Saturated Particle Filter: Almost sure convergence and improved resampling

Stano, Paweł Mirosław; Lendek, Zsófia; Babuška, Robert

doi:10.1016/j.automatica.2012.10.006

Cited by 19 publications

(8 citation statements)

References 39 publications

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“…For example, methods based on empirical Gramians in low-dimensional systems [14][15][16][17][18] are not applicable to large-scale networks due to their high computational complexity and, as we show in this paper, low accuracy under realistic conditions. State estimation (problem (ii )), on the other hand, has been studied extensively in nonlinear systems, and various approaches have been proposed, such as nonlinear extensions of the Kalman filter [19,20], particle filters [21,22], moving horizon estimation (MHE) techniques [23,24],…”

Section: Introductionmentioning

confidence: 99%

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State Observation and Sensor Selection for Nonlinear Networks

Haber

Molnár

Motter

2018

IEEE Trans. Control Netw. Syst.

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A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system. However, network states are usually unknown, and only a fraction of the state variables are directly measurable. The observability problem concerns reconstructing the network state from this limited information. Here, we propose a general optimization-based approach for observing the states of nonlinear networks and for optimally selecting the observed variables. Our results reveal several fundamental limitations in network observability, such as the trade-off between the fraction of observed variables and the observation length on one side, and the estimation error on the other side. We also show that, owing to the crucial role played by the dynamics, purely graphtheoretic observability approaches cannot provide conclusions about one's practical ability to estimate the states. We demonstrate the effectiveness of our methods by finding the key components in biological and combustion reaction networks from which we determine the full system state. Our results can lead to the design of novel sensing principles that can greatly advance prediction and control of the dynamics of such networks.

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Section: Introductionmentioning

confidence: 99%

“…of the Kalman filter [19,20], particle filters [21,22], moving horizon estimation (MHE) techniques [23,24], and others [25]. However, the applicability of such approaches to large-scale nonlinear networks has not been investigated under the realistic conditions of a limited number of sensor nodes and a limited observation horizon.…”

mentioning

confidence: 99%

State Observation and Sensor Selection for Nonlinear Networks

Haber

Molnár

Motter

2018

IEEE Trans. Control Netw. Syst.

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“…To circumvent this, the constraint can be taken into account at earlier stages of the filtering, such as in the proposal distribution design and the likelihood weight update calculation [ 103 ]. For the case that the state variables are defined on a compact, bounded or saturated state space, the so-called saturated PF (SPF) has been developed [ 9 ], which exploits the structure of the saturated system using a specific importance sampling distribution. More generally, [ 104 ] considers the constraints on the prior particle set, the posterior particle set and the state estimation (akin to the acceptance-rejection approach), respectively.…”

Section: Single-target Pfmentioning

confidence: 99%

A Survey of Recent Advances in Particle Filters and Remaining Challenges for Multitarget Tracking

Wang

Sun

et al. 2017

Sensors

126

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We review some advances of the particle filtering (PF) algorithm that have been achieved in the last decade in the context of target tracking, with regard to either a single target or multiple targets in the presence of false or missing data. The first part of our review is on remarkable achievements that have been made for the single-target PF from several aspects including importance proposal, computing efficiency, particle degeneracy/impoverishment and constrained/multi-modal systems. The second part of our review is on analyzing the intractable challenges raised within the general multitarget (multi-sensor) tracking due to random target birth and termination, false alarm, misdetection, measurement-to-track (M2T) uncertainty and track uncertainty. The mainstream multitarget PF approaches consist of two main classes, one based on M2T association approaches and the other not such as the finite set statistics-based PF. In either case, significant challenges remain due to unknown tracking scenarios and integrated tracking management.

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“…A straightforward, popular method is resampling, which randomly replaces low-weight particles with high-weight ones [1]. More sophisticated mechanisms have also been developed, e.g., [2,3,4,5]. Among them, the method of implicit sampling has inspired much attention.…”

Section: Introductionmentioning

confidence: 99%

Implicit Particle Filtering via a Bank of Nonlinear Kalman Filters

Askari,

Haile,

et al. 2022

Preprint

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The implicit particle filter seeks to mitigate particle degeneracy by identifying particles in the target distribution's highprobability regions. This study is motivated by the need to enhance computational tractability in implementing this approach. We investigate the connection of the particle update step in the implicit particle filter with that of the Kalman filter and then formulate a novel realization of the implicit particle filter based on a bank of nonlinear Kalman filters. This realization is more amenable and efficient computationally.

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Saturated Particle Filter: Almost sure convergence and improved resampling

Cited by 19 publications

References 39 publications

State Observation and Sensor Selection for Nonlinear Networks

State Observation and Sensor Selection for Nonlinear Networks

A Survey of Recent Advances in Particle Filters and Remaining Challenges for Multitarget Tracking

Implicit Particle Filtering via a Bank of Nonlinear Kalman Filters

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