A Systematization of the Unscented Kalman Filter Theory

Menegaz, Henrique M. T.; Ishihara, J.Y.; Borges, Geovany A.; Vargas, Alessandro N.

doi:10.1109/tac.2015.2404511

Cited by 209 publications

(167 citation statements)

References 54 publications

(199 reference statements)

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“…In the literature, the parametrization

α : = 1, β : = 0, κ : = 3 - n,

is widely used and considered to be the classical one, nowadays. Besides, other (nonclassical) values of the scalars α, β, and κ are possible and applied in practice as well as the number of the SP utilized can also be reduced to n +1 . However, reducing the SP set might affect the accuracy and robustness of the UKF and, hence, it is not addressed in our paper.…”

Section: The Accurate Continuous‐discrete Extended‐unscented Kalman Fmentioning

confidence: 99%

Hyperbolic‐singular‐value‐decomposition‐based square‐root accurate continuous‐discrete extended‐unscented Kalman filters for estimating continuous‐time stochastic models with discrete measurements

Kulikov

Kulikova

2019

Intl J Robust & Nonlinear

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Summary This paper presents novel square‐root accurate continuous‐discrete extended‐unscented Kalman filtering (ACD‐EUKF) algorithms for treating continuous‐time stochastic systems with discrete measurements. The time updates in such methods are fulfilled as those in the extended Kalman filter whereas their measurement updates are copied from the unscented Kalman filter. All this allows accurate predictions of the state mean and covariance to be combined with accurate measurement updates. The main weakness of this technique is the need for the Cholesky decomposition of predicted covariances derived in time‐update steps. Such a factorization is highly sensitive to numerical integration and round‐off errors committed, which may result in losing the covariance's positivity and, hence, failing the Cholesky decomposition. The latter problem is usually solved in the form of square‐root filtering implementations, which propagate not the covariance matrix but its square root instead. Here, we devise square‐root ACD‐EUKF methods grounded in the singular value decomposition (SVD). The SVD rooted in orthogonal transforms is applicable to any ACD‐EUKF with nonnegative weights, whereas the remaining ones, which can enjoy negative weights as well, are treated by means of the hyperbolic SVD based on J‐orthogonal transforms. The filters constructed are presented in a concise algorithmic form, which is convenient for practical use. Their two particular versions grounded in the classical and cubature unscented Kalman filtering parameterizations are examined in severe conditions of tackling a radar tracking problem, where an aircraft executes a coordinated turn. These are also compared to their non‐square‐root predecessor and other methods within the target tracking scenario with ill‐conditioned measurements.

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“…In the literature, the parametrization

α : = 1, β : = 0, κ : = 3 - n,

Section: The Accurate Continuous‐discrete Extended‐unscented Kalman Fmentioning

confidence: 99%

Hyperbolic‐singular‐value‐decomposition‐based square‐root accurate continuous‐discrete extended‐unscented Kalman filters for estimating continuous‐time stochastic models with discrete measurements

Kulikov

Kulikova

2019

Intl J Robust & Nonlinear

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“…alignment uncertainty ∆p) and world state (viz. start pose p start ), we have to use a version of a Square-Root Unscented Kalman Filter for a system in general form (see [17]). This filter uses an unscented transform that first creates so-called sigma points to approximate the probability distribution of the current multi-pose world state (plus the noise state ∆p), then applies the non-linear function to the set of sigma points, and finally computes a new µ * k , Σ * k from the function outputs.…”

Section: Probabilistic Poses and Square-root Unscented Kalman Filter mentioning

confidence: 99%

Dense-HOG-based drift-reduced 3D face tracking for infant pain monitoring

Saeijs

Ten

2017

SPIE Proceedings

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“…For this reason, we first recall the version referred to as Additive Homogeneous Symmetric Minimum UKF [15] (see also [19]). …”

Section: A Algorithms For Unscented Kalman Filtersmentioning

confidence: 99%

Unscented Kalman Filters for Estimating the Position of an Automotive Electronic Throttle Valve

Vargas

Menegaz

Ishihara

et al. 2016

IEEE Trans. Veh. Technol.

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Abstract-The paper presents an application of unscented Kalman filters to an automotive electronic throttle device. The motivation of this study is on estimating the position of the throttle device when measurements of position are inaccessible, e.g., due to failures in the sensor of position. In this case, an external wattmeter is connected in the circuitry to measure the power consumed by the throttle, and this information feeds unscented Kalman filters to produce the estimation for the position. Experimental data support the findings of this paper.Note to Practitioners: Abstract-Almost all of the brand-new vehicles based on spark-ignition combustion engines have an electronic throttle valve to control the power produced by the engine. The electronic throttle has a unique sensor for measuring the position of the throttle valve, and this feature can represent a serious problem when the sensor of position fails. As an attempt to prevent the effects of a failure from such sensor, we present an algorithm (unscented Kalman filter) combined with the use of an additional sensor, a wattmeter. The wattmeter is detached from the throttle's structure but is arranged so as to measure the electric power consumed by the throttle. Measurements of the power consumption then feed the unscented Kalman filter-this filter then produces an estimation of the position of the throttle valve. Experimental data illustrate the practical benefits of our approach.

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A Systematization of the Unscented Kalman Filter Theory

Cited by 209 publications

References 54 publications

Hyperbolic‐singular‐value‐decomposition‐based square‐root accurate continuous‐discrete extended‐unscented Kalman filters for estimating continuous‐time stochastic models with discrete measurements

Hyperbolic‐singular‐value‐decomposition‐based square‐root accurate continuous‐discrete extended‐unscented Kalman filters for estimating continuous‐time stochastic models with discrete measurements

Dense-HOG-based drift-reduced 3D face tracking for infant pain monitoring

Unscented Kalman Filters for Estimating the Position of an Automotive Electronic Throttle Valve

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