Constrained Extended Kalman Filter based on Kullback-Leibler (KL) Divergence

Li, Ruoxia; Jan, Nabil Magbool; Prasad, Vinay; Huang, Biao

doi:10.23919/ecc.2018.8550441

Cited by 4 publications

(6 citation statements)

References 14 publications

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“…To improve the TDOA estimation accuracy, we seek another Gaussian PDF N (h k ; r k , Q r k ) closest to the unconstrained TDOA posterior N (h k ;r k , Qr k ) in terms of KLD and satisfying the inequality constraints on h k in (3). For this purpose, we shall follow [14] and express the confidence ellipsoid of the constrained posterior N (h k ; r k , Q r k ) as…”

Section: Kld Minimization-based Constrained Tdoa Estimationmentioning

confidence: 99%

“…To proceed, following [14] and [16], we introduce an auxiliary matrix Y k that satisfies the following linear matrix inequality…”

Section: Kld Minimization-based Constrained Tdoa Estimationmentioning

confidence: 99%

“…This SDP problem can be globally solved using convex optimization toolboxes such as YALMIP [17]. The solution to (14) gives the desired constrained TDOA posterior N (h k ; r k , Q r k ) with Q r k = S k S T k . Within the proposed KLD-CORKF+RBGF algorithm, the constrained posterior obtained above will be fed to RBGF for target position tracking.…”

Section: Kld Minimization-based Constrained Tdoa Estimationmentioning

confidence: 99%

“…By following [14], the constrained KLD minimization task is formulated as a semidefinite programming (SDP) problem that can be solved globally. Simulation results show that the newly developed KLD minimization-based CORKF (KLD-CORKF) offers better TDOA estimation accuracy than PDFT-CORKF.…”

Section: Introductionmentioning

confidence: 99%

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Kld Minimization-Based Constrained Measurement Filtering For Two-Step TDOA Indoor Tracking

Huang

Yang

Tao

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper presents an enhanced two-step method for tracking an indoor point target using the time difference of arrival (TDOA) measurements from an ultra wideband (UWB) positioning system. Again, the algorithm preprocesses the raw TDOAs and then feeds the results to a recursively bounded grid-based filter (RBGF) for position tracking. Different from the state-of-the-art, inequality constraints on the true TDOAs from the RBGF are exploited in the preprocessing step through constrained Kullback-Leibler divergence (KLD) minimization. In particular, a semidefinite programming (S-DP) problem is formulated and solved to find a Gaussian T-DOA posterior closest in terms of KLD to the unconstrained one while satisfying all inequality constraints. Simulations show that the newly developed algorithm outperforms the one we recently proposed to impose the inequality constraints via probability density function (PDF) truncation.

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Section: Kld Minimization-based Constrained Tdoa Estimationmentioning

confidence: 99%

“…To proceed, following [14] and [16], we introduce an auxiliary matrix Y k that satisfies the following linear matrix inequality…”

Section: Kld Minimization-based Constrained Tdoa Estimationmentioning

confidence: 99%

Section: Kld Minimization-based Constrained Tdoa Estimationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Kld Minimization-Based Constrained Measurement Filtering For Two-Step TDOA Indoor Tracking

Huang

Yang

Tao

et al. 2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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show abstract

“…The resulting covariance calculations are, however, still similar to the Kalman filter: that is, unconstrained propagation and correction involving the Kalman gain, which can affect the accuracy of the estimates. To eliminate this deficiency, [26] proposed a Kullback-Leibler based method to update states and error covariances by solving a convex optimization problem involving conic constraints.…”

Section: Literature Reviewmentioning

confidence: 99%

Ensemble Kalman methods with constraints

et al. 2019

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Ensemble Kalman methods constitute an increasingly important tool in both state and parameter estimation problems. Their popularity stems from the derivative-free nature of the methodology which may be readily applied when computer code is available for the underlying state-space dynamics (for state estimation) or for the parameter-to-observable map (for parameter estimation). There are many applications in which it is desirable to enforce prior information in the form of equality or inequality constraints on the state or parameter. This paper establishes a general framework for doing so, describing a widely applicable methodology, a theory which justifies the methodology, and a set of numerical experiments exemplifying it.

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An improved recursive non-linear dynamic data reconciliation for non-linear state estimation subject to bound constraints

Prakash

Anbumalar²

2023

Int J Adv Eng Sci Appl Math

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Constrained Extended Kalman Filter based on Kullback-Leibler (KL) Divergence

Cited by 4 publications

References 14 publications

Kld Minimization-Based Constrained Measurement Filtering For Two-Step TDOA Indoor Tracking

Kld Minimization-Based Constrained Measurement Filtering For Two-Step TDOA Indoor Tracking

Ensemble Kalman methods with constraints

An improved recursive non-linear dynamic data reconciliation for non-linear state estimation subject to bound constraints

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