| 1. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
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A Graphics Processing Unit Implementation of the Particle Filter
- 2007
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Ingår i: Proceedings of the 15th European Statistical Signal Processing Conference. - Linköping : European Association for Signal, Speech, and Image Processing. - 9788392134022 ; , s. 1639-1643
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Konferensbidrag (refereegranskat)abstract
- Modern graphics cards for computers, and especially their graphics processing units (GPUs), are designed for fast rendering of graphics. In order to achieve this GPUs are equipped with a parallel architecture which can be exploited for general-purpose computing on GPU (GPGPU) as a complement to the central processing unit (CPU). In this paper GPGPU techniques are used to make a parallel GPU implementation of state-of-the-art recursive Bayesian estimation using particle filters (PF). The modifications made to obtain a parallel particle filter, especially for the resampling step, are discussed and the performance of the resulting GPU implementation is compared to one achieved with a traditional CPU implementation. The resulting GPU filter is faster with the same accuracy as the CPU filter for many particles, and it shows how the particle filter can be parallelized.
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| 2. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
-
A New Formulation of the Rao-Blackwellized Particle Filter
- 2007
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Ingår i: Proceedings of the 14th IEEE/SP Statistical Signal Processing Workshop. - Linköping : Linköping University Electronic Press. - 9781424411986 ; , s. 84-88
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Konferensbidrag (refereegranskat)abstract
- For performance gain and efficiency it is important to utilize model structure in particle filtering. Applying Bayes- rule, present linear Gaussian substructure can be efficiently handled by a bank of Kalman filters. This is the standard formulation of the Rao-Blackwellized particle filter (RBPF), by some authors denoted the marginalized particle filter (MPF), and usually presented in a way that makes it hard to implement in an object oriented fashion. This paper discusses how the solution can be rewritten in order to increase the understanding as well as simplify the implementation and reuse of standard filtering components, such as Kalman filter banks and particle filters. Calculations show that the new algorithm is equivalent to the classical formulation, and the new algorithm is exemplified in a target tracking simulation study.
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| 3. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
-
Detection Limits for Linear Non-Gaussian State-Space Models
- 2006
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Ingår i: Proceedings of the 6th IFAC Symposium on Fault Detection, Supervision and Safty of Technical Processes. - Linköping : Linköping University Electronic Press. - 9783902661142 ; , s. 282-287
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Konferensbidrag (refereegranskat)abstract
- The performance of nonlinear fault detection schemes is hard to decide objectively, so Monte Carlo simulations are often used to get a subjective measure and relative performance for comparing different algorithms. There is a strong need for a constructive way of computing an analytical performance bound, similar to the Cramér-Rao lower bound for estimation. This paper provides such a result for linear non-Gaussian systems. It is first shown how a batch of data from a linear state-space model with additive faults and non-Gaussian noise can be transformed to a residual described by a general linear non-Gaussian model. This also involves a parametric description of incipient faults. The generalized likelihood ratio test is then used as the asymptotic performance bound. The test statistic itself may be impossible to compute without resorting to numerical algorithms, but the detection performance scales analytically with a constant that depends only on the distribution of the noise. It is described how to compute this constant, and a simulation study illustrates the results.
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| 4. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
-
Fundamental Fault Detection Limitations in Linear Non-Gaussian Systems
- 2005
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Ingår i: Proceedings of the 44th IEEE Conference on Decision and Control and European Control Conference. - Linköping : Linköping University Electronic Press. - 0780395670 ; , s. 338-343
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Konferensbidrag (refereegranskat)abstract
- Sophisticated fault detection (FD) algorithms often include nonlinear mappings of observed data to fault decisions, and simulation studies are used to support the methods. Objective statistically supported performance analysis of FDalgorithms is only possible for some special cases, including linear Gaussian models. The goal here is to derive general statistical performance bounds for any FD algorithm, given a nonlinear non-Gaussian model of the system. Recent advances in numerical algorithms for nonlinear filtering indicate that such bounds in many practical cases are attainable. This paper focuses on linear non-Gaussian models. A couple of different fault detection setups based on parity space and Kalman filter approaches are considered, where the fault enters a computable residual linearly. For this class of systems, fault detection can be based on the best linear unbiased estimate (BLUE) of the fault vector. Alternatively, a nonlinear filter can potentially compute the maximum likelihood (ML) state estimate, whose performance is bounded by the Cramér-Rao lower bound (CRLB). The contribution in this paper is general expressions for the CRLB for this class of systems, interpreted in terms offault detectability. The analysis is exemplified for a case with measurements affected by outliers.
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| 5. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
-
Fundamental Filtering Limitations in Linear Non-Gaussian Systems
- 2005
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Ingår i: Proceedings of the 16th IFAC World Congress. - Linköping : Linköping University Electronic Press. - 9783902661753 ; , s. 45-45
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Konferensbidrag (refereegranskat)abstract
- The Kalman filter is known to be the optimal linear filter for linear non-Gaussian systems. However, nonlinear filters such as Kalman filter banks and more recent numerical methods such as the particle filter are sometimes superior in performance. Here a procedure to a priori decide how much can be gained using nonlinear filters, without having to resort to Monte Carlo simulations, is outlined. The procedure is derived in terms of the posterior Cramér-Rao lower bound. Results are shown for a class of standard distributions and models in practice.
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| 6. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
-
Graphics Processing Unit Implementation of the Particle Filter
- 2006
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Modern graphics cards for computers, and especially their graphics processing units (GPUs), are designed for fast rendering of graphics. In order to achieve this GPUs are equipped with a parallel architecture which can be exploited for general-purpose computing on GPU (GPGPU) as a complement to the central processing unit (CPU). In this paper GPGPU techniques are used to make a parallel GPU implementation of state-of-the-art recursive Bayesian estimation using particle filters (PF). The modifications made to obtain a parallel particle filter, especially for the resampling step, are discussed and the performance of the resulting GPU implementation is compared to one achieved with a traditional CPU implementation. The resulting GPU filter is faster with the same accuracy as the CPU filter for many particles, and it shows how the particle filter can be parallelized.
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| 7. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
-
On Nonlinear Transformations of Stochastic Variables and its Application to Nonlinear Filtering
- 2007
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A class of nonlinear transformation-based filters (NLTF) for state estimation is proposed. The nonlinear transformations that can be used include first (TT1) and second (TT2) order Taylor expansions, the unscented transformation (UT), and the Monte Carlo transformation (MCT) approximation. The unscented Kalman filter (UKF) is by construction a special case, but also nonstandard implementations of the Kalman filter (KF) and the extended Kalman filter (EKF) are included, where there are no explicit Riccati equations. The theoretical properties of these mappings are important for the performance of the NLTF. TT 2 does by definition take care of the bias and covariance of the second order term that is neglected in the TT 1 based EKF. The UT computes this bias term accurately, but the covariance is correct only for scalar state vectors. This result is demonstrated with a simple example and a general theorem, which explicitly shows the difference between TT 1, TT 2, UT, and MCT.
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| 8. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
-
On Performance Measures for Approximative Parameter Estimation
- 2004
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Ingår i: Proceedings of Reglermöte 2004. - Linköping : Linköping University Electronic Press.
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- The Kalman filter computes the minimum variance state estimate as a linear function of measurements in the case of a linear model with Gaussian noise processes. There are plenty of examples of non-linear estimators that outperform the Kalman filter when the noise processes deviate from Gaussianity, for instance in target tracking with occasionally maneuvering targets. Here we present, in a preliminary study, a detailed analysis of the well-known parameter estimation problem. This time with Gaussian mixture measurement noise. We compute the discrepancy of the best linear unbiased estimator BLUE and the Cramer-Rao lower bound, and based on this conclude when computationally intensive Kalman filter banks or particle filters may be used to improve performance.
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| 9. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
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Performance Issues in Non-Gaussian Filtering Problems
- 2006
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Ingår i: Proceedings of the 2006 IEEE Nonlinear Statistical Signal Workshop. - Linköping : Linköping University Electronic Press. - 9781424405817 ; , s. 65-68
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Konferensbidrag (refereegranskat)abstract
- Performance for many filtering problems is usually measured using the second order moment. For non-Gaussian application this measure is not always sufficient. In the paper the Kullback divergence is extensively used to compare distributions. Several estimation techniques are compared, and methods such as the particle filter are shown to give superior performance over some classical second-order estimators.
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| 10. |
- Hendeby, Gustaf, 1978-, et al.
(författare)
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Recursive Triangulation Using Bearings-Only Sensors
- 2006
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Ingår i: Proceedings of the 2006 IEE Seminar on Target Tracking: Algorithms and Applications. - Linköping : Institution of Electrical Engineers (IEE). - 086341608X - 9780863416088 ; , s. 3-10
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Konferensbidrag (refereegranskat)abstract
- Recursive triangulation, using a bearings-only sensor, is investigated for a fly-by scenario. In a simulation study, several estimators are compared, fundamental estimation limits are calculated for different measurement noise assumptions. The quality of the estimated state distributions is evaluated.
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