• 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 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.

• 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 the Society of Naval Architects of Korea
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• v.40 no.5
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• pp.43-52
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• 2003

Two methods which estimate manoeuvring derivatives in the model of hydrodynamic force and moment acting on a manoeuvring ship using sea trial data were compared. One is the widely used parameter estimation method by using the Extended Kalman Filter (EKF), which estimates state variables of linearized state space model at every instant after dealing with the coefficients as the augmented state variables. The other one is the Estimation-Before-Modeling (EBM) technique, so called the two-step method. In the first step, hydrodynamic force of which dynamic model is assumed the third-order Gauss-Markov process is estimated along with motion variables by the EKF and the modified Bryson-Frazier smoother. Then, in the next step, manoeuvring derivatives are identified through the regression analysis. If the exact structure of hydrodynamic force could be known, which was an ideal case, the EKF method would be regarded as being more superior compared to the EBM technique. However the EBM technique was more robust than the EKF method from a realistic point of view where the assumed model structure was slightly different from the real one.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.7
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• pp.123-129
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• 2002

This paper reveals determination of orbital elements of the satellite using GPS data collected by the low-end GPS receiver installed at KITSAT-3 which is a small scientific experimental satellite of Korea and launched in May 1999. An extended Kalman filter is designed for a forward estimation of real-time 3-dimensional position and velocity, and a smoother is used for a backward post-processing estimation of the same states. After finishing estimation of position and velocity, the corresponding orbital elements are estimated. Finally, the result of each orbital element is analyzed.

• Journal of Astronomy and Space Sciences
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• v.36 no.4
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• pp.293-306
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• 2019

In this study, the observational arc-length effect on orbit determination (OD) for the Korea Pathfinder Lunar Orbiter (KPLO) in the Earth-Moon Transfer phase was investigated. For the OD, we employed a sequential estimation using the extended Kalman filter and a fixed-point smoother. The mission periods, comprised between the perigee maneuvers (PM) and the lunar orbit insertion (LOI) maneuver in a 3.5 phasing loop of the KPLO, was the primary target. The total period was divided into three phases: launch-PM1, PM1-PM3, and PM3-LOI. The Doppler and range data obtained from three tracking stations [included in the deep space network (DSN) and Korea Deep Space Antenna (KDSA)] were utilized for the OD. Six arc-length cases (24 hrs, 48 hrs, 60 hrs, 3 days, 4 days, and 5 days) were considered for the arc-length effect investigation. In order to evaluate the OD accuracy, we analyzed the position uncertainties, the precision of orbit overlaps, and the position differences between true and estimated trajectories. The maximum performance of 3-day OD approach was observed in the case of stable flight dynamics operations and robust navigation capability. This study provides a guideline for the flight dynamics operations of the KPLO in the trans-lunar phase.