• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2000.10a
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• pp.188-188
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• 2000

The most important problem in target tracking can be said to be modeling the tracking system correctly. Although the simple linear dynamic equation for this model has used until now, the satisfactory performance could not be obtained owing to uncertainties of the real systems in the case of designing the filters baged on the dynamic equations. In this paper, we propose the extended robust Kalman filter (ERKF) which can be applied to the real target tracking system with the parameter uncertainties. A nonlinear dynamic equation with parameter uncertainties is used to express the uncertain system model mathematically, and a measurement equation is represented by a nonlinear equation to show data from the radar in a Cartesian coordinate frame. To solve the robust nonlinear filtering problem, we derive the extended robust Kalman filter equation using the Krein space approach and sum quadratic constraint. We show the proposed filter has better performance than the existing extended Kalman filter (EKF) via 3-dimensional target tracking example.

• Journal of Aerospace System Engineering
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• v.10 no.1
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• pp.21-28
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• 2016

Orbit determination problems have been interest of many researchers for long time. Due to the high nonlinearity of the equation of motion and the measurement model, it is necessary to linearize the both equations. To avoid linearization, the filter based on Fokker-Planck equation is designed. with the extended Kalman filter 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 extended Kalman filter update mechanism. This filter based on the DQMOM and the EKF update is applied to the orbit determination problem with appropriate modification to mitigate the filter smugness. Unlike the extended Kalman filter, the hybrid filter based on the DQMOM and the EKF update does not require the burdensome evaluation of the Jacobian matrix and Gaussian assumption for the system, and can still provide more accurate estimations of the state than those of the extended Kalman filter especially when measurements are sparse. Simulation results indicate that the advantages of the hybrid filter based on the DQMOM and the EKF update make it a promising alternative to the extended Kalman filter for orbit estimation problems.

• Particle and aerosol research
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• v.19 no.4
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• pp.145-154
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• 2023

Granular bed filters are widely used to remove particulate matter in flue gas and are filled with various shapes of packing material. The packing material plays an important role in determining the overall collection performance, such as pressure drop and collection efficiency. The pressure drop of a granular bed filter has been calculated using the Ergun equation, while the collection efficiency has been predicted using the log-penetration equation based on the single sphere theory. However, a prediction equation of collection efficiency for a granular bed filter filled with non-spherical packing materials has not been suggested yet. Therefore, in this study, three different shapes of packing materials (sphere, cylinder, and irregular) were prepared to propose a prediction equation. The pressure drop and collection efficiency in a granular bed filter filled with each shape of packing material were measured experimentally and compared with theoretically predicted values. We found that experimentally measured pressure drops matched well with values theoretically predicted using the Ergun equation considering the shape factor. However, experimental collection efficiencies were higher than theoretical ones predicted by the log-penetration equation using the single sphere theory. We modified the log-penetration equation by employing a shape factor and found a good relationship between experimental and theoretical collection efficiencies.

• Structural Engineering and Mechanics
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• v.83 no.5
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• pp.593-607
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• 2022

To solve the problem of detecting structural damage, a two-stage method using the Kalman filter and Particle Swarm Optimization (PSO) is proposed. In this method, the first PSO population is enhanced using the Kalman filter method based on dynamic responses. Due to noise in the sensor responses and errors in the damage detection process, the accuracy of the damage detection process is reduced. This method proposes a novel approach for solve this problem by integrating the Kalman filter and sensitivity analysis. In the Kalman filter, an approximate damage equation is considered as the equation of state and the damage detection equation based on sensitivity analysis is considered as the observation equation. The first population of PSO are the random damage scenarios. These damage scenarios are estimated using a step of the Kalman filter. The results of this stage are then used to detect the exact location of the damage and its severity with the PSO algorithm. The efficiency of the proposed method is investigated using three numerical examples: a 31-element planer truss, a 52-element space dome, and a 56-element space truss. In these examples, damage is detected for several scenarios in two states: using the no noise responses and using the noisy responses. The results show that the precision and efficiency of the proposed method are appropriate in structural damage detection.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.48 no.11
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• pp.881-888
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• 2020

In this paper, research on estimation of states of a target of interest using Line Of Sight(LOS) angle measurement is performed. Target's position, velocity, and acceleration are chosen to be the states of interests. The LOS measurement is known to be highly non-linear, making target dynamic modeling hard to be implemented into a filter. To solve this issue, the Pseudomeasurement equation was applied to the LOS measurement equation. With the help of this equation, 3D variable turn target dynamic model is applied to the filter model. For better performance, Kinematic Constraint is also implemented into the filter model. As for the filter, Bias Compensation Pseudomeasurement Filter (BCPMF) is used which is known for its robustness to initial conditions. Moreover, Two-Stage Kalman Filter (TSKF) form was also implemented to benefit from the parallel computation. As a result, TBCPMF 3DVT-KC is proposed and simulated to assess performance.

• International Journal of Internet, Broadcasting and Communication
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• v.4 no.1
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• pp.18-22
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• 2012

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.

• Journal of Aerospace System Engineering
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• v.10 no.1
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• pp.8-14
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• 2016

The optimal estimation of a bearing only target tracking problem be achieved through the solution of the Fokker-Planck equation and the Bayesian update. Recently, a nonlinear filtering algorithm using a direct quadrature method of moments in which the associated Fokker-Planck equation can be propagated efficiently and accurately was proposed. Although this approach has demonstrated its promising in the field of nonlinear filtering in several examples, the "degeneracy" phenomenon, similar to that which exists in a typical particle filter, occasionally appears because only the weights are updated in the modified Bayesian rule in this algorithm. Therefore, in this paper to enhance the performance, a more stable measurement update process based upon the update equation in the Extended Kalman filters and a more accurate initialization and re-sampling strategy for weight and abscissas are proposed. Simulations are used to show the effectiveness of the proposed filter and the obtained results are promising.

• Journal of information and communication convergence engineering
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• v.9 no.5
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• pp.500-504
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• 2011

In this paper, we propose an equivalent Wiener-Hopf equation. The proposed algorithm can obtain the weight vector of a TDL(tapped-delay-line) filter and the error simultaneously if the inputs are orthogonal to each other. The equivalent Wiener-Hopf equation was analyzed theoretically based on the MMSE(minimum mean square error) method. The results present that the proposed algorithm is equivalent to original Wiener-Hopf equation. The new algorithm was applied into the identification of an unknown system for evaluating the performance of the proposed method. We compared the Wiener-Hopf solution with the equivalent Wiener-Hopf solution. The simulation results were similar to those obtained in the theoretical analysis. In conclusion, our method can find the coefficient of the TDL (tapped-delay-line) filter where a lattice filter is used, and also when the process of Gram-Schmidt orthogonalization is used. Furthermore, a new cost function is suggested which may facilitate research in the adaptive signal processing area.

• Journal of Institute of Control, Robotics and Systems
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• v.8 no.11
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• pp.984-990
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• 2002

We propose a new type of nonlinear fixed interval smoother to which an existing nonlinear smoother is modified. The nonlinear smoother is derived from two-filter formulas. For the backward filter. the propagation and the update equation of error states are derived. In particular, the modified update equation of the backward filter uses the estimated error terms from the forward filter. Data fusion algorithm, which combines the forward filter result and the backward filter result, is altered into the compatible form with the new type of the backward filter. The proposed algorithm is more efficient than the existing one because propagation in backward filter is very simple from the implementation point of view. We apply the proposed nonlinear smoothing algorithm to off-line navigation system and show the proposed algorithm estimates position, and altitude fairly well through the computer simulation.