Gain function approximation in the feedback particle filter

Taghvaei, Amirhossein; Mehta, Prashant G.

doi:10.1109/cdc.2016.7799105

Cited by 24 publications

(21 citation statements)

References 68 publications

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“…Here we instead follow the presentation of Taghvaei and Mehta (2016) and Taghvaei et al (2017) and assume that we have M samples z i from a PDF π. The method is based on Since T reproduces constant functions, (155) determines φ i up to a constant contribution, which we fix by requiring for tackling this problem.…”

Section: Discussionmentioning

confidence: 99%

Data assimilation: The Schrödinger perspective

Reich

2019

Acta Numerica

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Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete-and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger's boundary value problem for stochastic processes in particular.

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Section: Discussionmentioning

confidence: 99%

Data assimilation: The Schrödinger perspective

Reich

2019

Acta Numerica

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“…For the purposes of this article, the question of how to optimally estimate the gain shall be left aside and we refer to e.g. [9], [10], [11] and the references therein. The aim is to show that the construction of an FPF-like algorithm for point processes can be fully reduced to the same types of equations as for the FPF gain, i.e.…”

Section: E Uniqueness Approximation and Estimation Of The Gainmentioning

confidence: 99%

Asymptotically Exact Unweighted Particle Filter for Manifold-Valued Hidden States and Point Process Observations

Surace

Kutschireiter

Pfister

2020

IEEE Control Syst. Lett.

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The filtering of a Markov diffusion process on a manifold from counting process observations leads to 'large' changes in the conditional distribution upon an observed event, corresponding to a multiplication of the density by the intensity function of the observation process. If that distribution is represented by unweighted samples or particles, they need to be jointly transformed such that they sample from the modified distribution. In previous work, this transformation has been approximated by a translation of all the particles by a common vector. However, such an operation is ill-defined on a manifold, and on a vector space, a constant gain can lead to a wrong estimate of the uncertainty over the hidden state. Here, taking inspiration from the feedback particle filter (FPF), we derive an asymptotically exact filter (called ppFPF) for point process observations, whose particles evolve according to intrinsic (i.e. parametrization-invariant) dynamics that are composed of the dynamics of the hidden state plus additional control terms. While not sharing the gain-times-error structure of the FPF, the optimal control terms are expressed as solutions to partial differential equations analogous to the weighted Poisson equation for the gain of the FPF. The proposed filter can therefore make use of existing approximation algorithms for solutions of weighted Poisson equations.

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“…In the following, we present a recent approach from [48] whose attractive feature is that it does not involve selection of basis functions. In the numerical results presented in Sec.…”

Section: Basis Functions On So(2)mentioning

confidence: 99%

“…For the second term on the right hand side of (47), taking A in (48) to be V α · f (X i t ) and B to be B α,i t ,…”

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confidence: 99%

Feedback particle filter on matrix lie groups

Zhang

Taghvaei

Mehta

2016

2016 American Control Conference (ACC)

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This paper is concerned with the problem of continuous-time nonlinear filtering for stochastic processes on a connected matrix Lie group. The main contribution of this paper is to derive the feedback particle filter (FPF) algorithm for this problem. In its general form, the FPF is shown to provide a coordinate-free description of the filter that automatically satisfies the geometric constraints of the manifold. The particle dynamics are encapsulated in a Stratonovich stochastic differential equation that retains the feedback structure of the original (Euclidean) FPF. The implementation of the filter requires a solution of a Poisson equation on the Lie group, and two numerical algorithms are described for this purpose. As an example, the FPF is applied to the problem of attitude estimation -a nonlinear filtering problem on the Lie group SO(3). The formulae of the filter are described using both the rotation matrix and the quaternion coordinates. Comparisons are also provided between the FPF and some popular algorithms for attitude estimation, namely the multiplicative EKF, the unscented quaternion estimator, the left invariant EKF, and the invariant ensemble Kalman filter. Numerical simulations are presented to illustrate the comparisons.

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Gain function approximation in the feedback particle filter

Cited by 24 publications

References 68 publications

Data assimilation: The Schrödinger perspective

Data assimilation: The Schrödinger perspective

Asymptotically Exact Unweighted Particle Filter for Manifold-Valued Hidden States and Point Process Observations

Feedback particle filter on matrix lie groups

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