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Simo Sarkka - One of the best experts on this subject based on the ideXlab platform.

  • Student-t Process Quadratures for Filtering of Non-Linear Systems with Heavy-Tailed Noise
    arXiv: Methodology, 2017
    Co-Authors: Jakub Pruher, Filip Tronarp, Simo Sarkka, Toni Karvonen, Ondřej Straka
    Abstract:

    The aim of this article is to design a moment transformation for Student- t distributed random variables, which is able to account for the error in the numerically computed mean. We employ Student-t process quadrature, an instance of Bayesian quadrature, which allows us to treat the integral itself as a random variable whose variance provides information about the incurred integration error. Advantage of the Student- t process quadrature over the traditional Gaussian process quadrature, is that the integral variance depends also on the function values, allowing for a more robust modelling of the integration error. The moment transform is applied in nonlinear Sigma-Point filtering and evaluated on two numerical examples, where it is shown to outperform the state-of-the-art moment transforms.

  • Sigma Point filtering for nonlinear systems with non additive heavy tailed noise
    International Conference on Information Fusion, 2016
    Co-Authors: Filip Tronarp, Roland Hostettler, Simo Sarkka
    Abstract:

    This paper is concerned with Sigma-Point methods for filtering in nonlinear systems, where the process and measurement noise are heavy tailed and enter the system non-additively. The problem is approached within the framework of assumed density filtering and the necessary statistics are approximated using Sigma-Point methods developed for Student's t-distribution. This leads to UKF/CKF-type of filters for Student's t-distribution. Four different Sigma-Point methods are considered that compute exact expectations of polynomials for orders up to 3, 5, 7, and 9, respectively. The resulting algorithms are evaluated in a simulation example and real data from a pedestrian dead-reckoning experiment. In the simulation experiment the nonlinear Student's t filters are found to be faster in suppressing large errors in the state estimates in comparison to the UKF when filtering in nonlinear Gaussian systems with outliers in process and measurement noise. In the pedestrian dead-reckoning experiment the Sigma-Point Student's t filter was found to yield better loop closure and path length estimates as well as significantly improved robustness towards extreme accelerometer measurement spikes.

  • Sigma Point filtering and smoothing based parameter estimation in nonlinear dynamic systems
    Journal of Advances in Information Fusion, 2016
    Co-Authors: Juho Kokkala, Arno Solin, Simo Sarkka
    Abstract:

    We consider approximate maximum likelihood parameter estimation in nonlinear state-space models. We discuss both direct optimization of the likelihood and expectation--maximization (EM). For EM, we also give closed-form expressions for the maximization step in a class of models that are linear in parameters and have additive noise. To obtain approximations to the filtering and smoothing distributions needed in the likelihood-maximization methods, we focus on using Gaussian filtering and smoothing algorithms that employ Sigma-Points to approximate the required integrals. We discuss different Sigma-Point schemes based on the third, fifth, seventh, and ninth order unscented transforms and the Gauss--Hermite quadrature rule. We compare the performance of the methods in two simulated experiments: a univariate nonlinear growth model as well as tracking of a maneuvering target. In the experiments, we also compare against approximate likelihood estimates obtained by particle filtering and extended Kalman filtering based methods. The experiments suggest that the higher-order unscented transforms may in some cases provide more accurate estimates

  • posterior linearization filter principles and implementation using Sigma Points
    IEEE Transactions on Signal Processing, 2015
    Co-Authors: Angel F Garciafernandez, Lennart Svensson, Mark R Morelande, Simo Sarkka
    Abstract:

    This paper is concerned with Gaussian approximations to the posterior probability density function (PDF) in the update step of Bayesian filtering with nonlinear measurements. In this setting, Sigma-Point approximations to the Kalman filter (KF) recursion are widely used due to their ease of implementation and relatively good performance. In the update step, these Sigma-Point KFs are equivalent to linearizing the nonlinear measurement function by statistical linear regression (SLR) with respect to the prior PDF. In this paper, we argue that the measurement function should be linearized using SLR with respect to the posterior rather than the prior to take into account the information provided by the measurement. The resulting filter is referred to as the posterior linearization filter (PLF). In practice, the exact PLF update is intractable but can be approximated by the iterated PLF (IPLF), which carries out iterated SLRs with respect to the best available approximation to the posterior. The IPLF can be seen as an approximate recursive Kullback-Leibler divergence minimization procedure. We demonstrate the high performance of the IPLF in relation to other Gaussian filters in two numerical examples.

  • gaussian filtering and variational approximations for bayesian smoothing in continuous discrete stochastic dynamic systems
    Signal Processing, 2015
    Co-Authors: Juha Alaluhtala, Simo Sarkka, Robert Piche
    Abstract:

    The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the true smoothing distribution. In this work, we present a comparison between two Gaussian approximation methods. The Gaussian filtering based Gaussian smoother uses a Gaussian approximation for the filtering distribution to form an approximation for the smoothing distribution. The variational Gaussian smoother is based on minimizing the Kullback-Leibler divergence of the approximate smoothing distribution with respect to the true distribution. The results suggest that for highly nonlinear systems, the variational Gaussian smoother can be used to iteratively improve the Gaussian filtering based smoothing solution. We also present linearization and Sigma-Point methods to approximate the intractable Gaussian expectations in the variational Gaussian smoothing equations. In addition, we extend the variational Gaussian smoother for certain class of systems with singular diffusion matrix. HighlightsComparison of Gaussian filtering based and variational Gaussian smoothers for SDEs.Sigma-Point approximations of the variational Gaussian smoother.Extension of variational Gaussian smoother to singular systems.Variational Gaussian smoother improves results in highly nonlinear systems.

Jaison Thomas Ambadan - One of the best experts on this subject based on the ideXlab platform.

  • Sigma Point particle filter for parameter estimation in a multiplicative noise environment
    Journal of Advances in Modeling Earth Systems, 2011
    Co-Authors: Jaison Thomas Ambadan, Youmin Tang
    Abstract:

    [1] A pre-requisite for the “optimal estimate” by the ensemble-based Kalman filter (EnKF) is the Gaussian assumption for background and observation errors, which is often violated when the errors are multiplicative, even for a linear system. This study first explores the challenge of the multiplicative noise to the current EnKF schemes. Then, a Sigma Point Kalman Filter based Particle Filter (SPPF) is presented as an alternative to solve the issues associated with multiplicative noise. The classic Lorenz '63 model and a higher dimensional Lorenz '96 model are used as test beds for the data assimilation experiments. Performance of the SPPF algorithm is compared against a standard EnKF as well as an advanced square-root Sigma-Point Kalman Filters (SPKF). The results show that the SPPF outperforms the EnKF and the square-root SPKF in the presence of multiplicative noise. The super ensemble structure of the SPPF makes it computationally attractive compared to the standard Particle Filter (PF).

  • Sigma Point kalman filter data assimilation methods for strongly nonlinear systems
    Journal of the Atmospheric Sciences, 2009
    Co-Authors: Jaison Thomas Ambadan, Youmin Tang
    Abstract:

    Abstract Performance of an advanced, derivativeless, Sigma-Point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) schemes. Three particular cases—namely, the state, parameter, and joint estimation of states and parameters from a set of discontinuous noisy observations—are studied. The problems associated with the use of tangent linear model (TLM) or Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced Sigma-Point subspace model is proposed and investigated for higher-dimensional systems. A low-dimensional Lorenz 1963 model and a higher-dimensional Lorenz 1995 model are used as the test beds for data assimilation experiments. The ...

Youmin Tang - One of the best experts on this subject based on the ideXlab platform.

  • Sigma Point particle filter for parameter estimation in a multiplicative noise environment
    Journal of Advances in Modeling Earth Systems, 2011
    Co-Authors: Jaison Thomas Ambadan, Youmin Tang
    Abstract:

    [1] A pre-requisite for the “optimal estimate” by the ensemble-based Kalman filter (EnKF) is the Gaussian assumption for background and observation errors, which is often violated when the errors are multiplicative, even for a linear system. This study first explores the challenge of the multiplicative noise to the current EnKF schemes. Then, a Sigma Point Kalman Filter based Particle Filter (SPPF) is presented as an alternative to solve the issues associated with multiplicative noise. The classic Lorenz '63 model and a higher dimensional Lorenz '96 model are used as test beds for the data assimilation experiments. Performance of the SPPF algorithm is compared against a standard EnKF as well as an advanced square-root Sigma-Point Kalman Filters (SPKF). The results show that the SPPF outperforms the EnKF and the square-root SPKF in the presence of multiplicative noise. The super ensemble structure of the SPPF makes it computationally attractive compared to the standard Particle Filter (PF).

  • Sigma Point kalman filter data assimilation methods for strongly nonlinear systems
    Journal of the Atmospheric Sciences, 2009
    Co-Authors: Jaison Thomas Ambadan, Youmin Tang
    Abstract:

    Abstract Performance of an advanced, derivativeless, Sigma-Point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and ensemble Kalman filter (EnKF) schemes. Three particular cases—namely, the state, parameter, and joint estimation of states and parameters from a set of discontinuous noisy observations—are studied. The problems associated with the use of tangent linear model (TLM) or Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced Sigma-Point subspace model is proposed and investigated for higher-dimensional systems. A low-dimensional Lorenz 1963 model and a higher-dimensional Lorenz 1995 model are used as the test beds for data assimilation experiments. The ...

Gregory L Plett - One of the best experts on this subject based on the ideXlab platform.

  • Electrochemical Model and Sigma Point Kalman Filter Based Online Oriented Battery Model
    'Institute of Electrical and Electronics Engineers (IEEE)', 2021
    Co-Authors: E. Miguel, Gregory L Plett, Scott M. Trimboli, I. Lopetegi, L. Oca, U. Iraola, E. Bekaert
    Abstract:

    This paper presents a reduced-order electrochemical battery model designed for the online implementation of battery control systems. The model is based on porous-electrode and concentrated-solution theory frameworks and is able to predict voltage as well as the internal electrochemical variables of a battery. The reduction of the model leads to a physics-based one-dimensional discrete-time state-space reduced-order model (ROM), which is especially beneficial for online systems. Models optimized around different operational setPoints are combined to predict cell variables over a wide range of temperatures and state of charges (SOCs) using the output-blending method. A Sigma-Point Kalman filter is further used to manage inaccuracies generated by the reduction process and experimental-related issues such as measurement error (noise) in the current and voltage sensors. The state-estimation accuracies are measured against a full-order model (FOM) developed in COMSOL. The whole system is able to track the internal variables of the cell, as well as the cell voltage and SOC with very high accuracy, demonstrating its suitability for an online battery control system

  • Sigma Point kalman filtering for battery management systems of lipb based hev battery packs part 1 introduction and state estimation
    Journal of Power Sources, 2006
    Co-Authors: Gregory L Plett
    Abstract:

    Abstract We have previously described algorithms for a battery management system (BMS) that uses Kalman filtering (KF) techniques to estimate such quantities as: cell self-discharge rate, state-of-charge (SOC), nominal capacity, resistance, and others. Since the dynamics of electrochemical cells are not linear, we used a non-linear extension to the original KF called the extended Kalman filter (EKF). We were able to achieve very good estimates of SOC and other states and parameters using EKF. However, some applications e.g., that of the battery-management-system (BMS) of a hybrid-electric-vehicle (HEV) can require even more accurate estimates than these. To see how to improve on EKF, we must examine the mathematical foundation of that algorithm in more detail than we presented in the prior work to discover the assumptions that are made in its derivation. Since these suppositions are not met exactly in BMS application, we explore an alternative non-linear Kalman filtering techniques known as “Sigma-Point Kalman filtering” (SPKF), which has some theoretical advantages that manifest themselves in more accurate predictions. The computational complexity of SPKF is of the same order as EKF, so the gains are made at little or no additional cost. The SPKF method as applied to BMS algorithms is presented here in a series of two papers. This first paper is devoted primarily to deriving the EKF and SPKF algorithms using the framework of sequential probabilistic inference. This is done to show that the two algorithms, which at first may look quite different, are actually very similar in most respects; also, we discover why we might expect the SPKF to outperform EKF in non-linear estimation applications. Results are presented for a battery pack based on a third-generation prototype LiPB cell, and compared with prior results using EKF. As expected, SPKF outperforms EKF, both in its estimate of SOC and in its estimate of the error bounds thereof. The second paper presents some more advanced algorithms for simultaneous state and parameter estimation, and gives results for a fourth-generation prototype LiPB cell.

  • Sigma Point kalman filtering for battery management systems of lipb based hev battery packs part 2 simultaneous state and parameter estimation
    Journal of Power Sources, 2006
    Co-Authors: Gregory L Plett
    Abstract:

    Abstract We have previously described algorithms for a battery management system (BMS) that uses Kalman filtering (KF) techniques to estimate such quantities as: cell self-discharge rate, state-of-charge, nominal capacity, resistance, and others. Since the dynamics of electrochemical cells are not linear, we used a nonlinear extension to the original KF called the extended Kalman filter (EKF). Now, we introduce an alternative nonlinear Kalman filtering technique known as “Sigma-Point Kalman filtering” (SPKF), which has some theoretical advantages that manifest themselves in more accurate predictions. The computational complexity of SPKF is of the same order as EKF, so the gains are made at little or no additional cost. This paper is the second in a two-part series. The first paper explored the theoretical background to the Kalman filter, the extended Kalman filter, and the Sigma-Point Kalman filter. It explained why the SPKF is often superior to the EKF and applied SPKF to estimate the state of a third-generation prototype lithium-ion polymer battery (LiPB) cell in dynamic conditions, including the state-of-charge of the cell. In this paper, we first investigate the use of the SPKF method to estimate battery parameters. A numerically efficient “square-root Sigma-Point Kalman filter” (SR-SPKF) is introduced for this purpose. Additionally, we discuss two SPKF-based methods for simultaneous estimation of both the quickly time-varying state and slowly time-varying parameters. Results are presented for a battery pack based on a fourth-generation prototype LiPB cell, and some limitations of the current approach, based on the probability density functions of estimation error, are also discussed.

R Van Der Merwe - One of the best experts on this subject based on the ideXlab platform.

  • gaussian mixture Sigma Point particle filters for sequential probabilistic inference in dynamic state space models
    International Conference on Acoustics Speech and Signal Processing, 2003
    Co-Authors: R Van Der Merwe
    Abstract:

    For sequential probabilistic inference in nonlinear non-Gaussian systems, approximate solutions must be used. We present a novel recursive Bayesian estimation algorithm that combines an importance sampling based measurement update step with a bank of Sigma-Point Kalman filters for the time-update and proposal distribution generation. The posterior state density is represented by a Gaussian mixture model that is recovered from the weighted particle set of the measurement update step by means of a weighted EM algorithm. This step replaces the resampling stage needed by most particle filters and mitigates the "sample depletion" problem. We show that this new approach has an improved estimation performance and reduced computational complexity compared to other related algorithms.