Optimization Based Constrained Unscented Gaussian Sum Filter

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

doi:10.1016/b978-0-444-63577-8.50131-5

Cited by 3 publications

(5 citation statements)

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“…This completes one cycle of the PIUGSF approach obtaining constrained point estimate for the k th instant starting from the given initial posterior moments at (k − 1) th time instant in PIUGSF approach. Note that if the Projection step is replaced with Density truncation step it will result in Truncated Interval UGSF or TIUGSF approach [24]. Further, if the sum of Gaussians representation of the prior density in PIUGSF and TIUGSF is replaced with a single Gaussian prior, then these approaches will converges to PIUKF and TIUKF approaches available in literature [4].…”

Section: Projection Of Posterior Mean [4]mentioning

confidence: 95%

“…The constrained filters can be summarized as (1) the pdf truncated versions with ICUT generation of sigma points for UKF, UGSF, and GS-UKF resulting in TIUKF, TIUGSF and GS-TIUKF filters; and (2) the corresponding projected versions resulting in PIUKF, PIUGSF and GS-PIUKF. The comparison of UKF and UGSF with the constrained measurement update for constraint handling has been studied elsewhere [22]. Based on simulation of a 3-state batch process using 100 different noise realizations, it is observed that absence of constraint handling results in large number of constraint violations by the state estimates.…”

Section: Introductionmentioning

confidence: 99%

“…(ii) Projection to feasible region [4]: The unconstrained posterior mean is obtained by minimizing the distance to the feasible space. (iii) Constrained measurement update [21], [22]: The measurement update step is solved as a constrained optimization problem. In absence of constraints, the solution is identical to the linear update as in Kalman filter (KF).…”

Section: Introductionmentioning

confidence: 99%

“… (24). to (26), x 1 , x 2 and x 3 represent the concentrations of the species of A, B and C, respectively, and k c i , i = 1, 2, 3, 4 represents the rate constant for i th reaction.…”

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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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Section: Projection Of Posterior Mean [4]mentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“… (24). to (26), x 1 , x 2 and x 3 represent the concentrations of the species of A, B and C, respectively, and k c i , i = 1, 2, 3, 4 represents the rate constant for i th reaction.…”

mentioning

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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“…The mixture Gaussian KF was derived by assuming that the sum of the Gaussians can approximate any density with arbitrary accuracy. 24,25 However, it is not easy to determine the number of filters and the corresponding computation burden is large.…”

Section: Introductionmentioning

confidence: 99%

Laplace ℓ₁ robust Student’s T-filter for attitude estimation of satellites

He²,

Guo³

et al. 2020

Measurement and Control

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A Laplace ℓ1 robust student’s T-filter is presented for satellites to estimate their attitude state despite severe measurement noise and modeling error. Although the student’s T-filter (STF) has the capability of handling measurement noise, it cannot address the unknown modeling error. It is further sensitive to the degree of freedom (DOF). Hence, the measurement covariance is updated by using the maximum correntropy criterion to accommodate the covariance of unknown modeling error in robust filtering design. Moreover, the Laplace distribution is derived to reduce the influence of the DOF parameter by forming a surrogate function of an optimization problem. Then, the majorization minimization approach is formulated to solve such an optimization problem and present the proposed filtering algorithm in the STF framework. Numerical simulation of applying the proposed attitude estimation scheme is performed by comparing it with the third/fifth-order cubature Kalman filters.

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Monte Carlo Gaussian Sum Filter For State Estimation of Nonlinear Dynamical Systems∗∗The authors would like to thank Dept. of Science and Technology for partially funding this research under the grant 13DST057.

2016

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Optimization Based Constrained Unscented Gaussian Sum Filter

Cited by 3 publications

References 10 publications

Projection based constrained nonlinear state estimation using Gaussian sum filters

Projection based constrained nonlinear state estimation using Gaussian sum filters

Laplace ℓ₁ robust Student’s T-filter for attitude estimation of satellites

Monte Carlo Gaussian Sum Filter For State Estimation of Nonlinear Dynamical Systems∗∗The authors would like to thank Dept. of Science and Technology for partially funding this research under the grant 13DST057.

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Optimization Based Constrained Unscented Gaussian Sum Filter

Cited by 3 publications

References 10 publications

Projection based constrained nonlinear state estimation using Gaussian sum filters

Projection based constrained nonlinear state estimation using Gaussian sum filters

Laplace ℓ1 robust Student’s T-filter for attitude estimation of satellites

Monte Carlo Gaussian Sum Filter For State Estimation of Nonlinear Dynamical Systems∗∗The authors would like to thank Dept. of Science and Technology for partially funding this research under the grant 13DST057.

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Laplace ℓ₁ robust Student’s T-filter for attitude estimation of satellites