• Journal of Biomedical Engineering Research
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• v.27 no.3
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• pp.131-141
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• 2006

A visual decision by clinical experts like physical therapists is a best way to detect onset and offset time of muscle activation. The current computer-based algorithms are being researched toward similar results of clinical experts. The new algorithm in this paper has an ability to extract a trend from noisy input data. Kalman smoother is used to recognize the trend to be revealed from disorderly signals. Histogram of smoothed signals by Kalman smoother has a clear boundary to separate muscle contractions from relaxations. To verify that the Kalman smoother algorithm is reliable way to detect onset and offset time of muscle contractions, the algorithm of Robert P. Di Fabio (published in 1987) is compared with Kalman smoother. For 31 templates of subjects, an average and a standard deviation are compared. The average of errors between Di Fabio's algorithm and experts is 109 milliseconds in onset detection and 142 milliseconds in offset detection. But the average between Kalman smoother and experts is 90 and 137 milliseconds in each case. Moreover, the standard deviations of errors are 133 (onset) and 210 (offset) milliseconds in Di Fabio's one, but 48 (onset) and 55 (offset) milliseconds in Kalman smoother. As a result, the Kalman smoother is much closer to determinations of clinical experts and more reliable than Di Fabio's one.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.5
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• pp.471-478
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• 2012

A foot motion is estimated using an inertial sensor unit, which is installed on a shoe. The inertial sensor unit consists of 3 axis accelerometer and 3 axis gyroscopes. Attitude and position of a foot are estimated using an inertial navigation algorithm. To increase estimation performance, a smoother is used, where the smoother employs a forward and backward filter structure. An indirect Kalman filter is used as a forward filter and backward filter. A new combining algorithm for the smoother is proposed to combine a forward indirect Kalman filter and a backward indirect Kalman filter. Through experiments, the estimation performance of the proposed smoother is verified.

• Journal of the Korean Association of Geographic Information Studies
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• v.13 no.2
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• pp.157-167
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• 2010

Unscented Kalman filter based backward filter is derived and the positions from extended Kalman filter, unscented Kalman filter, and extended Kalman smoother are compared and analyzed through a simulation test. Considering the poor GPS signal reception, the simulation is performed under the assumption of only the start and end points of the trajectory, composed of 4 curves and 5 straight sections in the area of $40m{\times}40m $, are known. The test shows that the smoothers generate much better positioning results of 8~9m improvement compared to those from the forward filters. For the comparison between the smoothers, the analysis is performed separately for the curves and straight segments. In both cases, the unscented Kalman smoother generates better positioning error; 10cm and 23cm improved positioning results in straight segment and curves, respectively.

• Journal of Positioning, Navigation, and Timing
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• v.10 no.2
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• pp.83-89
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• 2021

The extended Kalman filter (EKF) is widely used for global navigation satellite system (GNSS) applications. It is difficult to obtain precise positions with an EKF one-way (forward or backward) filter. In this paper, we propose an EKF smoother to improve the positioning accuracy by integrating forward and backward filters. For the EKF smoother experiment, we performed PPP using GNSS data received at the DAEJ reference station for a month. The effectiveness of the proposed approach is validated with multi-GNSS kinematic PPP experiments. The EKF smoother showed 35%, 6%, and 22% improvement in east, north, and up directions, respectively. In addition, accurate tropospheric zenith total delay (ZTD) values were calculated by a smoother. Therefore, the results from EKF smoother demonstrate that better accuracy of position can be achieved.

• Journal of KIISE:Software and Applications
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• v.31 no.2
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• pp.245-254
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• 2004

This paper deals with the problem of estimating structure and motion from long continuous image sequences, applying the Expectation Maximization algorithm based on extended Kalman smoother to impose the time-continuity of the motion parameters. By repeatedly estimating the state transition matrix of the dynamic equation and the parameters of noise processes in the dynamic and measurement equations, this optimization gives the maximum likelihood estimates of the motion and structure parameters. Practically, this research is essential for dealing with a long video-rate image sequence with partially unknown system equation and noise. The algorithm is implemented and tested for a real image sequence.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.9
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• pp.807-810
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• 2015

In this paper, a finite impulse response(FIR) fixed-lag smoother is proposed for discrete-time nonlinear systems. If the actual state trajectory is sufficiently close to the nominal state trajectory, the nonlinear system model can be divided into two parts: The error-state model and the nominal model. The error state can be estimated by adapting the optimal time-varying FIR smoother to the error-state model, and the nominal state can be obtained directly from the nominal trajectory model. Moreover, in order to obtain more robust estimates, the linearization errors are considered as a linear function of the estimation errors. Since the proposed estimator has an FIR structure, the proposed smoother can be expected to have better estimation performance than the IIR-structured estimators in terms of robustness and fast convergence. Additionally the proposed method can give a more general solution than the optimal FIR filtering approach, since the optimal FIR smoother is reduced to the optimal FIR filter by setting the fixed-lag size as zero. To illustrate the performance of the proposed method, simulation results are presented by comparing the method with an optimal FIR filtering approach and linearized Kalman filter.

• 제어로봇시스템학회:학술대회논문집
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• 2005.06a
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• pp.2516-2520
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• 2005

In this paper, finite impulse response (FIR) smoothers are proposed for discrete-time systems. The proposed FIR smoother is designed under the constraints of linearity, unbiasedness, FIR structure, and independence of the initial state information. It is also obtained by directly minimizing the performance criterion with unbiased constraints. The approach to the MVF smoother proposed in this paper is logical and systematic, while existing results have heuristic assumption, such as infinite covariance of the initial state. Additionally, the proposed MVF smoother is based on the general system model that may have the singular system matrix and has both system and measurement noises. Thorough simulation studies, it is shown that the proposed MVF smoother is more robust against modeling uncertainties numerical errors than fixed-lag Kalman smoother which is infinite impulse response (IIR) type estimator.

• 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.

• Journal of Institute of Control, Robotics and Systems
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• v.20 no.1
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• pp.1-5
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• 2014

In this paper, we propose an optimal fixed-lag FIR (Finite-Impulse-Response) smoother for a class of discrete time-varying state-space signal models. The proposed fixed-lag FIR smoother is linear with respect to inputs and outputs on the recent finite horizon and estimates the delayed state so that the variance of the estimation error is minimized with the unbiased constraint. Since the proposed smoother is derived with system inputs, it can be adapted to feedback control system. Additionally, the proposed smoother can give more general solution than the optimal FIR filter, because it reduced to the optimal FIR filter by setting the fixed-lag size as zero. A numerical example is presented to illustrate the performance of the proposed smoother by comparing with an optimal FIR filter and a conventional fixed-lag Kalman smoother.

• Journal of the Society of Naval Architects of Korea
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• v.38 no.4
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• pp.30-38
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• 2001

The current is considered in the conventional manoeuvering equation. This equation is represented as the nonlinear state and measurement equations in which external forces and the direction and the velocity of current are augmented as that variables. The external forces are modeled as the third-order Gauss-Markov processes and the direction and the velocity of current are assumed to be constant. The augmented state variables are estimated with extended Kalman-Bucy filter and the fixed-interval smoother. While Hwang estimated motion state variables, hydrodynamic coefficients and the current variables simultaneously by using extended Kalman filter, external forces of surge, sway and yaw and the direction and the velocity of current are the only parameters to be estimated in the estimation-before-modeling method. The current variables are satisfactorily estimated in simulation process where the measurement noise is present.