| 1. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Approximate inference in state space models with intractable likelihoods using Gaussian process optimisation
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We propose a novel method for MAP parameter inference in nonlinear state space models with intractable likelihoods. The method is based on a combination of Gaussian process optimisation (GPO), sequential Monte Carlo (SMC) and approximate Bayesian computations (ABC). SMC and ABC are used to approximate the intractable likelihood by using the similarity between simulated realisations from the model and the data obtained from the system. The GPO algorithm is used for the MAP parameter estimation given noisy estimates of the log-likelihood. The proposed parameter inference method is evaluated in three problems using both synthetic and real-world data. The results are promising, indicating that the proposed algorithm converges fast and with reasonable accuracy compared with existing methods.
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| 2. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Bayesian inference for mixed effects models with heterogeneity
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- We are interested in Bayesian modelling of panel data using a mixed effects model with heterogeneity in the individual random effects. We compare two different approaches for modelling the heterogeneity using a mixture of Gaussians. In the first model, we assume an infinite mixture model with a Dirichlet process prior, which is a non-parametric Bayesian model. In the second model, we assume an over-parametrised finite mixture model with a sparseness prior. Recent work indicates that the second model can be seen as an approximation of the former. In this paper, we investigate this claim and compare the estimates of the posteriors and the mixing obtained by Gibbs sampling in these two models. The results from using both synthetic and real-world data supports the claim that the estimates of the posterior from both models agree even when the data record is finite.
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| 3. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Hierarchical Bayesian approaches for robust inference in ARX models
- 2012
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Ingår i: Proceedings from the 16th IFAC Symposium on System Identification, 2012. - : International Federation of Automatic Control. - 9783902823069 ; , s. 131-136
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Konferensbidrag (refereegranskat)abstract
- Gaussian innovations are the typical choice in most ARX models but using other distributions such as the Student's t could be useful. We demonstrate that this choice of distribution for the innovations provides an increased robustness to data anomalies, such as outliers and missing observations. We consider these models in a Bayesian setting and perform inference using numerical procedures based on Markov Chain Monte Carlo methods. These models include automatic order determination by two alternative methods, based on a parametric model order and a sparseness prior, respectively. The methods and the advantage of our choice of innovations are illustrated in three numerical studies using both simulated data and real EEG data.
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| 4. |
- Dahlin, Johan, 1986-, et al.
(författare)
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Quasi-Newton particle Metropolis-Hastings
- 2015
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Ingår i: Proceedings of the 17th IFAC Symposium on System Identification.. - : Elsevier. ; , s. 981-986
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Konferensbidrag (refereegranskat)abstract
- Particle Metropolis-Hastings enables Bayesian parameter inference in general nonlinear state space models (SSMs). However, in many implementations a random walk proposal is used and this can result in poor mixing if not tuned correctly using tedious pilot runs. Therefore, we consider a new proposal inspired by quasi-Newton algorithms that may achieve similar (or better) mixing with less tuning. An advantage compared to other Hessian based proposals, is that it only requires estimates of the gradient of the log-posterior. A possible application is parameter inference in the challenging class of SSMs with intractable likelihoods.We exemplify this application and the benefits of the new proposal by modelling log-returns offuture contracts on coffee by a stochastic volatility model with alpha-stable observations.
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| 5. |
- Geng, Li-Hui, et al.
(författare)
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Smoothed State Estimation via Efficient Solution of Linear Equations
- 2023
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Ingår i: IEEE Transactions on Automatic Control. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9286 .- 1558-2523 .- 2334-3303. ; 68:10, s. 5877-5889
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Tidskriftsartikel (refereegranskat)abstract
- This article addresses the problem of computing fixed-interval smoothed state estimates of a linear time-varying Gaussian stochastic system. There already exist many algorithms that perform this computation, but all of them impose certain restrictions on system matrices in order for them to be applicable, and the restrictions vary considerably between the various existing algorithms. This article establishes a new sufficient condition for the fixed-interval smoothing density to exist in a Gaussian form that can be completely characterized by associated means and covariances. It then develops an algorithm to compute these means and covariances with no further assumptions required. This results in an algorithm more generally applicable than any one of the multitude of existing algorithms available to date.
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| 6. |
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| 7. |
- Hol, Jeroen D., 1981-
(författare)
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Sensor Fusion and Calibration of Inertial Sensors, Vision, Ultra-Wideband and GPS
- 2011
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The usage of inertial sensors has traditionally been confined primarily to the aviation and marine industry due to their associated cost and bulkiness. During the last decade, however, inertial sensors have undergone a rather dramatic reduction in both size and cost with the introduction of MEMS technology. As a result of this trend, inertial sensors have become commonplace for many applications and can even be found in many consumer products, for instance smart phones, cameras and game consoles. Due to the drift inherent in inertial technology, inertial sensors are typically used in combination with aiding sensors to stabilize andimprove the estimates. The need for aiding sensors becomes even more apparent due to the reduced accuracy of MEMS inertial sensors.This thesis discusses two problems related to using inertial sensors in combination with aiding sensors. The first is the problem of sensor fusion: how to combine the information obtained from the different sensors and obtain a good estimate of position and orientation. The second problem, a prerequisite for sensor fusion, is that of calibration: the sensors themselves have to be calibrated and provide measurement in known units. Furthermore, whenever multiple sensors are combined additional calibration issues arise, since the measurements are seldom acquired in the same physical location and expressed in a common coordinate frame. Sensor fusion and calibration are discussed for the combination of inertial sensors with cameras, UWB or GPS.Two setups for estimating position and orientation in real-time are presented in this thesis. The first uses inertial sensors in combination with a camera; the second combines inertial sensors with UWB. Tightly coupled sensor fusion algorithms and experiments with performance evaluation are provided. Furthermore, this thesis contains ideas on using an optimization based sensor fusion method for a multi-segment inertial tracking system used for human motion capture as well as a sensor fusion method for combining inertial sensors with a dual GPS receiver.The above sensor fusion applications give rise to a number of calibration problems. Novel and easy-to-use calibration algorithms have been developed and tested to determine the following parameters: the magnetic field distortion when an IMU containing magnetometers is mounted close to a ferro-magnetic object, the relative position and orientation of a rigidly connected camera and IMU, as well as the clock parameters and receiver positions of an indoor UWB positioning system.
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| 8. |
- Nordh, Jerker, et al.
(författare)
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Particle filtering based identification for autonomous nonlinear ODE models
- 2015
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Ingår i: IFAC-PapersOnLine. - : Elsevier BV. - 2405-8963. ; 48:28, s. 415-420, s. 415-420
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Tidskriftsartikel (refereegranskat)abstract
- This paper presents a new black-box algorithm for identification of a nonlinear autonomous system in stable periodic motion. The particle filtering based algorithm models the signal as the output of a continuous-time second order ordinary differential equation (ODE). The model is selected based on previous work which proves that a second order ODE is sufficient to model a wide class of nonlinear systems with periodic modes of motion, also systems that are described by higher order ODEs. Such systems are common in systems biology. The proposed algorithm is applied to data from the well-known Hodgkin-Huxley neuron model. This is a challenging problem since the Hodgkin-Huxley model is a fourth order model, but has a mode of oscillation in a second order subspace. The numerical experiments show that the proposed algorithm does indeed solve the problem.
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| 9. |
- Schön, Thomas Bo, et al.
(författare)
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Sequential Monte Carlo Methods for System Identification
- 2015
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Ingår i: Proceedings of the 17th IFAC Symposium on System Identification.. - : Elsevier. ; , s. 775-786
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Konferensbidrag (refereegranskat)abstract
- One of the key challenges in identifying nonlinear and possibly non-Gaussian state space models (SSMs) is the intractability of estimating the system state. Sequential Monte Carlo (SMC) methods, such as the particle filter (introduced more than two decades ago), provide numerical solutions to the nonlinear state estimation problems arising in SSMs. When combined with additional identification techniques, these algorithms provide solid solutions to the nonlinear system identification problem. We describe two general strategies for creating such combinations and discuss why SMC is a natural tool for implementing these strategies.
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