A square root formulation of the Kalman- Schmidt filter.

Bellantoni, Juan F.; Dodge, K.

doi:10.2514/3.4189

Cited by 120 publications

(15 citation statements)

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“…One way to deal with problem of state estimation of nonlinear systems is by using a nonlinear extension of the well‐known Kalman filter (KF) , known as EKF . The principle of work of the EKF is briefly illustrated in Figure .…”

Section: Methodsmentioning

confidence: 99%

Friction estimation in wind turbine blade bearings

Stevanović

Green

Worden

et al. 2015

Struct. Control Health Monit.

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Summary The influence of friction on wind turbines (WTs) is often seen as undesirable as it has been proven to be the root cause of different severe damages, where the most vulnerable WT's components are bearings. Accurate modelling and identification of friction affects are thus required in order to characterise frictional behaviour and prevent severe damages. This paper addresses the problem on the real‐time estimation of friction levels that vary in time with different rates in the WT's blade bearings. Because of ageing or damage progression in bearings, friction parameters change in time. Knowing the material properties and a damage model, monitoring of the friction can be used for condition monitoring of WT's blade bearings. The considered nonlinear identification methods suitable for estimation of fast varying parameters are the extended Kalman filter (EKF), the unscented Kalman filter, the particle filter (PF) and the PF combined with the EKF. This paper also proposes a novel modification of a differential evolution algorithm for the identification of parameters that slowly vary in time. The main contribution of this paper is the algorithm, which combines the modified differential evolution algorithm with optimal nonlinear filters for the estimation of parameters which vary at different rates. A LuGre friction model and a realistic WT sensor setup are selected. The techniques are benchmarked against simulated WT data, and their performances are compared and discussed. Copyright © 2015 John Wiley & Sons, Ltd.

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Section: Methodsmentioning

confidence: 99%

Friction estimation in wind turbine blade bearings

Stevanović

Green

Worden

et al. 2015

Struct. Control Health Monit.

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“…The following subsections discuss the properties of the function h, which has the form (5) where r B is the bistatic range, u and v are the direction cosines providing the angles of arrival of the return, and ṙ B is the bistatic range rate. Equations for the components are subsequently given in (22)- (24) and (39).…”

Section: The Measurement Modelmentioning

confidence: 99%

“…1.8]. 24 For the purposes of 24 Equation (43) implies that the noise has infinite variance at any point in time. That is, the derivative of the Wiener process does not this tutorial, the important part of this formal definition is that the value of an integral over a Gaussian white noise process is distributed Gaussian.…”

Section: The Dynamic Modelmentioning

confidence: 99%

Basic tracking using nonlinear 3D monostatic and bistatic measurements

Crouse¹

2014

IEEE Aerosp. Electron. Syst. Mag.

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Monostatic and bistatic position and Doppler measurements used in radar and sonar systems are nonlinear transformations of a Cartesian state. These nonlinearities pose a challenge for many target tracking algorithms, causing the so-called contact lens problem, which describes the nonlinear appearance of the measurement probability density function in Cartesian coordinates. This tutorial considers methods for measurement filtering (tracking without considering data association) using a single-Gaussian approximation when monostatic and bistatic position and Doppler measurements are available. The connection between the cubature Kalman filter and numerous other filtering algorithms is shown, and the accuracy and consistency of different algorithms are compared through simulation. An effort is made to express the geometric relationships associated with multistatic tracking in a simple vectorial manner. This tutorial focuses on basic tracking, and the companion tutorials "Tracking Using 3D Monostatic and Bistatic Measurements in Refractive Environments" and "Basic Tracking Using Nonlinear Continuous-Time Dynamic Models" extend the results to more sophisticated physical models.

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“…One approach that helps to mitigate the loss of positive definiteness is operating on a factorized form of the covariance matrix. This technique was pioneered by Potter (1963) and expanded upon and refined by Bellantoni and Dodge (1967), Andrews (1968), Schmidt (1970), Carlson (1973), Choe and Tapley (1975), Tapley and Choe (1976), Bierman (1976), and Thornton (1976), among others. Owing to its superior numerical properties, Potter's approach was implemented in the Apollo navigation filter (Battin & Levine, 1970).…”

Section: Introductionmentioning

confidence: 99%

Modular framework for implementation and analysis of recursive filters with considered and neglected parameters

DeMars

Ward

2020

Navigation

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This paper develops novel covariance and square-root factor formulations of a consider-neglect Kalman filter for navigation applications. The proposed filter partitions system parameters into three distinct categories: those to be estimated by the filter, those whose contribution to the system are considered without being explicitly estimated, and those with sufficiently low effect on the system such that their contribution can be neglected altogether. Discussion on appropriate selection of parameters to be considered and neglected is provided with specific attention given to descent-to-landing navigation. Monte Carlo simulations and analysis are performed to assess the performance of the developed square-root consider-neglect filter in a descent-to-landing navigation scenario.

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A square root formulation of the Kalman- Schmidt filter.

Cited by 120 publications

References 0 publications

Friction estimation in wind turbine blade bearings

Friction estimation in wind turbine blade bearings

Basic tracking using nonlinear 3D monostatic and bistatic measurements

Modular framework for implementation and analysis of recursive filters with considered and neglected parameters

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