Filtering method for nonlinear systems with constraints

Wang, Li-Sheng; Chiang, Yi-Te; Chang, Fi‐John

doi:10.1049/ip-cta:20020799

Cited by 64 publications

(39 citation statements)

References 7 publications

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“…Our approach to this problem is similar to the iterative method discussed by Julier in [23] and is in some ways similar to Wang's maximum likelihood approach, presented in [19], due to its use of iteration.…”

Section: A Equality Constrained Kalman Filteringmentioning

confidence: 99%

“…We will now introduce our iterative algorithm, which is related to the pseudo-measurement approaches developed in [17]- [19]. Our approach to this problem is similar to the iterative method discussed by Julier in [23] and is in some ways similar to Wang's maximum likelihood approach, presented in [19], due to its use of iteration.…”

Section: A Equality Constrained Kalman Filteringmentioning

confidence: 99%

“…Finally, we update the mean of the Kalman filterx + k|k with the state x i at convergence. The reason that our method relates to the pseudo-measurement technique for constrained filtering which was presented in [17]- [19] is that we are essentially performing an iterated extended Kalman filter (IEKF) update step [24] with a zero variance pseudo-measurement g(x).…”

Section: A Equality Constrained Kalman Filteringmentioning

confidence: 99%

“…In [22], Simon and Chia present a method for equality constrained Kalman filtering in which linear constraints are incorporated into the Kalman filter update by projecting the unconstrained estimate onto the constraint hyperplane. Another method, which in [20], [21] is shown to be equivalent to the projection approach, is to use a pseudo-measurement technique that simulates a perfect measurement to enforce equality constraints [17]- [19].…”

Section: A Equality Constrained Kalman Filteringmentioning

confidence: 99%

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Constrained filtering with contact detection data for the localization and registration of continuum robots in flexible environments

Tully

Bajo

Kantor

et al. 2012

2012 IEEE International Conference on Robotics and Automation

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Abstract-This paper presents a novel filtering technique that uses contact detection data and environmental stiffness estimates to register and localize a robot with respect to an a priori 3D surface model. The algorithm leverages geometric constraints within a Kalman filter framework and relies on two distinct update procedures: 1) an equality constrained step for when the robot is forcefully contacting the environment, and 2) an inequality constrained step for when the robot lies in the freespace of the environment. This filtering procedure registers the robot by incrementally eliminating probabilistically infeasible state space regions until a high likelihood solution emerges. In addition to registration and localization, the algorithm can estimate the deformation of the surface model and can detect false positives with respect to contact estimation. This method is experimentally evaluated with an experiment involving a continuum robot interacting with a bench-top flexible structure. The presented algorithm produces an experimental error in registration (with respect to the end-effector position) of 1.1 mm, which is less than 0.8 percent of the robot length.

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Section: A Equality Constrained Kalman Filteringmentioning

confidence: 99%

Section: A Equality Constrained Kalman Filteringmentioning

confidence: 99%

Section: A Equality Constrained Kalman Filteringmentioning

confidence: 99%

Section: A Equality Constrained Kalman Filteringmentioning

confidence: 99%

See 2 more Smart Citations

Constrained filtering with contact detection data for the localization and registration of continuum robots in flexible environments

Tully

Bajo

Kantor

et al. 2012

2012 IEEE International Conference on Robotics and Automation

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“…One and possibly the more popular of these is the use of constraints as fictitious (pseudo) measurements where the constraint equation is considered as a (possibly noisy) information source about the state [13][14][15]. A conceptually similar method which uses the so called three block Kalman filter of [16] is given in [17]. The second approach of handling constraints is the projection type methods in which the unconstrained estimates are projected onto the constraint surface (manifold) at the end of each estimation cycle [18].…”

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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Robust linearly constrained extended Kalman filter for mismatched nonlinear systems

Hrustic

Abdallah

Vilà‐Valls

et al. 2020

Intl J Robust & Nonlinear

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SummaryStandard state estimation techniques, ranging from the linear Kalman filter (KF) to nonlinear extended KF (EKF), sigma‐point or particle filters, assume a perfectly known system model, that is, process and measurement functions and system noise statistics (both the distribution and its parameters). This is a strong assumption which may not hold in practice, reason why several approaches have been proposed for robust filtering, mainly because the filter performance is particularly sensitive to different model mismatches. In the context of linear filtering, a solution to cope with possible system matrices mismatch is to use linear constraints. In this contribution we further explore the extension and use of recent results on linearly constrained KF for robust nonlinear filtering under both process and measurement model mismatch. We first investigate how linear equality constraints can be incorporated within the EKF and derive a new linearly constrained extended KF (LCEKF). Then we detail its use to mitigate parametric modeling errors in the nonlinear process and measurement functions. Numerical results are provided to show the performance improvement of the new LCEKF for robust vehicle navigation.

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Filtering method for nonlinear systems with constraints

Cited by 64 publications

References 7 publications

Constrained filtering with contact detection data for the localization and registration of continuum robots in flexible environments

Constrained filtering with contact detection data for the localization and registration of continuum robots in flexible environments

Target Tracking With Particle Filters Under Signal Propagation Delays

Robust linearly constrained extended Kalman filter for mismatched nonlinear systems

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