Reduced-Order Unscented Kalman Filter With Observations in the Frequency Domain: Application to Computational Hemodynamics

2019 ◽  
Vol 66 (5) ◽  
pp. 1269-1276 ◽  
Author(s):  
Lucas O. Muller ◽  
Alfonso Caiazzo ◽  
Pablo Javier Blanco
Keyword(s):  
Kalman Filter ◽  
Frequency Domain ◽  
Unscented Kalman Filter ◽  
Reduced Order ◽  
Computational Hemodynamics

Model-Based Control of Electroslag Remelting Process Using Unscented Kalman Filter

2008 ◽  
Author(s):  
Seokyoung Ahn ◽  
Joseph J. Beaman ◽  
Rodney L. Williamson ◽  
David K. Melgaard
Keyword(s):  
Kalman Filter ◽  
Temperature Distribution ◽  
Controller Design ◽  
Unscented Kalman Filter ◽  
Liquid Pool ◽  
Electroslag Remelting ◽  
Superior Performance ◽  
Process Conditions ◽  
Reduced Order ◽  
Highly Nonlinear

Electroslag Remelting (ESR) is used widely throughout the specialty metals industry. The process generally consists of a regularly shaped electrode that is immersed a small amount in liquid slag at a temperature higher than the melting temperature of the electrode. Melting droplets from the electrode fall through the lower density slag into a liquid pool constrained by a crucible and solidify into an ingot. High quality ingots require that electrode melt rate and immersion depth be controlled. This can be difficult when process conditions are such that the temperature distribution in the electrode is not at steady state. A new method of ESR control has been developed that incorporates an accurate, reduced-order melting model to continually estimate the temperature distribution in the electrode. The ESR process is highly nonlinear, noisy, and has coupled dynamics. An extended Kalman filter and an unscented Kalman filter were chosen as possible estimators and compared in the controller design. During the highly transient periods in melting, the unscented Kalman filter showed superior performance for estimating and controlling the system.

scholarly journals Regular design equations for the discrete reduced-order Kalman filter

2012 ◽  
Vol 22 (2) ◽  
pp. 175-189
Author(s):  
Peter Hippe
Keyword(s):  
Kalman Filter ◽  
Frequency Domain ◽  
Time Domain ◽  
Filter Design ◽  
Minimum Variance ◽  
Reduced Order ◽  
Regular Design ◽  
The Stability ◽  
The Time Domain ◽  
Standard Software

Regular design equations for the discrete reduced-order Kalman filter In the presence of white Gaussian noises at the input and the output of a system Kalman filters provide a minimum-variance state estimate. When part of the measurements can be regarded as noise-free, the order of the filter is reduced. The filter design can be carried out both in the time domain and in the frequency domain. In the case of full-order filters all measurements are corrupted by noise and therefore the design equations are regular. In the presence of noise-free measurements, however, they are not regular so that standard software cannot readily be applied in a time-domain design. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation causes no problems. However, the known proof of optimality of the factorization result requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for the reduced-order discrete-time Kalman filter in the time and in the frequency domains so that standard software is applicable. They also allow to formulate the conditions for the stability of the filter and to prove the optimality of the existing solutions.

Improved Unscented Kalman Filter Based on Decimation in Frequency Domain Fast Fourier Transform for Attitude Estimation Applied to Underwater Gliders

2014 ◽  
Vol 556-562 ◽  
pp. 4372-4375 ◽  
Author(s):  
Hao Qian Huang ◽  
Xi Yuan Chen ◽  
Hu Liu ◽  
Yuan Xu
Keyword(s):  
Fourier Transform ◽  
Kalman Filter ◽  
Fast Fourier Transform ◽  
Frequency Domain ◽  
Navigation System ◽  
Inertial Sensors ◽  
Unscented Kalman Filter ◽  
Underwater Gliders ◽  
Underwater Navigation ◽  
Better Than

In order to estimate the attitude fast and accurately for the underwater glider using the lower cost and lower power underwater navigation system, this paper designs a new underwater navigation system which is made up of the inertial sensors aided the magnetometer and proposes an improved unscented Kalman filter based on decimation in frequency domain fast Fourier transform (UKF-DF). UKF-DF makes better use of the estimate advantage of UKF in the nonlinear system, and in this basis DIF-FFT is integrated into UKF to increase the speed of calculation. Therefore, the attitude of a glider can be estimated fast and accurately. The real vehicle experiment is done to assess the performance of the proposed UKF-DF algorithm, the experimental results show that the attitude convergence of UKF-DF is better than EKF (extended Kalman filter) and the attitude estimated by UKF-DF is more precise than EKF.

scholarly journals Regular design equations for the continuous reduced-order Kalman filter

2011 ◽  
Vol 21 (4) ◽  
pp. 349-361 ◽  
Author(s):  
Peter Hippe
Keyword(s):  
Kalman Filter ◽  
Frequency Domain ◽  
Time Domain ◽  
Matrix Equation ◽  
Kalman Filters ◽  
Polynomial Matrix ◽  
Reduced Order ◽  
Regular Design ◽  
The Time Domain ◽  
Standard Software

Regular design equations for the continuous reduced-order Kalman filter Reduced-order Kalman filters yield an optimal state estimate for linear dynamical systems, where parts of the output are not corrupted by noise. The design of such filters can either be carried out in the time domain or in the frequency domain. Different from the full-order case where all measurements are noisy, the design equations of the reduced-order filter are not regular. This is due to the rank deficient measurement covariance matrix and it can cause problems when using standard software for the solution of the Riccati equations in the time domain. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation does not cause problems. However, the known proof of optimality of the factorization result also requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for reduced-order Kalman filters in the time and in the frequency domains for linear continuous-time systems. They allow to use standard software for the design of the filter, to formulate the conditions for the stability of the filter and they also prove that the existing frequency domain solutions obtained by spectral factorization of a non-regular polynomial matrix equation are indeed optimal.

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