Use of the Kalman Filter for Inference in State-Space Models With Unknown Noise Distributions

Maryak, J.L.; Spall, James C.; Heydon, B.D.

doi:10.1109/tac.2003.821415

Cited by 68 publications

(27 citation statements)

References 20 publications

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“…First, we can deal with any closed convex set of probability distributions used to characterize uncertainty in the prior, likelihood and state transition models. This is the main contribution of the paper and generalizes the results in [11], [13], [14], [15], [17], [18], [19] and [20]. Second, our solution allows us to work directly with CLPs, i.e., the lower envelopes of the set of probability distributions.…”

Section: Introductionsupporting

confidence: 64%

“…We should also like to mention here a slightly different approach to robustness that is presented in [18], [19] for the case of linear state models. The authors assume that the distributions of the noise terms belong to a set of unknown (nonGaussian) distributions with known finite second moments.…”

Section: Introductionmentioning

confidence: 99%

“…This is another reason the proposed method differs from the one we present in this paper which, conversely, aims to compute exact robust confidence intervals. A similar path to [18], [19] is followed in [20]; the method there is based on asymptotic theory that requires that the distributions of the noise terms become asymptotically Gaussian.…”

Section: Introductionmentioning

confidence: 99%

“…This allows us to derive more reliable inferences. In this respect, the idea of computing a robust credibility region is similar to the approach followed in [18], [19] for decision making. However, as already discussed above in this section, our approach differs from the one in [18], [19] in the way these credibility regions are derived.…”

Section: Introductionmentioning

confidence: 99%

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Robust Filtering Through Coherent Lower Previsions

Benavoli

Zaffalon

Miranda

2011

IEEE Trans. Automat. Contr.

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Abstract-The classical filtering problem is re-examined to take into account imprecision in the knowledge about the probabilistic relationships involved. Imprecision is modeled in this paper by closed convex sets of probabilities. We derive a solution of the state estimation problem under such a framework that is very general: it can deal with any closed convex set of probability distributions used to characterize uncertainty in the prior, likelihood, and state transition models. This is made possible by formulating the theory directly in terms of coherent lower previsions, that is, of the lower envelopes of the expectations obtained from the set of distributions. The general solution is specialized to two particular classes of coherent lower previsions. The first consists of a family of Gaussian distributions whose means are only known to belong to an interval. The second is the so-called linear-vacuous mixture model, which is a family made of convex combinations of a known nominal distribution (e.g., a Gaussian) with arbitrary distributions. For the latter case, we empirically compare the proposed estimator with the Kalman filter. This shows that our solution is more robust to the presence of modelling errors in the system and that, hence, appears to be a more realistic approach than the Kalman filter in such a case.Index Terms-Coherent lower previsions, epistemic irrelevance, robustness, Kalman filter.

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Section: Introductionsupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robust Filtering Through Coherent Lower Previsions

Benavoli

Zaffalon

Miranda

2011

IEEE Trans. Automat. Contr.

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“…The KF is also applicable to linear state space models with a wide range of non-Gaussian noise distributions [2]. General filtering theory for non-linear and non-Gaussian models was already presented in [3], [4], but in practice, numerical solutions derived as approximations to the general theory are usually computationally more demanding than the Gaussian approximations derived as extensions to the KF.…”

Section: Introductionmentioning

confidence: 99%

Fourier-Hermite Kalman Filter

Sarmavuori

Särkkä

2012

IEEE Trans. Automat. Contr.

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A Novel Robust MM Filter against Outliers

Liu

Liang

Liu

2014

Asian Journal of Control

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An Interacting Multiple Model (IMM) filter suppresses outliers by integrating model‐conditioned estimation and model mode recognition through adaptive mode switches based on a Bayesian probability update. However, it may face significant outlier‐caused peak errors, which are undesirable or even impermissible in many applications, for example, target tracking. This paper considers that, from the view of the Dempster‐Shafer Theory, the IMM filter actually fuses the Bayesian beliefs of the model mode with Dempster's Rule of Combination, which can deal with uncertainties instead of the evidence conflicts that may exist as outliers appear. Therefore, we propose the adaptive robust multiple model (RMM) filter through introducing practical expert knowledge in the belief function framework, which runs online to reduce outlier‐caused peak errors. In RMM, the Likelihood Temporal Ratio (LTR) is incorporated to provide extra information on the tendency of mode switching. Moreover, expert rules are introduced to construct adaptive belief functions using discount techniques and to select the combination rule that better deals with evidence conflicts when outliers appear. The simulations in target tracking scenarios show that the proposed RMM filter significantly reduces outlier‐caused peak errors and hence obtains a lower rate of track loss in the cluttered environment.

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Use of the Kalman Filter for Inference in State-Space Models With Unknown Noise Distributions

Cited by 68 publications

References 20 publications

Robust Filtering Through Coherent Lower Previsions

Robust Filtering Through Coherent Lower Previsions

Fourier-Hermite Kalman Filter

A Novel Robust MM Filter against Outliers

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