State estimation of nonlinear dynamical systems using nonlinear update based Unscented Gaussian Sum Filter

Kottakki, Krishna Kumar; Bhartiya, Sharad; Bhushan, Mani

doi:10.1016/j.jprocont.2014.06.013

Cited by 31 publications

(27 citation statements)

References 15 publications

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“…Although OC-GS-UKF uses sum of Gaussians prior to represent, these individual Gaussians are also obtained after reapproximation of non-Gaussian densities. This, in turn can limit the performance of OC-GS-UKF [Kottakki et al 2014a] and can be improved by representing with a local sum of Gaussians density [Kottakki et al 2014b]. However, it is not considered in this present work.…”

Section: Resultsmentioning

confidence: 99%

Optimization Based Constrained Gaussian Sum Unscented Kalman Filter∗∗The authors thank the Department of Science and Technology, India, for partial financial assistance under grant 13DST057.

2016

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This work presents a novel constrained nonlinear state estimation approach for nonlinear dynamical systems. The proposed approach combines two key elements from well know Gaussian Sum Unscented Kalman Filter (GS-UKF) and Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) approaches. The proposed approach uses sum of Gaussians representation in GS-UKF and explicit constrained update in URNDDR to obtain feasible state estimates. The benefits of the proposed approach are demonstrated over the available constrained GS-UKF variants using a three state isothermal batch process case study available in literature.

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Section: Resultsmentioning

confidence: 99%

Optimization Based Constrained Gaussian Sum Unscented Kalman Filter∗∗The authors thank the Department of Science and Technology, India, for partial financial assistance under grant 13DST057.

2016

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“…This filter represents an augmentation of the recently proposed UGSF [2] with feasible sigma point generation using ICUT and projection based constraint handling capability.…”

Section: Projection Interval Unscented Gaussian Sum Filter (Piugsf)mentioning

confidence: 99%

“…of India, for funding through the project 13DST057. 2 krishnadfs@iitb.ac.in estimates for the temperatures in an oil bath system must ensure that the estimated hot oil temperature is higher than the temperature of the fluid being heated. Similarly, the sum of the estimates for the partial pressures in a multicomponent mixture must equal the total pressure, or estimates for the mole fractions of components must be between 0 and 1 and moreover should add to 1.…”

Section: Introductionmentioning

confidence: 99%

“…Nonlinear State Estimation: Several nonlinear recursive Bayesian estimation approaches such as Extended Kalman Filter (EKF) [7], Unscented Kalman Filter (UKF) [8], [1], Unscented Gaussian Sum Filter (UGSF) [2], Ensemble Kalman Filter (EnKF) [9]; Gaussian Sum Filters (GSF) [10], [11], [12]; and Particle Filters (PF) [13], [14] have been developed in literature to address the problem of nonlinear state estimation. Among these, EKF and UKF assume that all underlying densities are Gaussian.…”

Section: Introductionmentioning

confidence: 99%

“…The GS-UKF approach may therefore be conceptualized as N parallel UKFs. (iii) UGSF [2]: assumes the prior to be a sum of N = 2n + 1 Gaussians, with the covariance of each individual Gaussian being identical and their means located at the transformed 2n + 1 sigma points. The updated posterior is also a Gaussian sum, which is reapproximated as a single Gaussian and represented by 2n + 1 UT sigma points as in UKF.…”

Section: Introductionmentioning

confidence: 99%

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Projection based constrained nonlinear state estimation using Gaussian sum filters

Kottakki

Bhushan

Bhartiya

2016

2016 Indian Control Conference (ICC)

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Constraint handling is an integral part of any practical state estimation procedure. Most current approaches to constrained state estimation ensure that the point estimate is feasible with respect to the constraints and are based on popular unconstrained approaches such as sampling based approaches such as Unscented Kalman Filter (UKF) [1], which use deterministically chosen set of sigma points. However, UKF is based on an implicit assumption that the conditional state densities at various steps are Gaussian. In a recent work [2], a new filter termed as Unscented Gaussian Sum Filter (UGSF) was proposed that represents the prior density as a Gaussian sum. It was shown, using simulation studies, that the UGSF outperforms UKF thereby demonstrating the advantage of using a non-Gaussian prior. In this work, we propose to extend UGSF to constrained UGSF by incorporation of constraints on the states in the estimation process. In particular, we propose to use Interval Constrained Unscented Transformation (ICUT) [3] and projection algorithm [4] with the UGSF framework. Implementation on the three state isothermal batch reactor case study [5] shows that the proposed constrained UGSF using the projection method outperforms constrained UKF while maintaining the computation effort similar to the constrained UKF version.

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Extended moving horizon estimation for chemical processes under non‐Gaussian noises

Valipour

Ricardez‐Sandoval

2021

AIChE Journal

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Studies on moving horizon estimation (MHE) for applications featuring process uncertainties and measurement noises that follow time-dependent non-Gaussian distributions are absent from the literature. An extended version of MHE (EMHE) is proposed here to improve the estimation for a general class of non-Gaussian process uncertainties and measurement noises at no significant additional computational costs. Gaussian mixture models are introduced to the proposed EMHE to approximate offline the non-Gaussian densities of these random variables. Moreover, the proposed EMHE-based estimation scheme can be updated online by re-approximating the corresponding Gaussian mixture models when the distributions of noises/uncertainties change due to sudden or seasonal changes in the operating conditions. These updates are not expected to increase the central processing unit times considerably. Illustrative case studies featuring open-loop operation and closed-loop control using nonlinear model predictive control have shown that the practical features offered by EMHE resulted in significant improvements in state estimation and online control.

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State estimation of nonlinear dynamical systems using nonlinear update based Unscented Gaussian Sum Filter

Cited by 31 publications

References 15 publications

Optimization Based Constrained Gaussian Sum Unscented Kalman Filter∗∗The authors thank the Department of Science and Technology, India, for partial financial assistance under grant 13DST057.

Optimization Based Constrained Gaussian Sum Unscented Kalman Filter∗∗The authors thank the Department of Science and Technology, India, for partial financial assistance under grant 13DST057.

Projection based constrained nonlinear state estimation using Gaussian sum filters

Extended moving horizon estimation for chemical processes under non‐Gaussian noises

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