A skewed unscented Kalman filter

Rezaie, Javad; Eidsvik, Jo

doi:10.1080/00207179.2016.1171912

Cited by 13 publications

(4 citation statements)

References 15 publications

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“…In recent years, high-order filters have been presented continuously, such as the fourth order unscented filter [47], fifth order UKF [9], and a skewed unscented Kalman filter [48], which achieve higher accuracy than the traditional second-order filter. However, the above mentioned high-order methods don't have an analytic solution and fail to complete the selection of sigma points and weights of high-order UT changes, thus they cannot constitute as a high-order UKF.…”

Section: Other Nonlinear Transformation Methods Mainly Include Thementioning

confidence: 99%

A New Adaptive High-Order Unscented Kalman Filter for Improving the Accuracy and Robustness of Target Tracking

Zhou

Hou

2019

IEEE Access

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In target tracking, the tracking process needs to constantly update the data information. For maneuvering target, model mismatch and loss of high-order moment information disrupt the accuracy of the state estimation. In this paper, an adaptive high-order unscented Kalman filter (AHUKF) algorithm is proposed for the case of errors occurring in the capturing of model dynamic behavior using the classical unscented Kalman filter (UKF) algorithm. By introducing the free parameter, the analytical solution of the high-order unscented transformation (UT) was obtained, the basis for choosing free parameters was analyzed, and the stability of the algorithm was discussed. A method for obtaining the optimal adaptive factor based on the prediction residual estimation covariance matrix was proposed, which reduces the influence of the dynamic model error and was applied to the target tracking model. In this paper, the proposed AHUKF is applied to a target tracking problem with state mutation, different sampling intervals, and different turn rates, respectively. Simulation results for target tracking illustrate that the proposed algorithm is more accurate and robust than the UKF, high-order unscented Kalman filter (HUKF) and adaptive unscented Kalman filter (AUKF). INDEX TERMS UKF, optimal adaptive factor, adaptive filtering, orthogonality principle, high-order UT sampling.

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Section: Other Nonlinear Transformation Methods Mainly Include Thementioning

confidence: 99%

A New Adaptive High-Order Unscented Kalman Filter for Improving the Accuracy and Robustness of Target Tracking

Zhou

Hou

2019

IEEE Access

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“…The closed skew-normal and the SUN distributions have been applied in a wide range of applied domains, and their relevance appears to be growing. The following is a non-exhaustive list of methodologies and applied domains where these distributions have been employed: stochastic frontier analysis in the context of productivity analysis, considered by Domínguez-Molina et al (2007), Colombi (2013), Colombi et al (2014), Kumbhakar & Lai (2016); various models for the analysis of spatial data have been introduced by Allard & Naveau (2007), Hosseini et al (2011), Karimi & Mohammadzadeh (2012), Rimstad & Omre (2014), among others; analysis of longitudinal data for the distribution of random effects in work of Ghalani & Zadkarami (2019), and again Colombi (2013); combination of phase II and III clinical trials, by Azzalini & Bacchieri (2010); seismic inversion methodology for geological problems, by and Rezaie et al (2014); extended formulations of Kalman filter by Kim et al (2014) and Rezaie & Eidsvik (2016); application to small area estimation by Diallo & Rao (2018). In the context of binary data, Durante (2019) has shown that, under Gaussian priors for the probit coefficients, the posterior distribution has an exact unified skew-normal distribution; this formulation lends itself to interesting developments, such as those of Fasano et al (2019) and Fasano & Durante (2020).…”

Section: Early Development Applications and Some Open Problemsmentioning

confidence: 99%

Some properties of the unified skew-normal distribution

Arellano–Valle¹,

Azzalini²

2020

Preprint

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For the family of multivariate probability distributions variously denoted as unified skewnormal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia's measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, and closure with respect to conditioning on intervals.

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“…This property can be found in variables that range from truncated Gaussian to normal distributions. Some examples of variables with such properties can be found in the domains of actuarial science [2], aerospace engineering [3], biology [4], chemical engineering [5], [6], climatology [7], communication/electronics [8], defense [9], earth sciences [10], economics/finance [11], forestry/remote sensing [12], mathematics [13], process systems and control [14], [15], and statistics [16]. In the presence of noisy measurements, Bayesian estimation with distributions like skew-t [17] or Weibull can provide optimal estimations for these variables.…”

Section: Introductionmentioning

confidence: 99%

“…[3] provides an overview of the filtering schemes for linear systems with CSN noise. Additionally, several methods such as ensemble filter [3], unscented Kalman filter [13], etc. have been developed for nonlinear systems with CSN noise.…”

Section: Introductionmentioning

confidence: 99%

Skew Filtering for Online State Estimation and Control

DOGRU¹,

Chiplunkar²,

Huang³

2022

Preprint

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<div>Process optimization and control can become challenging when the measurements are affected by irregular noise. Classical approaches utilize Gaussian method like Kalman filtering to alleviate the sensory noise. However, many industries involve skewed noise in their processes. While the closed skew normal (CSN) distribution generalizes a Gaussian distribution with additional parameters, its dimension increases during recursive estimation, making it impractical. Even though there exist some techniques for the solution, they are typically either too complicated or inaccurate for the higher dimensional problems. This study proposes a novel online optimization scheme to reduce the dimensionality of a CSN distribution while considering the properties of the complete empirical distribution. Since the objective function used during the optimization step considers the geometry of the metric space, the proposed scheme achieves the higher accuracy without sacrificing computational efficiency. After finding the reliable combination of objective function and optimizer, the proposed filter is applied to two real-time pilot-scale experiments. The results indicate that it is beneficial for recursive state estimation in the presence of skewed noise.<br></div>

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A skewed unscented Kalman filter

Cited by 13 publications

References 15 publications

A New Adaptive High-Order Unscented Kalman Filter for Improving the Accuracy and Robustness of Target Tracking

A New Adaptive High-Order Unscented Kalman Filter for Improving the Accuracy and Robustness of Target Tracking

Some properties of the unified skew-normal distribution

Skew Filtering for Online State Estimation and Control

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