibliographically approved
2. Marginalized Particle Filter for Accurate and Reliable Terrain-Aided Navigation
Open this publication in new window or tab >>Marginalized Particle Filter for Accurate and Reliable Terrain-Aided Navigation
2009 (English)In: IEEE Transactions on Aerospace and Electronic Systems, ISSN 0018-9251, Vol. 45, no 4, 1385-1399 p.Article in journal (Refereed) Published
Abstract [en]

This paper details an approach to the integration of INS (Inertial Navigation System) and TAP (Terrain-Aided Positioning). The solution is characterized by a joint design of INS and TAP, meaning that the highly nonlinear TAP is not designed separately but jointly with the INS using one and the same filter. The applied filter extends the theory of the MPF (Marginalized Particle Filter) given by [1]. The key idea with MPF is to estimate the nonlinear part using the particle filter and the part which is linear, conditionally upon the nonlinear part, is estimated using the Kalman filter. The extension lies in the possibility to deal with a third multi-modal part, where the discrete mode variable is also estimated jointly with the linear and nonlinear parts. Conditionally upon the mode and the nonlinear part, the resulting subsystem is linear and estimated using the Kalman filter. Given the nonlinear motion equations which the INS uses to compute navigation data, the INS equations must be linearized for the MPF to work. A set of linearized equations is derived and the linearization errors are shown to be insignificant with respect to the final result. Simulations are performed and the result indicates near-optimal accuracy when compared to the Cramer-Rao lower bound.

Keyword
Terrain-aided navigation, Particle filter, Kalman filter, Marginalized
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-15825 (URN)10.1109/TAES.2009.5310306 (DOI)000274144200011 ()
Available from: 2008-12-08 Created: 2008-12-08 Last updated: 2013-09-15Bibliographically approved
3. Probabilistic Conflict Detection for Piecewise Straight Paths
Open this publication in new window or tab >>Probabilistic Conflict Detection for Piecewise Straight Paths
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
Probability, Conflict, Detection, Level-crossing
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-15830 (URN)
Available from: 2008-12-08 Created: 2008-12-08 Last updated: 2013-07-23Bibliographically approved
4. Probabilistic Noncooperative Near Mid-Air Collision Avoidance
Open this publication in new window or tab >>Probabilistic Noncooperative Near Mid-Air Collision Avoidance
2011 (English)In: IEEE Transactions on Aerospace and Electronic Systems, ISSN 0018-9251, Vol. 47, no 2, 1265-1276 p.Article in journal (Refereed) Published
Abstract [en]

We propose a probabilistic method to compute the near mid-air collision risk as a function of predicted flight trajectory. The computations use state estimate and covariance from a target tracking filter based on angle-only sensors such as digital video cameras. The majority of existing work is focused on risk estimation at a certain time instant. Here we derive an expression for the integrated risk over the critical time horizon. This is possible using probability for level-crossing, and the expression applies to a three-dimensional piecewise straight flight trajectory. The Monte Carlo technique provides a method to compute the probability, but a huge number of simulations is needed to get sufficient reliability for the small risks that the applications require. Instead we propose a method which through sound geometric and numerical approximations yield a solution suitable for real-time implementations. The algorithm is applied to realistic angle-only tracking data, and shows promising results when compared to the Monte Carlo solution.

Keyword
Probability, Near mid-air collision, Avoidance
National Category
Control Engineering
Identifiers
urn:nbn:se:liu:diva-15831 (URN)10.1109/TAES.2011.5751257 (DOI)000289844100034 ()
Available from: 2008-12-08 Created: 2008-12-08 Last updated: 2015-01-29Bibliographically approved

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Nordlund, Per-Johan

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