A Backward-Simulation Based Rao-Blackwellized Particle Smoother for Conditionally Linear Gaussian Models

Särkkä, Simo; Bunch, Pete; Godsill, Simon

doi:10.3182/20120711-3-be-2027.00115

Cited by 13 publications

(15 citation statements)

References 17 publications

(31 reference statements)

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“…The expressions derived in this section have previously been presented by [32] who, independently from our preliminary work in [27], have derived an RBPS for hierarchical CLG models. Nevertheless, we believe that the present section will be useful in order to make the derivation for the (more involved) mixed linear/nonlinear model in Section 4.3 more accessible.…”

Section: Remarkmentioning

confidence: 99%

“…The same holds for the conditional backward information filter. In this section, we show how to implement the backward recursions given by (25), (27) and (33) on square-root form.…”

Section: Square-root Implementationmentioning

confidence: 99%

“…Let Ω 1/2 t be a matrix such that Ω t = Ω 1/2 t Ω T/2 , and similarly for Ω t . Rather than computing the information matrices Ω t and Ω t in the backward filter, we will propagate the square-roots Ω Consider first the backward measurement update (27). We compute a QRfactorization of the matrix,…”

Section: Square-root Implementationmentioning

confidence: 99%

“…Furthermore, independently of [27], Whiteley et al [32] have derived essentially the same RBPS for hierarchical models as we present here, although they study explicitly the special case of jump Markov systems. The present work goes beyond [27,22] on several accounts. First, the techniques used for the derivations and, as an effect, details of the algorithmic specifications in these two proceedings differ substantially.…”

mentioning

confidence: 97%

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Rao-Blackwellized Particle Smoothers for Conditionally Linear Gaussian Models

Lindsten

Bunch

Särkkä

et al. 2016

IEEE J. Sel. Top. Signal Process.

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Sequential Monte Carlo (SMC) methods, such as the particle filter, are by now one of the standard computational techniques for addressing the filtering problem in general state-space models. However, many applications require post-processing of data offline. In such scenarios the smoothing problem-in which all the available data is used to compute state estimates-is of central interest. We consider the smoothing problem for a class of conditionally linear Gaussian models. We present a forward-backward-type Rao-Blackwellized particle smoother (RBPS) that is able to exploit the tractable substructure present in these models. Akin to the well known Rao-Blackwellized particle filter, the proposed RBPS marginalizes out a conditionally tractable subset of state variables, effectively making use of SMC only for the "intractable part" of the model. Compared to existing RBPS, two key features of the proposed method are: (i) it does not require structural approximations of the model, and (ii) the aforementioned marginalization is done both in the forward direction and in the backward direction.

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Section: Remarkmentioning

confidence: 99%

“…The same holds for the conditional backward information filter. In this section, we show how to implement the backward recursions given by (25), (27) and (33) on square-root form.…”

Section: Square-root Implementationmentioning

confidence: 99%

Section: Square-root Implementationmentioning

confidence: 99%

mentioning

confidence: 97%

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Rao-Blackwellized Particle Smoothers for Conditionally Linear Gaussian Models

Lindsten

Bunch

Särkkä

et al. 2016

IEEE J. Sel. Top. Signal Process.

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“…Even though solutions that (asymptotically) achieve linear computational cost have been proposed [11]- [13], these methods might not be feasible in practice due to numerical issues or high rejection rates. Other approaches try to exploit the inherent structure of the system in order to reduce the dimensionality of the problem, for example by using Rao-Blackwellization [14], [15]. When using two filter smoothers on the other hand, it is not quite obvious how to address the backward filtering pass and different solutions have been proposed.…”

Section: Introductionmentioning

confidence: 99%

A two filter particle smoother for Wiener state-space systems

Hostettler

2015

2015 IEEE Conference on Control Applications (CCA)

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Abstract-In this article, a two filter particle smoothing algorithm for Wiener state-space systems is proposed. The smoother is obtained by exploiting the model structure. This leads to a suitable proposal density for the backward filter inherent in the problem instead of introducing an artificial one. Numerical examples are provided in order to illustrate the proposed algorithm's performance and to compare it to current state of the art smoothers from the literature. It is found that the proposed method yields comparable results with less computational complexity as backward simulation-based particle smoothing algorithms.

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Combining particle MCMC with Rao-Blackwellized Monte Carlo data association for parameter estimation in multiple target tracking

Kokkala

Särkkä

2015

Digital Signal Processing

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We consider state and parameter estimation in multiple target tracking problems with data association uncertainties and unknown number of targets.We show how the problem can be recast into a conditionally linear Gaussian state-space model with unknown parameters and present an algorithm for computationally efficient inference on the resulting model. The proposed algorithm is based on combining the Rao-Blackwellized Monte Carlo data association algorithm with particle Markov chain Monte Carlo algorithms to jointly estimate both parameters and data associations. Both particle marginal Metropolis-Hastings and particle Gibbs variants of particle MCMC are considered. We demonstrate the performance of the method both using simulated data and in a real-data case study of using multiple target tracking to estimate the brown bear population in Finland.

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A Backward-Simulation Based Rao-Blackwellized Particle Smoother for Conditionally Linear Gaussian Models

Cited by 13 publications

References 17 publications

Rao-Blackwellized Particle Smoothers for Conditionally Linear Gaussian Models

Rao-Blackwellized Particle Smoothers for Conditionally Linear Gaussian Models

A two filter particle smoother for Wiener state-space systems

Combining particle MCMC with Rao-Blackwellized Monte Carlo data association for parameter estimation in multiple target tracking

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