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Marginalized Particle Filter for Accurate and Reliable Terrain-Aided Navigation
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, The Institute of Technology. Linköping University, Department of Electrical Engineering, Automatic Control.
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.

Place, publisher, year, edition, pages
2009. Vol. 45, no 4, 1385-1399 p.
Keyword [en]
Terrain-aided navigation, Particle filter, Kalman filter, Marginalized
National Category
Control Engineering
URN: urn:nbn:se:liu:diva-15825DOI: 10.1109/TAES.2009.5310306ISI: 000274144200011OAI: diva2:127531
Available from: 2008-12-08 Created: 2008-12-08 Last updated: 2013-09-15Bibliographically 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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