Kalman Filtering in the Presence of State Space Equality Constraints

Gupta, Nachi

doi:10.1109/chicc.2006.4347158

Cited by 11 publications

(6 citation statements)

References 9 publications

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“…-The recursive structure of the algorithm allows for integration of iterative corrections for non-linear systems [40] as well as hard constraints (see the discussion in the introduction of [23,24,25]) to respect the conservativity of the model equations. However, these corrections may result in an increase of the computational resources required.…”

Section: Fine Grid Coarse Gridmentioning

confidence: 99%

“…-The model is chosen to be the discretized version of (24). The numerical test consists of one main simulation, which is run on the fine grid previously introduced, and an ensemble of N e = 100 coarse simulations used for assimilation purposes.…”

Section: Application: One-dimensional Burgers' Equationmentioning

confidence: 99%

“…Meldi & Poux [17] used a recursive procedure and a Lagrangian multiplier (the pressure field) to impose the zero-divergence condition of the velocity field for incompressible flows. Other proposals deal with imposing hard constraints in the framework of an optimization problem [23], ad-hoc augmented observation [24] and generalized regularization [25]. These approaches are responsible for a significant increase in the computational resources required, which is due to augmentation in size of the state estimation problem or to the optimization process, which usually needs the calculation of gradients of a cost function.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A multigrid/ensemble Kalman Filter strategy for assimilation of unsteady flows

Moldovan,

Lehnasch,

Cordier

et al. 2020

Preprint

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A sequential estimator based on the Ensemble Kalman Filter for Data Assimilation of fluid flows is presented in this research work. The main feature of this estimator is that the Kalman filter update, which relies on the determination of the Kalman gain, is performed exploiting the algorithmic features of the numerical solver employed as a model. More precisely, the multilevel resolution associated with the multigrid iterative approach for time advancement is used to generate several low-resolution numerical simulations. These results are used as ensemble members to determine the correction via Kalman filter, which is then projected on the high-resolution grid to correct a single simulation which corresponds to the numerical model. The assessment of the method is performed via the analysis of one-dimensional and two-dimensional test cases, using different dynamic equations. The results show an efficient trade-off in terms of accuracy and computational costs required. In addition, a physical regularization of the flow, which is not granted by classical KF approaches, is naturally obtained owing to the multigrid iterative calculations. The algorithm is also well suited for the analysis of unsteady phenomena and, in particular, for potential application to in-streaming Data Assimilation techniques.

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Section: Fine Grid Coarse Gridmentioning

confidence: 99%

Section: Application: One-dimensional Burgers' Equationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A multigrid/ensemble Kalman Filter strategy for assimilation of unsteady flows

Moldovan,

Lehnasch,

Cordier

et al. 2020

Preprint

View full text Add to dashboard Cite

show abstract

“…Two popular approaches for addressing state constraints within the Kalman filter framework are the pseudomeasurement method and the projection method. The pseudomeasurement method, as discussed in [4][5][6], augments the Kalman filter by considering the constraint as a perfect measurement without noise. The drawback to this method is that it causes the measurement noise covariance to be singular, which in turn can lead to numerical problems when implemented [7].…”

Section: Introductionmentioning

confidence: 99%

Norm-Constrained Consider Kalman Filtering

Chee

Forbes

2014

Journal of Guidance, Control, and Dynamics

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“…Another more useful form of projection based method has been proposed in [19]. In [20], a comparison of these two types of algorithms is presented along with some cases which yield equivalent results. A conceptually different method which can be related to both approaches is to search for optimal filter gains that yield estimates satisfying the constraints.…”

Section: Introductionmentioning

confidence: 99%

Target Tracking With Particle Filters Under Signal Propagation Delays

Orguner

Gustafsson

2011

IEEE Trans. Signal Process.

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Abstract-Signal propagation delays are hardly a problem for target tracking with standard sensors such as radar and vision due to the fact that the speed of light is much higher than the speed of the target. This contribution studies the case where the ratio of the target and the propagation speed is not negligible, as in the case of sensor networks with microphones, geophones or sonars for instance, where the signal speed in air, ground and water causes a state dependent and stochastic delay of the observations. The proposed approach utilizes an augmentation of the state vector with the propagation delay in a particle filtering framework to compensate for the negative effects of the delays. The model of the physics rules governing the propagation delays is used in interaction with the target motion model to yield an iterative prediction update step in the particle filter which is called the propagation delayed measurement particle filter (PDM-PF). The performance of PDM-PF is illustrated in a challenging target tracking scenario by making comparisons to alternative particle filters that can be used in similar cases.

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Kalman Filtering in the Presence of State Space Equality Constraints

Cited by 11 publications

References 9 publications

A multigrid/ensemble Kalman Filter strategy for assimilation of unsteady flows

A multigrid/ensemble Kalman Filter strategy for assimilation of unsteady flows

Norm-Constrained Consider Kalman Filtering

Target Tracking With Particle Filters Under Signal Propagation Delays

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