Multivariable feedback particle filter

Yang, Tao; Laugesen, Richard S.; Mehta, Prashant G.; Meyn, Sean

doi:10.1016/j.automatica.2016.04.019

Cited by 68 publications

(71 citation statements)

References 38 publications

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“…An asymptotically exact filter has been found in [9] and [10] based on mean-field optimal control. It is usually referred to simply as Feedback Particle Filter, but in order to distinguish it from similar algorithms, we will refer to this specific algorithm as stochastic feedback particle filter (sFPF).…”

Section: Feedback Particle Filter (Fpf)mentioning

confidence: 99%

Gauge Freedom within the Class of Linear Feedback Particle Filters

Abedi

Surace

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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Feedback particle filters (FPFs) are Monte-Carlo approximations of the solution of the filtering problem in continuous time. The samples or particles evolve according to a feedback control law in order to track the posterior distribution. However, it is known that by itself, the requirement to track the posterior does not lead to a unique algorithm. Given a particle filter, another one can be constructed by applying a time-dependent transformation of the particles that keeps the posterior distribution invariant. Here, we characterize this gauge freedom within the class of FPFs for the linear-Gaussian filtering problem, and thereby extend previously known parametrized families of linear FPFs.

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Section: Feedback Particle Filter (Fpf)mentioning

confidence: 99%

Gauge Freedom within the Class of Linear Feedback Particle Filters

Abedi

Surace

2019

2019 IEEE 58th Conference on Decision and Control (CDC)

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“…Two examples of the controlled interacting particle systems are the classical ensemble Kalman filter (EnKF) [9]- [12] and the more recently developed feedback particle filter (FPF) [13], [14]. The EnKF algorithm is the workhorse in applications (such as weather prediction) where the state dimension d is very high; cf., [12], [15].…”

Section: B Literature Surveymentioning

confidence: 99%

An optimal transport formulation of the linear feedback particle filter

Taghvaei

Mehta

2016

2016 American Control Conference (ACC)

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Controlled interacting particle systems such as the ensemble Kalman filter (EnKF) and the feedback particle filter (FPF) are numerical algorithms to approximate the solution of the nonlinear filtering problem in continuous time. The distinguishing feature of these algorithms is that the Bayesian update step is implemented using a feedback control law. It has been noted in the literature that the control law is not unique. This is the main problem addressed in this paper. To obtain a unique control law, the filtering problem is formulated here as an optimal transportation problem. An explicit formula for the (mean-field type) optimal control law is derived in the linear Gaussian setting. Comparisons are made with the control laws for different types of EnKF algorithms described in the literature. Via empirical approximation of the mean-field control law, a finite-N controlled interacting particle algorithm is obtained. For this algorithm, the equations for empirical mean and covariance are derived and shown to be identical to the Kalman filter. This allows strong conclusions on convergence and error properties based on the classical filter stability theory for the Kalman filter. It is shown that, under certain technical conditions, the mean squared error (m.s.e.) converges to zero even with a finite number of particles. A detailed propagation of chaos analysis is carried out for the finite-N algorithm. The analysis is used to prove weak convergence of the empirical distribution as N → ∞. For a certain simplified filtering problem, analytical comparison of the m.s.e. with the importance sampling-based algorithms is described. The analysis helps explain the favorable scaling properties of the control-based algorithms reported in several numerical studies in recent literature.

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“…The scalar models are assumed here for the ease of presentation; cf., [15] for the multivariable FPF.…”

Section: Preliminaries a Feedback Particle Filtermentioning

confidence: 99%

“…II. A Galerkin approximation is used to approximate the gain function; cf., [15]. The common control is given by (17):…”

Section: Numerics a Summary Of Closed-loop Equationsmentioning

confidence: 99%

Control with rhythms: A CPG architecture for pumping a swing

Tilton

Mehta

2014

2014 American Control Conference

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This paper presents a bio-inspired central pattern generator (CPG) architecture for feedback control of rhythmic behavior. The CPG circuit is realized as a coupled oscillator feedback particle filter. The collective dynamics of the filter are used to approximate a posterior distribution that is used to construct the optimal control input. The architecture is illustrated with the aid of a model problem involving pumping up of a swing, modeled as a parametrically forced pendulum. For this problem, the coupled oscillator particle filter is designed and its control performance demonstrated in a simulation environment.

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Multivariable feedback particle filter

Cited by 68 publications

References 38 publications

Gauge Freedom within the Class of Linear Feedback Particle Filters

Gauge Freedom within the Class of Linear Feedback Particle Filters

An optimal transport formulation of the linear feedback particle filter

Control with rhythms: A CPG architecture for pumping a swing

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