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  • 51.
    Hol, Jeroen
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sensor Fusion for Augmented Reality2006Ingår i: Proceedings of Reglermöte 2006, 2006Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    In Augmented Reality (AR), the position and orientation of the camera have to be estimated with high accuracy and low latency. This nonlinear estimation problem is studied in the present paper. The proposed solution makes use of measurements from inertial sensors and computer vision. These measurements are fused using a Kalman filtering framework, incorporating a rather detailed model for the dynamics of the camera. Experiments show that the resulting filter provides good estimates of the camera motion, even during fast movements.

  • 52.
    Hol, Jeroen
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Slycke, Per
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Sensor Fusion for Augmented Reality2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In Augmented Reality (AR), the position and orientation of the camera have to be estimated with high accuracy and low latency. This nonlinear estimation problem is studied in the present paper. The proposed solution makes use of measurements from inertial sensors and computer vision. These measurements are fused using a Kalman filtering framework, incorporating a rather detailed model for the dynamics of the camera. Experiments show that the resulting filter provides good estimates of the camera motion, even during fast movements.

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  • 53.
    Hol, Jeroen
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Luinge, Henk
    Xsens Technologies B.V, The Netherlands.
    Slycke, Per
    Xsens Technologies B.V, The Netherlands.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Robust Real-Time Tracking by Fusing Measurements from Inertial and Vision Sensors2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The problem of estimating and predicting position and orientation (pose) of a camera is approached by fusing measurements from inertial sensors (accelerometers and rate gyroscopes) and vision. The sensor fusion approach described in this contribution is based on non-linear filtering of these complementary sensors. This way, accurate and robust pose estimates are available for the primary purpose of augmented reality applications, but with the secondary effect of reducing computation time and improving the performance in vision processing. A real-time implementation of a multi-rate extended Kalman filter is described, using a dynamic model with 22 states, where 12.5 Hz correspondences from vision and 100 Hz inertial measurements are processed. An example where an industrial robot is used to move the sensor unit is presented. The advantage with this configuration is that it provides ground truth for the pose, allowing for objective performance evaluation. The results show that we obtain an absolute accuracy of 2 cm in position and 1° in orientation.

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  • 54.
    Hol, Jeroen
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Luinge, Henk
    Xsens Technologies B.V, The Netherlands.
    Slycke, Per
    Xsens Technologies B.V, The Netherlands.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Robust Real-Time Tracking by Fusing Measurements from Inertial and Vision Sensors2007Ingår i: Journal of Real-Time Image Processing, ISSN 1861-8200, E-ISSN 1861-8219, Vol. 2, nr 2-3, s. 149-160Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The problem of estimating and predicting position and orientation (pose) of a camera is approached by fusing measurements from inertial sensors (accelerometers and rate gyroscopes) and vision. The sensor fusion approach described in this contribution is based on non-linear filtering of these complementary sensors. This way, accurate and robust pose estimates are available for the primary purpose of augmented reality applications, but with the secondary effect of reducing computation time and improving the performance in vision processing. A real-time implementation of a multi-rate extended Kalman filter is described, using a dynamic model with 22 states, where 12.5 Hz correspondences from vision and 100 Hz inertial measurements are processed. An example where an industrial robot is used to move the sensor unit is presented. The advantage with this configuration is that it provides ground truth for the pose, allowing for objective performance evaluation. The results show that we obtain an absolute accuracy of 2 cm in position and 1° in orientation.

  • 55.
    Hol, Jeroen.D
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Dijkstra, Fred
    Xsens Technologies B.V., Netherlands.
    Luinge, Henk
    Xsens Technologies B.V., Netherlands.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Tightly Coupled UWB/IMU Pose Estimation2009Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we propose a 6DOF tracking system combining Ultra-Wideband measurements with low-cost MEMS inertial measurements. A tightly coupled system is developed which estimates position as well as orientation of the sensorunit while being reliable in case of multipath effects and NLOS conditions. The experimental results show robust and continuous tracking in a realistic indoor positioning scenario.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 56.
    Hu, Xiao-Li
    et al.
    China Jiliang University, China.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Basic Convergence Result for Particle Filtering2007Ingår i: Proceedings of the 7th IFAC Symposium on Nonlinear Control Systems, 2007, s. 288-293Konferensbidrag (Refereegranskat)
    Abstract [en]

    The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still, a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result.  

  • 57.
    Hu, Xiao-Li
    et al.
    Chinese Academy of Sciences, China.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Basic Convergence Result for Particle Filtering2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result for a rather general class of unbounded functions. Furthermore, a general framework, including many of the particle filter algorithms as special cases, is given.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 58.
    Hu, Xiao-Li
    et al.
    Chinese Academy of Sciences, China.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Basic Convergence Result for Particle Filtering2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still a clear cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result for a rather general class of unbounded functions. Furthermore, a general framework, including many of the particle filter algorithms as special cases, is given.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 59.
    Hu, Xiao-Li
    et al.
    Chinese Academy of Sciences, China.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Basic Convergence Result for Particle Filtering2008Ingår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 56, nr 4, s. 1337-1348Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The basic nonlinear filtering problem for dynamical systems is considered. Approximating the optimal filter estimate by particle filter methods has become perhaps the most common and useful method in recent years. Many variants of particle filters have been suggested, and there is an extensive literature on the theoretical aspects of the quality of the approximation. Still a clear-cut result that the approximate solution, for unbounded functions, converges to the true optimal estimate as the number of particles tends to infinity seems to be lacking. It is the purpose of this contribution to give such a basic convergence result for a rather general class of unbounded functions. Furthermore, a general framework, including many of the particle filter algorithms as special cases, is given.

    Ladda ner fulltext (pdf)
    fulltext
  • 60.
    Hu, Xiao-Li
    et al.
    University of Newcastle, Australia.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A General Convergence Result for Particle Filtering2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The particle filter has become an important tool in solving nonlinear filtering problems for dynamic systems. This correspondence extends our recent work, where we proved that the particle filter converges for unbounded functions, using L4-convergence. More specifically, the present contribution is that we prove that the particle filter converge for unbounded functions in the sense of Lp-convergence, for an arbitrary p ≥ 2.

  • 61.
    Hu, Xiao-Li
    et al.
    University of Newcastle, Australia.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A General Convergence Result for Particle Filtering2011Ingår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 59, nr 7, s. 3424-3429Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The particle filter has become an important tool in solving nonlinear filtering problems for dynamic systems. This correspondence extends our recent work, where we proved that the particle filter converges for unbounded functions, using L4-convergence. More specifically, the present contribution is that we prove that the particle filter converge for unbounded functions in the sense of Lp-convergence, for an arbitrary p ≥ 2.

    Ladda ner fulltext (pdf)
    fulltext
  • 62.
    Hu, Xiao-Li
    et al.
    China Jiliang University, China.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Robust Particle Filter for State Estimation - with Convergence Results2007Ingår i: Proceedings of the 46th IEEE Conference on Decision and Control, 2007, s. 312-317Konferensbidrag (Refereegranskat)
    Abstract [en]

    Particle filters are becoming increasingly important and useful for state estimation in nonlinear systems. Many filter versions have been suggested, and several results on convergence of filter properties have been reported. However, apparently a result on the convergence of the state estimate itself has been lacking. This contribution describes a general framework for particle filters for state estimation, as well as a robustified filter version. For this version a quite general convergence result is established. In particular, it is proved that the particle filter estimate convergences w.p.1 to the optimal estimate, as the number of particles tends to infinity.

  • 63.
    Hu, Xiao-Li
    et al.
    China Jiliang University, China.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    A Robust Particle Filter for State Estimation - with Convergence Results2007Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Particle filters are becoming increasingly important and useful for state estimation in nonlinear systems. Many filter versions have been suggested, and several results on convergence of filter properties have been reported. However, apparently a result on the convergence of the state estimate itself has been lacking. This contribution describes a general framework for particle filters for state estimation, as well as a robustified filter version. For this version a quite general convergence result is established. In particular, it is proved that the particle filter estimate convergences w.p.1 to the optimal estimate, as the number of particles tends to infinity.

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    FULLTEXT01
  • 64.
    Hu, Xiao-Li
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ljung, Lennart
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Basic Convergence Results for Particle Filtering Methods: Theory for the Users2009Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This work extends our recent work on proving that the particle filter converge for unbounded function to a more general case. More specifically, we prove that the particle filter converge for unbounded functions in the sense of L p-convergence, for an arbitrary p greater than 1. Related to this, we also provide proofs for the case when the function we are estimating is bounded. In the process of deriving the main result we also established a new Rosenthal type inequality.

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  • 65.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Complexity Analysis of the Marginalized Particle Filter2004Ingår i: Proceedings of the 5th Conference on Computer Science and Systems Engineering, 2004, s. 169-Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    In this paper the computational complexity of the marginalized particle lter is analyzed. We introduce an equivalent flop measure to capture floating-point operations as well as other features, which cannot be measured using flops, such as the complexity in generating random numbers and performing the resampling. From the analysis we conclude how to partition the estimation problem in an optimal way for some common target tracking models. Some guidelines on how to increase performance based on the analysis is also given. In an extensive Monte Carlo simulation we study different computational aspects and compare with theoretical results.

  • 66.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Complexity Analysis of the Marginalized Particle Filter2004Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper the computational complexity of the marginalized particle lter is analyzed. We introduce an equivalent flop measure to capture floating-point operations as well as other features, which cannot be measured using flops, such as the complexity in generating random numbers and performing the resampling. From the analysis we conclude how to partition the estimation problem in an optimal way for some common target tracking models. Some guidelines on how to increase performance based on the analysis is also given. In an extensive Monte Carlo simulation we study different computational aspects and compare with theoretical results.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 67.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Complexity Analysis of the Marginalized Particle Filter2005Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this paper the computational complexity of the marginalized particle lter is analyzed. We introduce an equivalent flop measure to capture floating-point operations as well as other features, which cannot be measured using flops, such as the complexity in generating random numbers and performing the resampling. From the analysis we conclude how to partition the estimation problem in an optimal way for some common target tracking models. Some guidelines on how to increase performance based on the analysis is also given. In an extensive Monte Carlo simulation we study different computational aspects and compare with theoretical results.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 68.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Complexity Analysis of the Marginalized Particle Filter2005Ingår i: IEEE Transactions on Signal Processing, ISSN 1053-587X, E-ISSN 1941-0476, Vol. 53, nr 11, s. 4408-4411Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper, the computational complexity of the marginalized particle filter is analyzed and a general method to perform this analysis is given. The key is the introduction of the equivalent flop measure. In an extensive Monte Carlo simulation, different computational aspects are studied and compared with the derived theoretical results.

    Ladda ner fulltext (pdf)
    fulltext
  • 69.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Conte, Gianpaolo
    Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerad datorsystem. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Utilizing Model Structure for Efficient Simultaneous Localization and Mapping for a UAV Application2008Ingår i: Proceedings of Reglermöte 2008, 2008, s. 313-322Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    This contribution aims at unifying two recent trends in applied particle filtering (PF). The first trend is the major impact in simultaneous localization and mapping (SLAM) applications, utilizing the FastSLAM algorithm. Thesecond one is the implications of the marginalized particle filter (MPF) or the Rao-Blackwellized particle filter (RBPF) in positioning and tracking applications. Using the standard FastSLAM algorithm, only low-dimensional vehicle modelsare computationally feasible. In this work, an algorithm is introduced which merges FastSLAM and MPF, and the result is an algorithm for SLAM applications, where state vectors of higher dimensions can be used. Results using experimental data from a UAV (helicopter) are presented. The algorithmfuses measurements from on-board inertial sensors (accelerometer and gyro) and vision in order to solve the SLAM problem, i.e., enable navigation over a long period of time.

  • 70.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Conte, Gianpaolo
    Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerad datorsystem. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Utilizing Model Structure for Efficient Simultaneous Localization and Mapping for a UAV Application2008Ingår i: Proceedings of the 2008 IEEE Aerospace Conference, 2008, s. 1-10Konferensbidrag (Refereegranskat)
    Abstract [en]

    This contribution aims at unifying two recent trends in applied particle filtering (PF). The first trend is the major impact in simultaneous localization and mapping (SLAM) applications, utilizing the FastSLAM algorithm. The second one is the implications of the marginalized particle filter (MPF) or the Rao-Blackwellized particle filter (RBPF) in positioning and tracking applications. Using the standard FastSLAM algorithm, only low-dimensional vehicle models are computationally feasible. In this work, an algorithm is introduced which merges FastSLAM and MPF, and the result is an algorithm for SLAM applications, where state vectors of higher dimensions can be used. Results using experimental data from a UAV (helicopter) are presented. The algorithm fuses measurements from on-board inertial sensors (accelerometer and gyro) and vision in order to solve the SLAM problem, i.e., enable navigation over a long period of time.

  • 71.
    Karlsson, Rickard
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Conte, Gianpolo
    Linköpings universitet, Institutionen för datavetenskap, Artificiell intelligens och integrerad datorsystem. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Utilizing Model Structure for Efficient Simultaneous Localization and Mapping for a UAV Application2008Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This contribution aims at unifying two recent trends in applied particle filtering (PF). The first trend is the major impact in simultaneous localization and mapping (SLAM) applications, utilizing the FastSLAM algorithm. Thesecond one is the implications of the marginalized particle filter (MPF) or the Rao-Blackwellized particle filter (RBPF) in positioning and tracking applications. Using the standard FastSLAM algorithm, only low-dimensional vehicle modelsare computationally feasible. In this work, an algorithm is introduced which merges FastSLAM and MPF, and the result is an algorithm for SLAM applications, where state vectors of higher dimensions can be used. Results using experimental data from a UAV (helicopter) are presented. The algorithmfuses measurements from on-board inertial sensors (accelerometer and gyro) and vision in order to solve the SLAM problem, i.e., enable navigation over a long period of time.

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  • 72.
    Kok, Manon
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Hol, Jeroen
    Xsens Technologies B.V., Enschede, the Netherlands.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Luinge, Henk
    Xsens Technologies B.V., Enschede, the Netherlands.
    Calibration of a magnetometer in combination with inertial sensors2012Ingår i: Proceedings of the 15th International Conference on Information Fusion (FUSION), IEEE conference proceedings, 2012, s. 787-793Konferensbidrag (Refereegranskat)
    Abstract [en]

    Measurements from magnetometers and inertial sensors (accelerometers and gyroscopes) can be combined to give 3D orientation estimates. In order to obtain accurate orientation estimates it is imperative that the magnetometer and inertial sensor axes are aligned and that the magnetometer is properly calibrated for both sensor errors as well as presence of magnetic distortions. In this work we derive an easy-to-use calibration algorithm that can be used to calibrate a combination of a magnetometer and inertial sensors. The algorithm compensates for any static magnetic distortions created by the sensor plat- form, magnetometer sensor errors and determines the alignment between the magnetometer and the inertial sensor axes. The resulting calibration procedure does not require any additional hardware. We make use of probabilistic models and obtain the calibration algorithm as the solution to a maximum likelihood problem. The efficacy of the proposed algorithm is illustrated using experimental data collected from a sensor unit placed in a magnetically disturbed environment onboard a jet aircraft. 

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  • 73.
    Kok, Manon
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Wahlström, Niklas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    MEMS-based inertial navigation based on a magnetic field map2013Ingår i: Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing (ICASSP), 2013, s. 6466-6470Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper presents an approach for 6D pose estimation where MEMS inertial measurements are complemented with magnetometer measurements assuming that a model (map) of the magnetic field is known. The resulting estimation problem is solved using a Rao-Blackwellized particle filter. In our experimental study the magnetic field is generated by a magnetic coil giving rise to a magnetic field that we can model using analytical expressions. The experimental results show that accurate position estimates can be obtained in the vicinity of the coil, where the magnetic field is strong.

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  • 74.
    Kolbe, Viktor
    et al.
    C3 Technologies, Sweden.
    Isaksson, Folke
    Saab Bofors Dynamics, Sweden.
    Beckman, Thomas
    Saab Bofors Dynamics, Sweden.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Indoor Photorealistic 3D Mapping using Stereo Images from SLR Cameras2009Ingår i: Proceedings of the '09 Swedish Symposium on Image Analysis (SSBA), 2009Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    Creating a 3D model from photos require an estimate of the position and orientation (pose) of the camera for each photo that is acquired. This paper presents a method to estimate the camera pose using only image data. The images are acquired at a low frequency using a stereo rig, consisting of two rigidly attached SLR cameras. Features are extracted and an optimization problem is solved for each new stereo image. The results are used to merge multiple stereo images and building a larger model of the scene. The accumulated error after processing 10 images can with the present methods be less than 1.2 mm in translation and 0.1 degrees in rotation.

  • 75.
    Kolbe, Viktor
    et al.
    C3 Technologies, Sweden.
    Isaksson, Folke
    Saab Bofors Dynamics, Sweden.
    Beckman, Thomas
    Saab Bofors Dynamics, Sweden.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Indoor Photorealistic 3D Mapping using Stereo Images from SLR Cameras2009Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Creating a 3D model from photos require an estimate of the position and orientation (pose) of the camera for each photo that is acquired. This paper presents a method to estimate the camera pose using only image data. The images are acquired at a low frequency using a stereo rig, consisting of two rigidly attached SLR cameras. Features are extracted and an optimization problem is solved for each new stereo image. The results are used to merge multiple stereo images and building a larger model of the scene. The accumulated error after processing 10 images can with the present methods be less than 1.2 mm in translation and 0.1 degrees in rotation.

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  • 76.
    Kronander, Joel
    et al.
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Medie- och Informationsteknik. Linköpings universitet, Tekniska högskolan.
    Dahlin, Johan
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Jönsson, Daniel
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Medie- och Informationsteknik. Linköpings universitet, Tekniska högskolan.
    Kok, Manon
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan. Uppsala Universitet.
    Unger, Jonas
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Medie- och Informationsteknik. Linköpings universitet, Tekniska högskolan.
    Real-time video based lighting using GPU raytracing2014Ingår i: Proceedings of the 22nd European Signal Processing Conference (EUSIPCO), 2014, IEEE Signal Processing Society, 2014Konferensbidrag (Refereegranskat)
    Abstract [en]

    The recent introduction of HDR video cameras has enabled the development of image based lighting techniques for rendering virtual objects illuminated with temporally varying real world illumination. A key challenge in this context is that rendering realistic objects illuminated with video environment maps is computationally demanding. In this work, we present a GPU based rendering system based on the NVIDIA OptiX framework, enabling real time raytracing of scenes illuminated with video environment maps. For this purpose, we explore and compare several Monte Carlo sampling approaches, including bidirectional importance sampling, multiple importance sampling and sequential Monte Carlo samplers. While previous work have focused on synthetic data and overly simple environment maps sequences, we have collected a set of real world dynamic environment map sequences using a state-of-art HDR video camera for evaluation and comparisons.

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  • 77.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Bunch, Pete
    University of Cambridge, United Kingdom.
    Godsill, Simon J.
    University of Cambridge, United Kingdom.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Rao-Blackwellized Particle Smoothers for Mixed Linear/Nonlinear State-Space Models2013Ingår i: Proceedings of the 38th International Conference on Acoustics, Speech, and Signal Processing, IEEE conference proceedings, 2013, s. 6288-6292Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction.

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    fulltext
  • 78.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Callmer, Jonas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ohlsson, Henrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Geo-Referencing for UAV Navigation using Environmental Classification2010Rapport (Övrigt vetenskapligt)
    Abstract [en]

    A UAV navigation system relying on GPS is vulnerable to signal failure, making a drift free backup system necessary. We introduce a vision based geo-referencing system that uses pre-existing maps to reduce the long term drift. The system classifies an image according to its environmental content and thereafter matches it to an environmentally classified map over the operational area. This map matching provides a measurement of the absolute location of the UAV, that can easily be incorporated into a sensor fusion framework. Experiments show that the geo-referencing system reduces the long term drift in UAV navigation, enhancing the ability of the UAV to navigate accurately over large areas without the use of GPS.

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  • 79.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Callmer, Jonas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ohlsson, Henrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Törnqvist, David
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Gustafsson, Fredrik
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Geo-Referencing for UAV Navigation using Environmental Classification2010Ingår i: Proceedings of the 2010 IEEE International Conference on Robotics and Automation, 2010, s. 1420-1425Konferensbidrag (Refereegranskat)
    Abstract [en]

    A UAV navigation system relying on GPS is vulnerable to signal failure, making a drift free backup system necessary. We introduce a vision based geo-referencing system that uses pre-existing maps to reduce the long term drift. The system classifies an image according to its environmental content and thereafter matches it to an environmentally classified map over the operational area. This map matching provides a measurement of the absolute location of the UAV, that can easily be incorporated into a sensor fusion framework. Experiments show that the geo-referencing system reduces the long term drift in UAV navigation, enhancing the ability of the UAV to navigate accurately over large areas without the use of GPS.

  • 80.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Jordan, Michael I.
    University of California, Berkeley.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Ancestor Sampling for Particle Gibbs2012Ingår i: Proceedings of the 26th Conference on Neural Information Processing Systems, 2012Konferensbidrag (Refereegranskat)
    Abstract [en]

    We present a novel method in the family of particle MCMC methods that we refer to as particle Gibbs with ancestor sampling (PG-AS). Similarly to the existing PG with backward simulation (PG-BS) procedure, we use backward sampling to (considerably) improve the mixing of the PG kernel. Instead of using separate forward and backward sweeps as in PG-BS, however, we achieve the same effect in a single forward sweep. We apply the PG-AS framework to the challenging class of non-Markovian state-space models. We develop a truncation strategy of these models that is applicable in principle to any backward-simulation-based method, but which is particularly well suited to the PG-AS framework. In particular, as we show in a simulation study, PG-AS can yield an order-of-magnitude improved accuracy relative to PG-BS due to its robustness to the truncation error. Several application examples are discussed, including Rao-Blackwellized particle smoothing and inference in degenerate state-space models.

  • 81.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Identification of Mixed Linear/Nonlinear State-Space Models2010Ingår i: Proceedings of the 49th IEEE Conference on Decision and Control, 2010, s. 6377-6382Konferensbidrag (Refereegranskat)
    Abstract [en]

    The primary contribution of this paper is an algorithm capable of identifying parameters in certain mixed linear/nonlinear state-space models, containing conditionally linear Gaussian substructures. More specifically, we employ the standard maximum likelihood framework and derive an expectation maximization type algorithm. This involves a nonlinear smoothing problem for the state variables, which for the conditionally linear Gaussian system can be efficiently solved using a so called Rao-Blackwellized particle smoother (RBPS). As a secondary contribution of this paper we extend an existing RBPS to be able to handle the fully interconnected model under study.

     

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  • 82.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Inference in Mixed Linear/Nonlinear State-Space Models using Sequential Monte Carlo2010Rapport (Övrigt vetenskapligt)
    Abstract [en]

    In this work we apply sequential Monte Carlo methods, i.e., particle filters and smoothers, to estimate the state in a certain class of mixed linear/nonlinear state-space models. Such a model has an inherent conditionally linear Gaussian substructure. By utilizing this structure we are able to address even high-dimensional nonlinear systems using Monte Carlo methods, as long as only a few of the states enter nonlinearly. First, we consider the filtering problem and give a self-constained derivation of the well known Rao-Blackellized particle filter. Therafter we turn to the smoothing problem and derive a Rao-Blackwellized particle smoother capable of handling the fully interconnected model under study.

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  • 83.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    On the Use of Backward Simulation in the Particle Gibbs Sampler2012Ingår i: Proceedings of the 37th IEEE International Conference on Acoustics, Speech, and Signal Processing, IEEE , 2012, s. 3845-3848Konferensbidrag (Refereegranskat)
    Abstract [en]

    The particle Gibbs (PG) sampler was introduced in [Andrieu et al. (2010)] as a way to incorporate a particle filter (PF) in a Markov chain Monte Carlo (MCMC) sampler. The resulting method was shown to be an efficient tool for joint Bayesian parameter and state inference in nonlinear, non-Gaussian state-space models. However, the mixing of the PG kernel can be very poor when there is severe degeneracy in the PF. Hence, the success of the PG sampler heavily relies on the, often unrealistic, assumption that we can implement a PF without suffering from any considerate degeneracy. However, as pointed out by Whiteley in the discussion following [Andrieu et al. (2010)], the mixing can be improved by adding a backward simulation step to the PG sampler. Here, we investigate this further, derive an explicit PG sampler with backward simulation (denoted PG-BSi) and show that this indeed is a valid MCMC method. Furthermore, we show in a numerical example that backward simulation can lead to a considerable increase in performance over the standard PG sampler.

  • 84.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Backward simulation methods for Monte Carlo statistical inference2013Ingår i: Foundations and Trends in Machine Learning, ISSN 1935-8237, Vol. 6, nr 1, s. 1-143Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Monte Carlo methods, in particular those based on Markov chains and on interacting particle systems, are by now tools that are routinely used in machine learning. These methods have had a profound impact on statistical inference in a wide range of application areas where probabilistic models are used. Moreover, there are many algorithms in machine learning which are based on the idea of processing the data sequentially, first in the forward direction and then in the backward direction. In this tutorial we will review a branch of Monte Carlo methods based on the forward-backward idea, referred to as backward simulators. These methods are useful for learning and inference in probabilistic models containing latent stochastic processes. The theory and practice of backward simulation algorithms have undergone a significant development in recent years and the algorithms keep finding new applications. The foundation for these methods is sequential Monte Carlo (SMC). SMC-based backward simulators are capable of addressing smoothing problems in sequential latent variable models, such as general, nonlinear/non-Gaussian state-space models (SSMs). However, we will also clearly show that the underlying backward simulation idea is by no means restricted to SSMs. Furthermore, backward simulation plays an important role in recent developments of Markov chain Monte Carlo (MCMC) methods. Particle MCMC is a systematic way of using SMC within MCMC. In this framework, backward simulation gives us a way to significantly improve the performance of the samplers. We review and discuss several related backward-simulation-based methods for state inference as well as learning of static parameters, both using a frequentistic and a Bayesian approach.

  • 85.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Maximum Likelihood Estimation in Mixed Linear/Nonlinear State-Space Models2010Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The primary contribution of this paper is an algorithm capable of identifying parameters in certain mixed linear/nonlinear state-space models, containing conditionally linear Gaussian substructures. More specifically, we employ the standard maximum likelihood framework and derive an expectation maximization type algorithm. This involves a nonlinear smoothing problem for the state variables, which for the conditionally linear Gaussian system can be efficiently solved using so called Rao-Blackwellized particle smoother (RBPS). As a secondary contribution of this paper we extend an existing RBPS to be able to handle the fully interconnected model under study.

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    FULLTEXT01
  • 86.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Rao-Blackwellized Particle Smoothers for Mixed Linear/Nonlinear State-Space Models2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We consider the smoothing problem for a class of conditionally linear Gaussian state-space (CLGSS) models, referred to as mixed linear/nonlinear models. In contrast to the better studied hierarchical CLGSS models, these allow for an intricate cross dependence between the linear and the nonlinear parts of the state vector. We derive a Rao-Blackwellized particle smoother (RBPS) for this model class by exploiting its tractable substructure. The smoother is of the forward filtering/backward simulation type. A key feature of the proposed method is that, unlike existing RBPS for this model class, the linear part of the state vector is marginalized out in both the forward direction and in the backward direction.

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    FULLTEXT01
  • 87.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Jordan, Michael I.
    University of California, Berkeley, USA.
    A Semiparametric Bayesian Approach to Wiener System Identification2012Ingår i: Proceedings of the 16th IFAC Symposium on System Identification, 2012, s. 1137-1142Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process (GP) model for the static nonlinearity. The GP model is a flexible model that can describe different types of nonlinearities while avoiding making strong assumptions such as monotonicity. We derive an inferential method based on recent advances in Monte Carlo statistical methods, known as Particle Markov Chain Monte Carlo (PMCMC). The idea underlying PMCMC is to use a particle filter (PF) to generate a sample state trajectory in a Markov chain Monte Carlo sampler. We use a recently proposed PMCMC sampler, denoted particle Gibbs with backward simulation, which has been shown to be efficient even when we use very few particles in the PF. The resulting method is used in a simulation study to identify two different Wiener systems with non-invertible nonlinearities.

  • 88.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Olsson, Jimmy
    Lund University, Sweden.
    An Explicit Variance Reduction Expression for the Rao-Blackwellised Particle Filter2010Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Particle filters (PFs) have shown to be very potent tools for state estimation in nonlinear and/or non-Gaussian state-space models. For certain models, containing a conditionally tractable substructure (typically conditionally linear Gaussian or with finite support), it is possible to exploit this structure in order to obtain more accurate estimates. This has become known as Rao-Blackwellised particle filtering (RBPF). However, since the RBPF is typically more computationally demanding than the standard PF per particle, it is not always beneficial to resort to Rao-Blackwellisation. For the same computational effort, a standard PF with an increased number of particles, which would also increase the accuracy, could be used instead. In this paper, we have analysed the asymptotic variance of the RBPF and provide an explicit expression for the obtained variance reduction. This expression could be used to make an efficient discrimination of when to apply Rao-Blackwellisation, and when not to.

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  • 89.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Svensson, Lennart
    Division of Signals and Systems, Chalmers University.
    A non-degenerate Rao-Blackwellised particle filter for estimating static parameters in dynamical models2012Ingår i: Proceedings of the 16th IFAC Symposium on System Identification, 2012Konferensbidrag (Refereegranskat)
    Abstract [en]

    The particle filter (PF) has emerged as a powerful tool for solving nonlinear and/or non-Gaussian filtering problems. When some of the states enter the model linearly, this can be exploited by using particles only for the "nonlinear" states and employing conditional Kalman filters for the "linear" states; this leads to the Rao-Blackwellised particle filter (RBPF). However, it is well known that the PF fails when the state of the model contains some static parameter. This is true also for the RBPF, even if the static states are marginalised analytically by a Kalman filter. The reason is that the posterior density of the static states is computed conditioned on the nonlinear particle trajectories, which are bound to degenerate over time. To circumvent this problem, we propose a method for targeting the posterior parameter density, conditioned on just the current nonlinear state. This results in an RBPF-like method, capable of recursive identification of nonlinear dynamical models with affine parameter dependencies.

  • 90.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Jordan, Michael I.
    University of California, Berkeley, USA.
    A Semiparametric Bayesian Approach to Wiener System Identification2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We consider a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process (GP) model for the static nonlinearity. The GP model is a flexible model that can describe different types of nonlinearities while avoiding making strong assumptions such as monotonicity. We derive an inferential method based on recent advances in Monte Carlo statistical methods, known as Particle Markov Chain Monte Carlo (PMCMC). The idea underlying PMCMC is to use a particle filter (PF) to generate a sample state trajectory in a Markov chain Monte Carlo sampler. We use a recently proposed PMCMC sampler, denoted particle Gibbs with backward simulation, which has been shown to be efficient even when we use very few particles in the PF. The resulting method is used in a simulation study to identify two different Wiener systems with non-invertible nonlinearities.

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  • 91.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Jordan, Michael I.
    University of Calif Berkeley, CA USA .
    Bayesian semiparametric Wiener system identification2013Ingår i: Automatica, ISSN 0005-1098, E-ISSN 1873-2836, Vol. 49, nr 7, s. 2053-2063Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We present a novel method for Wiener system identification. The method relies on a semiparametric, i.e. a mixed parametric/nonparametric, model of a Wiener system. We use a state-space model for the linear dynamical system and a nonparametric Gaussian process model for the static nonlinearity. We avoid making strong assumptions, such as monotonicity, on the nonlinear mapping. Stochastic disturbances, entering both as measurement noise and as process noise, are handled in a systematic manner. The nonparametric nature of the Gaussian process allows us to handle a wide range of nonlinearities without making problem-specific parameterizations. We also consider sparsity-promoting priors, based on generalized hyperbolic distributions, to automatically infer the order of the underlying dynamical system. We derive an inference algorithm based on an efficient particle Markov chain Monte Carlo method, referred to as particle Gibbs with ancestor sampling. The method is profiled on two challenging identification problems with good results. Blind Wiener system identification is handled as a special case.

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    fulltext
  • 92.
    Lindsten, Fredrik
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Olsson, Jimmy
    Lund University, Sweden.
    An Explicit Variance Reduction Expression for the Rao-Blackwellised Particle Filter2011Ingår i: Proceedings of the 18th IFAC World Congress, 2011, s. 11979-11984Konferensbidrag (Refereegranskat)
    Abstract [en]

    Particle filters (PFs) have shown to be very potent tools for state estimation in nonlinear and/or non-Gaussian state-space models. For certain models, containing a conditionally tractable substructure (typically conditionally linear Gaussian or with finite support), it is possible to exploit this structure in order to obtain more accurate estimates. This has become known as Rao-Blackwellised particle filtering (RBPF). However, since the RBPF is typically more computationally demanding than the standard PF per particle, it is not always beneficial to resort to Rao-Blackwellisation. For the same computational effort, a standard PF with an increased number of particles, which would also increase the accuracy, could be used instead. In this paper, we have analysed the asymptotic variance of the RBPF and provide an explicit expression for the obtained variance reduction. This expression could be used to make an efficient discrimination of when to apply Rao-Blackwellisation, and when not to.

  • 93.
    Lundquist, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Orguner, Umut
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Tracking Stationary Extended Objects for Road Mapping using Radar Measurements2009Ingår i: Proceedings of the '09 IEEE Intelligent Vehicle Symposium, IEEE , 2009, s. 405-410Konferensbidrag (Refereegranskat)
    Abstract [en]

    It is getting more common that premium cars areequipped with a forward looking radar and a forward looking camera. The data is often used to estimate the road geometry, tracking leading vehicles, etc. However, there is valuable information present in the radar concerning stationary objects, that is typically not used. The present work shows how stationary objects, such as guard rails, can be modeled and tracked as extended objects using radar measurements. The problem is cast within a standard sensor fusion framework utilizing the Kalman filter. The approach has been evaluated on real datafrom highways and rural roads in Sweden.

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    fulltext
  • 94.
    Lundquist, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Estimation of the Free Space in Front of a Moving Vehicle2009Ingår i: Proceedings of the '09 SAE World Congress & Exhibition, 2009Konferensbidrag (Refereegranskat)
    Abstract [en]

    There are more and more systems emerging making use of measurements from a forward looking radar and a forward looking camera. It is by now well known how to exploit this data in order to compute estimates of the road geometry, tracking leading vehicles, etc. However, there is valuable information present in the radar concerning stationary objects, that is typically not used. The present work shows how radar measurements of stationary objects can be used to obtain a reliable estimate of the free space in front of a moving vehicle. The approach has been evaluated on real data from highways and rural roads in Sweden.

    Ladda ner fulltext (pdf)
    fulltext
  • 95.
    Lundquist, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Joint Ego-Motion and Road Geometry Estimation2011Ingår i: Information Fusion, ISSN 1566-2535, E-ISSN 1872-6305, Vol. 12, nr 4, s. 253-263Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We provide a sensor fusion framework for solving the problem of joint egomotion and road geometry estimation. More specifically we employ a sensor fusion framework to make systematic use of the measurements from a forward looking radar and camera, steering wheel angle sensor, wheel speed sensors and inertial sensors to compute good estimates of the road geometry and the motion of the ego vehicle on this road. In order to solve this problem we derive dynamical models for the ego vehicle, the road and the leading vehicles. The main difference to existing approaches is that we make use of a new dynamic model for the road. An extended Kalman filter is used to fuse data and to filter measurements from the camera in order to improve the road geometry estimate. The proposed solution has been tested and compared to existing algorithms for this problem, using measurements from authentic traffic environments on public roads in Sweden. The results clearly indicate that the proposed method provides better estimates.

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    FULLTEXT01
  • 96.
    Lundquist, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Recursive Identification of Cornering Stiffness Parameters for an Enhanced Single Track Model2009Ingår i: Proceedings of the 15th IFAC Symposiumon System Identification, 2009, s. 1726-1731Konferensbidrag (Refereegranskat)
    Abstract [en]

    The current development of safety systems within the automotive industry heavily relies on the ability to perceive the environment. This is accomplished by using measurements from several different sensors within a sensor fusion framework. One important part of any system of this kind is an accurate model describing the motion of the vehicle. The most commonly used model for the lateral dynamics is the single track model, which includes the so called cornering stiffness parameters. These parameters describe the tire-road contact and are unknown and even time-varying. Hence, in order to fully make use of the single track model, these parameters have to be identified. The aim of this work is to provide a method for recursive identification of the cornering stiffness parameters to be used on-line while driving.

    Ladda ner fulltext (pdf)
    fulltext
  • 97.
    Lundquist, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Road Geometry Estimation and Vehicle Tracking using a Single Track Model2008Ingår i: Proceedings of the 2008 IEEE Intelligent Vehicles Symposium, 2008, s. 144-149Konferensbidrag (Refereegranskat)
    Abstract [en]

    This paper is concerned with the, by now rather well studied, problem of integrated road geometry estimation and vehicle tracking. The main differences to the existing approaches are that we make use of an improved host vehicle model and a new dynamic model for the road. The problem is posed within a standard sensor fusion framework, allowing us to make good use of the available sensor information. The performance of the solution is evaluated using measurements from real and relevant traffic environments from public roads in Sweden. The experiments indicates that the gain in using the extended host vehicle model is most prominent when driving on country roads without any vehicles in front.

    Ladda ner fulltext (pdf)
    fulltext
  • 98.
    Lundquist, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Recursive Identification of Cornering Stiffness Parameters for an Enhanced Single Track Model2009Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The current development of safety systems within the automotive industry heavily relies on the ability to perceive the environment. This is accomplished by using measurements from several different sensors within a sensor fusion framework. One important part of any system of this kind is an accurate model describing the motion of the vehicle. The most commonly used model for the lateral dynamics is the single track model, which includes the so called cornering stiffness parameters. These parameters describe the tire-road contact and are unknown and even time-varying. Hence, in order to fully make use of the single track model, these parameters have to be identified. The aim of this work is to provide a method for recursive identification of the cornering stiffness parameters to be used on-line while driving.

    Ladda ner fulltext (pdf)
    Recursive Identification of Cornering Stiffness Parameters for an Enhanced Single Track Model
    Ladda ner fulltext (pdf)
    FULLTEXT05
  • 99.
    Lundquist, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Road Geometry Estimation and Vehicle Tracking using a Single Track Model2008Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This paper is concerned with the, by now rather well studied, problem of integrated road geometry estimation and vehicle tracking. The main differences to the existing approaches are that we make use of an improved host vehicle model and a new dynamic model for the road. The problem is posed within a standard sensor fusion framework, allowing us to make good use of the available sensor information. The performance of the solution is evaluated using measurements from real and relevant traffic environments from public roads in Sweden. The experiments indicates that the gain in using the extended host vehicle model is most prominent when driving on country roads without any vehicles in front.

    Ladda ner fulltext (pdf)
    Road Geometry Estimation and Vehicle Tracking using a Single Track Mode
    Ladda ner fulltext (pdf)
    FULLTEXT03
  • 100.
    Lundquist, Christian
    et al.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Schön, Thomas B.
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Orguner, Umut
    Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
    Estimation of the Free Space in Front of a Moving Vehicle2009Rapport (Övrigt vetenskapligt)
    Abstract [en]

    There are more and more systems emerging making use of measurements from a forward looking radar and a forward looking camera. It is by now well known how to exploit this data in order to compute estimates of the road geometry, tracking leading vehicles, etc. However, there is valuable information present in the radar concerning stationary targets, that is typically not used. The present work shows how radar measurements of stationary targets can be used to provide a reliable estimate of the drivable space in front of a moving vehicle.

    In the present paper three conceptually different methods to estimate stationary objects or road borders are presented and compared. The first method considered is occupancy grid mapping, which discretizes the map surrounding the ego vehicle and the probability of occupancy is estimated for each grid cell. The second method applies a constrained quadratic program in order to estimate the road borders. The problem is stated as a constrained curve fitting problem. The third method associates the radar measurements to extended stationary objects and tracks them as extended targets.

    The required sensors, besides the standard proprioceptive sensors of a modern car, are a forward looking long range radar and a forward looking camera. Hence, there is no need to introduce any new sensors, it is just a matter of making better use of the sensor information that is already present in a modern car. The approach has been evaluated and tested on real data from highways and rural roads in Sweden and the results are very promising.

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    Estimation of the Free Space in Front of a Moving Vehicle
    Ladda ner fulltext (pdf)
    FULLTEXT03
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