• Journal of Electrical Engineering and Technology
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• v.11 no.2
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• pp.347-352
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• 2016

This paper investigates the application, design and implementation of unscented Kalman filter observer using the various scaling parameters for the sensorless speed control of a permanent magnet synchronous motor. The principles of unscented transformation and unscented Kalman filter are examined and their applications are explained. Typically the mapping transformation process is divided into two types, namely the basic unscented transformation and the general unscented transformation by virtue of the scaling parameter value. And resultantly, the number of sampling points, weights, code configuration and computation time are different. But there is no little information on the scaling parameter value or how this value influences the system performance. To analyze the unscented transformation with the various scaling parameters in this study, the experimental results under a wide range of operation condition have been demonstrated.

• Journal of Aerospace System Engineering
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• v.10 no.1
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• pp.15-20
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• 2016

The optimal estimation of a general continuous-discrete system can be achieved through the solution of the Fokker-Planck equation and the Bayesian update. Due the high nonlinearity of the equation of motion of the system and the measurement model, it is necessary to linearize the both equation. To avoid linearization, the filter based on Fokker-Planck equation is designed. with the unscented transformation update mechanism, in which the associated Fokker-Planck equation was solved efficiently and accurately via discrete quadrature and the measurement update was done through the unscented transformation update mechanism. This filter based on the Direct Quadrature Moment of Method(DQMOM) and the unscented transformation update is applied to the bearing only target tracking problem. The proposed filter can still provide more accurate estimation of the state than those of the extended Kalman filter especially when measurements are sparse. Simulation results indicate that the advantages of the proposed filter based on the DQMOM and the unscented transformation update make it a promising alternative to the extended Kalman filter.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.6
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• pp.1019-1025
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• 2016

This paper proposes a parallel reduced-order square-root unscented Kalman filter for state estimation of a sensorless permanent-magnet synchronous motor. The appearance of an unscented Kalman filter is caused by the linearization process error between a real system and classical Kalman model. The unscented transformation can make a more accurate Kalman model. However, the complexity is its main drawback. This paper investigates the design and implementation of the proposed filter with Potter and Carlson square-root form. The proposed parallel reduced-order square-root unscented Kalman filter reduces memory and code size, and improves numerical computation. And the performance is not significantly different from the unscented Kalman filter. The experimentation is performed for the verification of the proposed filter.

• Journal of Astronomy and Space Sciences
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• v.28 no.3
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• pp.183-192
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• 2011

The current study analyzes the effects of the scaling parameters of the batch unscented transformation on precision satellite orbit determination. Satellite laser ranging (SLR) data are used in the orbit determination algorithm, which consists of dynamics model, observation model and filtering algorithm composed of the batch unscented transformation. TOPEX/Poseidon SLR data are used by utilizing the normal point (NP) data observed from ground station. The filtering algorithm includes a repeated series of processes to determine the appropriate scaling parameters for the batch unscented transformation. To determine appropriate scaling parameters, general ranges of the scaling parameters of ${\alpha}$, ${\beta}$, k, $\lambda$ are established. Depending on the range settings, each parameter was assigned to the filtering algorithm at regular intervals. Appropriate scaling parameters are determined for observation data obtained from several observatories, by analyzing the relationship between tuning properties of the scaling parameters and estimated orbit precision. The orbit determination of satellite using the batch unscented transformation can achieve levels of accuracy within several tens of cm with the appropriate scaling parameters. The analyses in the present study give insights into the roles of scaling parameters in the batch unscented transformation method.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.6
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• pp.174-180
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• 2016

This paper study about an unscented Kalman filter with a variety type of unscented transformation to estimate state values for speed control without position sensor of a permanent-magnet synchronous motor. The principles of an unscented transformation and unscented Kalman filter are examined and their application is explained. Generally the mapping process can be divided into two type, such as a basic and a general form according to a scaling parameter. And computation time, the number of samples, and weights about samples are different from each other. But, there is no little information on the scaling parameter value how this value influences the system performance. Simulation and experimental results show the validity of the designed unscented transformation performance with the various scaling parameter values for sensorless motor drive.

• Journal of Electrical Engineering and Technology
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• v.12 no.2
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• pp.683-688
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• 2017

The unscented Kalman filter features a direct transforming process involving unscented transformation for removing the linearization process error that may occur in the extended Kalman filter. This paper proposes a reduced-order unscented Kalman filter for the sensorless control of a permanent magnet synchronous motor. The proposed method can reduce the computational load without degrading the accuracy compared to the conventional Kalman filters. Moreover, the proposed method can directly estimate the electrical rotor position and speed without a back-electromotive force. The proposed Kalman filter for the sensorless control of a permanent magnet synchronous motor is verified through the simulation and experimentation. The performance of the proposed method is evaluated over a wide range of operations, such as forward and reverse rotations in low and high speeds including the detuning parameters.

• Journal of Astronomy and Space Sciences
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• v.26 no.1
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• pp.75-88
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• 2009

The main purpose of the current research is to introduce the alternative algorithm of the non-recursive batch filter based on the unscented transformation in which the linearization process is unnecessary. The presented algorithm is applied to the orbit determination of a low earth orbiting satellite and compared its results with those of the well-known Bayesian batch least squares estimation and the iterative UKF smoother (IUKS). The system dynamic equations consist of the Earth's geo-potential, the atmospheric drag, solar radiation pressure and the lunar/solar gravitational perturbations. The range, azimuth and elevation angles of the satellite measured from ground stations are used for orbit determination. The characteristics of the non recursive unscented batch filter are analyzed for various aspects, including accuracy of the determined orbit, sensitivity to the initial uncertainty, measurement noise and stability performance in a realistic dynamic system and measurement model. As a result, under large non-linear conditions, the presented non-recursive batch filter yields more accurate results than the other batch filters about 5% for initial uncertainty test and 12% for measurement noise test. Moreover, the presented filter exhibits better convergence reliability than the Bayesian least squares. Hence, it is concluded that the non-recursive batch filter based on the unscented transformation is effectively applicable for highly nonlinear batch estimation problems.

• Bulletin of the Korean Space Science Society
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• 2008.10a
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• pp.34.2-34.2
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• 2008

The batch least square filter is widely used for ground estimations. However, in orbit determination (OD) under inaccurate initial conditions and few measurement data the performance by the batch least square filter can lead an unstable results. To complement weak part of the batch filter, the batch unscented transformation without any linearization process is developed by ACL (Astrodynamics and Control Laboratory) in YONSEI University. In this paper, the batch unscented transformation is introduced and applied to satellite orbit determination using Satellite Laser Ranging (SLR) data. Only range of the satellite measured from ground tracking stations is used for measurement data. The results of simulation test are compared with those of the weighted batch least square filter for various initial states errors (position and velocity). Simulation results show that the batch unscented transformation is comparable or slightly superior to batch least square filter in the orbit determination.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.9
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• pp.865-872
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• 2008

Spacecraft attitude estimation using the nonlinear unscented filter is addressed to fully utilize capabilities of the unscented transformation. To release significant computational load, an efficient technique is proposed by reasonably removing correlation between random variables. This modification introduces considerable reduction of sigma points and computational burden in matrix square-root calculation for most nonlinear systems. Unscented filter technique makes use of a set of sample points to predict mean and covariance. The general QUEST(QUaternion ESTimator) algorithm preserves explicitly the quaternion normalization, whereas extended Kalman filter(EKF) implicitly obeys the constraint. For spacecraft attitude estimation based on quaternion, an approach to computing quaternion means from sampled quaternions with guarantee of the quaternion norm constraint is introduced applying a constrained optimization technique. Finally, the performance of the new approach is demonstrated using a star tracker and rate-gyro measurements.

• Journal of Institute of Control, Robotics and Systems
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• v.12 no.8
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• pp.780-788
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• 2006

This paper deals with INS/GPS tightly coupled integration algorithms using extend Kalman filter (EKF) and unscented Kalman filter (UKF). In the tightly coupled approach, nonlinear pseudorange measurement models are used for the INS/GPS integration Kalman filter. Usually, an EKF is applied for this task, but it may diverge due to poor functional linearization of the nonlinear measurement. The UKF approximates a distribution about the mean using a set of calculated sigma points and achieves an accurate approximation to at least second-order. We introduce the generalized scaled unscented transformation which modifies the sigma points themselves rather than the nonlinear transformation. The generalized scaled method is used to transform the pseudo range measurement of the tightly coupled approach. To compare the performance of the EKF- and UKF-based tightly coupled approach, real van test and simulation have been carried out with feedforward and feedback indirect Kalman filter forms. The results show that the UKF and EKF have an identical performance in case of the feedback filter form, but the superiority of the UKF is demonstrated in case of the feedforward filer form.