An insight into the issue of dimensionality in particle filtering

Quang, Paul Bui; Musso, Christian; Gland, François Le

doi:10.1109/icif.2010.5712050

Cited by 31 publications

(25 citation statements)

References 17 publications

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“…Many authors have examined in detail what obstacles arise when one tries to apply a PF to a very high dimensional problem. [14,15] examine the behavior of the mean square error (MSE) between the filter approximation of the integral in Eq. (3) and its true value.…”

Section: Problems Which Arise In High Dimensional Systemsmentioning

confidence: 99%

Particle filtering and marginalization for parameter identification in structural systems

Olivier

Smyth

2016

Struct. Control Health Monit.

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In structural health monitoring, one wishes to use available measurements from a structure to assess structural condition, localize damage if present, and quantify remaining life. Nonlinear system identification methods are considered that use a parametric, nonlinear, physics-based model of the system, cast in the state-space framework. Various nonlinear filters and parameter learning algorithms can then be used to recover the parameters and quantify uncertainty. This paper focuses on the particle filter (PF), which shows the advantage of not assuming Gaussianity of the posterior densities. However, the PF is known to behave poorly in high dimensional spaces, especially when static parameters are added to the state vector. To improve the efficiency of the PF, the concept of Rao-Blackwellisation is applied, that is, we use conditional linearities present in the equations to marginalize out some of the states/parameters and infer their conditional posterior pdf using the Kalman filtering equations. This method has been studied extensively in the particle filtering literature, and we start our discussion by improving upon and applying two well-known algorithms on a benchmark structural system. Then, noticing that in structural systems, high nonlinearities are often localized while the remaining equations are bilinear in the states and parameters, a novel algorithm is proposed, which combines this marginalization approach with a second-order extended Kalman filter. This new approach enables us to marginalize out all the states/parameters, which do not contribute to any high nonlinearity in the equations and, thus, improve identification of the unknown parameters.The idea is then to use a parametric model of the structure (using the equations of motion) that can be discretized in time and cast in state-space form. In the event that there is uncertainty in the excitation, environmental disturbance, or modeling error, some process noise may exist in the system equation. The response of structural systems is assumed to be measured at (or between) certain degrees of freedom. Because of real-life imperfections and sensor noise, one must also consider a potential measurement noise in the measurement equations. Nonlinear system identification tools are then used to recover the parameters of the model (stiffness, damping, and possible nonlinear parameters) and thus identify possible damage.For state filtering, that is, inference of the hidden (non-measured) states, the unscented Kalman filter (UKF) and the particle filter (PF) are both extensively studied in the literature. For parameter estimation, many different algorithms can be used: point estimates can be obtained via optimization algorithms (minimization of an error function, maximization of the likelihood, and expectation-maximization algorithm), or one can perform Bayesian inference, that is, infer the whole posterior density function (pdf) of the parameters knowing the measurements (Markov Chain Monte Carlo methods, joint state/parameter filters).However, learning al...

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Section: Problems Which Arise In High Dimensional Systemsmentioning

confidence: 99%

Particle filtering and marginalization for parameter identification in structural systems

Olivier

Smyth

2016

Struct. Control Health Monit.

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“…Regarding the implementation of the marginal filter, unlike the Markovian case, closed forms for the elements of P (t) are very difficult to obtain, because they explicitly depend on the marginal measures of X t , for each t, as (26) suggests. Even if P X −1 is an invariant measure, implying that the transition matrix is time invariant, the closed form determination of P (i, j) requires proper choice of P X −1 , which, in most cases, cannot be made by the user.…”

Section: Marginal Filtermentioning

confidence: 99%

Grid Based Nonlinear Filtering Revisited: Recursive Estimation & Asymptotic Optimality

Kalogerias

Petropulu

2016

IEEE Trans. Signal Process.

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We revisit the development of grid based recursive approximate filtering of general Markov processes in discrete time, partially observed in conditionally Gaussian noise. The grid based filters considered rely on two types of state quantization: The Markovian type and the marginal type. We propose a set of novel, relaxed sufficient conditions, ensuring strong and fully characterized pathwise convergence of these filters to the respective MMSE state estimator. In particular, for marginal state quantizations, we introduce the notion of conditional regularity of stochastic kernels, which, to the best of our knowledge, constitutes the most relaxed condition proposed, under which asymptotic optimality of the respective grid based filters is guaranteed. Further, we extend our convergence results, including filtering of bounded and continuous functionals of the state, as well as recursive approximate state prediction. For both Markovian and marginal quantizations, the whole development of the respective grid based filters relies more on linear-algebraic techniques and less on measure theoretic arguments, making the presentation considerably shorter and technically simpler.

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“…Among them are the local-linearisation ap proach [9], progressive correction [10], particle flow [11], Laplace method [12], to name a few. Efficient importance distributions are particularly important in applications that involve high-dimensional state spaces [13] or highly informative models (i.e. models with small process or measurement noise) [14], [11].…”

Section: Introductionmentioning

confidence: 99%

Efficient update of persistent particles in the SMC-PHD filter

Ristić

2015

2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The paper is devoted to the implementation of the Sequential Monte Carlo Probability Hypothesis Density (SMC-PHD) filter. A mea surement driven proposal for persistent target particles requires the predicted persistent target particles to be partitioned in a probabilis tic manner using the received measurement set. Each partition is subsequently updated using a conveniently designed efficient pro posal distribution (in this paper we apply the progressive correc tion). The performance of the described algorithm is demonstrated in the context of autonomous tracking of multiple moving targets using bearings-only measurements.

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An insight into the issue of dimensionality in particle filtering

Cited by 31 publications

References 17 publications

Particle filtering and marginalization for parameter identification in structural systems

Particle filtering and marginalization for parameter identification in structural systems

Grid Based Nonlinear Filtering Revisited: Recursive Estimation & Asymptotic Optimality

Efficient update of persistent particles in the SMC-PHD filter

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