Marginalized adaptive particle filtering for nonlinear models with unknown time-varying noise parameters

Özkan, Emre; Šmı́dl, Václav; Saha, Saikat; Lundquist, Christian; Gustafsson, Fredrik

doi:10.1016/j.automatica.2013.02.046

Cited by 90 publications

(47 citation statements)

References 19 publications

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“…As detailed in appendix A of this paper, following the work of two-random-variable variational Bayes by Särkkä and Nummenmaa (2009) and Särkkä and Hartikainen (2013) in which x t and R t are unknown (with Q t as a known input), applying general Bayesian filtering framework and techniques (Özkana et al 2013(Özkana et al , Särkkä 2013) to a linear state space model where both Q t and R t are among the unknown time-varying stochastic variables to be estimated, and making the standard variational Bayesian approximation (Bishop 2006, Tzikas et al 2008, Grimmer 2011 to the joint distribution of the random variables, this paper developed a three-random-variable variational approximation of sequential Bayesian inference (VASB) algorithm to estimate the time-varying distributions of x t , Q t and R t jointly.…”

Section: Introductionmentioning

confidence: 99%

Time-varying forecasts by variational approximation of sequential Bayesian inference

Ling

Stone

2015

Quantitative Finance

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Methods developed for making time-varying forecasts in economic and financial analysis include (a) equal-weighted moving-window (or rolling) regression, (b) time-weighted (e.g. exponentially weighted) regression, (c) the Kalman filter (KF) and (d) adaptive Kalman filters. This paper developed a new method based on variational approximation of sequential Bayesian inference (VASB). Concepts and notions of the sequential Bayesian analysis and the variational approximation of an intractable posterior are simple and straightforward. Our VASB algorithm is not complicated and is easy to code. For a regression on multiple time-series, the regression coefficients, standard errors, prediction and residual error are time-varying and are estimated jointly at every time step. For a single time-series (e.g. price returns of an asset), its mean and variance are time-varying and are predicted jointly at every time step. The VASB algorithm performs better than the rolling and time-weighted statistics or regressions and the KF in terms of higher predictive power and stronger robustness. Derivations of the VASB algorithm are presented in the appendices.

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Section: Introductionmentioning

confidence: 99%

Time-varying forecasts by variational approximation of sequential Bayesian inference

Ling

Stone

2015

Quantitative Finance

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“…In the particle filtering framework, this leads to another Rao-Blackwellization approach. One typical application of the resulting RBPF is a noise adaptive particle filtering for a general statespace model [32,37,39]. A brief description of the general approach is given below.…”

Section: Conditionally Conjugate Latent Process Modelmentioning

confidence: 99%

“…Further, following [32], assume that the unknown noise parameters θ k are slowly varying in time. This slowly varying nature can arise, e.g., due to model misspecification [48].…”

Section: Rao-blackwellized Noise Adaptive Particle Filteringmentioning

confidence: 99%

“…However, typically the transition model p(θ k+1 |θ k ) is unknown. In [32], the evolution is defined implicitly as a Kullback-Leibler norm constraint on the time variability which leads to an exponential forgetting mechanism operating on the sufficient statistics. This keeps the predictive density p(θ k+1 |e 1:k ) in the same class as in (38) with statistics updated from (39) as…”

Section: Rao-blackwellized Noise Adaptive Particle Filteringmentioning

confidence: 99%

See 1 more Smart Citation

A Bayesian Uncertainty Analysis for Nonignorable Nonresponse

Saha¹,

Hendeby²,

Gustafsson³

2015

Current Trends in Bayesian Methodology With Applications

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The discrete time general state-space model is a flexible framework to deal with the nonlinear and/or non-Gaussian time series problems. However, the associated (Bayesian) inference problems are often intractable. Additionally, for many applications of interest, the inference solutions are required to be recursive over time. The particle filter (PF) is a popular class of Monte Carlo based numerical methods to deal with such problems in real time. However, PF is known to be computationally expensive and does not scale well with the problem dimensions. If a part of the state space is analytically tractable conditioned on the remaining part, the Monte Carlo based estimation is then confined to a space of lower dimension, resulting in an estimation method known as the Rao-Blackwellized particle filter (RBPF). In this chapter, we present a brief review of Rao-Blackwellized particle filtering. Especially, we outline a set of popular conditional tractable structures admitting such Rao-Blackwellization in practice. For some special and/or relatively new cases, we also provide reasonably detailed descriptions.We confine our presentation mostly to the practitioners’ point of view.

This is a review article on the models admitting Rao-Blackwellization in particle filtering.

COOP-LOCCADIC

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“…In the experiments, we employ an exponential forgetting factor in the time update of the sufficient statistics ν k|k and V k|k , which is shown to provide the maximum entropy distribution for the prediction when the transition density for the target extent is unknown but the change in the prediction density is upper bounded by a Kullback Leibler distance (see [28,Theorem 1]). This will help the elliptical model to adapt itself for possible orientation changes in the examples.…”

Section: A Alternative Models 1) Random Matrix Modelmentioning

confidence: 99%

Extended Target Tracking Using Gaussian Processes

Wahlström

Özkan

2015

IEEE Trans. Signal Process.

204

182

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Abstract-In this paper, we propose using Gaussian processes to track an extended object or group of objects, that generates multiple measurements at each scan. The shape and the kinematics of the object are simultaneously estimated, and the shape is learned online via a Gaussian process. The proposed algorithm is capable of tracking different objects with different shapes within the same surveillance region. The shape of the object is expressed analytically, with well-defined confidence intervals, which can be used for gating and association. Furthermore, we use an efficient recursive implementation of the algorithm by deriving a state space model in which the Gaussian process regression problem is cast into a state estimation problem.

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Marginalized adaptive particle filtering for nonlinear models with unknown time-varying noise parameters

Cited by 90 publications

References 19 publications

Time-varying forecasts by variational approximation of sequential Bayesian inference

Time-varying forecasts by variational approximation of sequential Bayesian inference

A Bayesian Uncertainty Analysis for Nonignorable Nonresponse

Extended Target Tracking Using Gaussian Processes

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