Sung-Hoon Mok

Terrain Slope Estimation Methods Using the Least Squares Approach for Terrain Referenced Navigation

This paper presents a study on terrain referenced navigation (TRN). The extended Kalman filter (EKF) is adopted as a filter method. A Jacobian matrix of measurement equations in the EKF consists of terrain slope terms, and accurate slope estimation is essential to keep filter stability. Two slope estimation methods are proposed in this study. Both methods are based on the least-squares approach. One is planar regression searching the best plane, in the least-squares sense, representing the terrain map over the region, determined by position error covariance. It is shown that the method could provide a more accurate solution than the previously developed linear regression approach, which uses lines rather than a plane in the least-squares measure. The other proposed method is weighted planar regression. Additional weights formed by Gaussian pdf are multiplied in the planar regression, to reflect the actual pdf of the position estimate of EKF. Monte Carlo simulations are conducted, to compare the performance between the previous and two proposed methods, by analyzing the filter properties of divergence probability and convergence speed. It is expected that one of the slope estimation methods could be implemented, after determining which of the filter properties is more significant at each mission.

Collision Avoidance Using Linear Quadratic Control in Satellite Formation Flying

This paper proposes a linear system control algorithm with collision avoidance in multiple satellites. Consideration of collision avoidance is augmented by adding a weighting term in the cost function of the original tracking problem in linear quadratic control (LQC). Because the proposed algorithm relies on a similar solution procedure to the original LQC, its inherent advantages, including gain-robustness and optimality, are preserved. To confirm and visualize the derived algorithm, a simple example of two-vehicle motion in the two-dimensional plane is illustrated. In addition, the proposed collision avoidance control is applied to satellite formation flying, and verified by numerical simulations.

Impulsive Control of Satellite Formation Flying using Orbital Period Difference

Abstract This paper is mainly concerned with impulsive control of satellite formation flying using orbital period difference. Gausss Variational Equation is used as a main equation and corresponding six orbital elements represent satellite status. Schaub and Alfriends three-impulse algorithm constitutes a basic algorithm of this paper. In three-impulse algorithm, required impulses are determined by orbit element difference between current and desired orbit. Among orbit element difference, mean anomaly difference is an only time-varying term, and it comes from orbital period difference. In this paper, we analytically derive an impulse time which minimizes required impulse magnitude using orbital period difference, based on three-impulse algorithm. In addition, considering a case when proposed delayed impulse maneuver is not useful, alternative impulse maneuver is suggested. Finally, simulation studies are presented with artificial mission examples.

Terrain Referenced Navigation for Autonomous Underwater Vehicles

Underwater TRN (Underwater Terrain Referenced Navigation) estimates an underwater vehicle state by measuring a distance between the vehicle and undersea terrain, and comparing it with the known terrain database. TRN belongs to absolute navigation methods, which are used to compensate a drift error of dead reckoning measurements such as IMU (Inertial Measurement Unit) or DVL (Doppler Velocity Log). However, underwater TRN is different to other absolute methods such as USBL (Ultra-Short Baseline) and LBL (Long Baseline), because TRN is independent of the external environment. As a magnetic-field-based navigation, TRN is a kind of geophysical navigation. This paper develops an EKF (Extended Kalman Filter) formulation for underwater TRN. A filter propagation part is composed by an inertial navigation system, and a filter update is executed with echo-sounder measurement. For large-initial-error cases, an adaptive EKF approach is also presented, to keep the filter be stable. At the end, simulation studies are given to verify the performance of the proposed TRN filter. With simplified sensor and terrain database models, the simulation results show that the underwater TRN could support conventional underwater navigation methods.

A Performance Comparison of Nonlinear Kalman Filtering Based Terrain Referenced Navigation

This paper focuses on a performance analysis of TRN among various nonlinear filtering methods. In a TRN research, extended Kalman filter(EKF) is a basic estimation algorithm. In this paper, iterated EKF(IEKF), EKF with stochastic linearization(SL), and unscented Kalman filter(UKF) algorithms are introduced to compare navigation performance with original EKF. In addition to introduced sequential filters, bank of Kalman filters method, which is one of the batch method, is also presented. Finally, by simulating an artificial aircraft mission, EKF with SL was chosen as the most consistent filter in the introduced sequential filters. Also, results suggested that the bank of Kalman filters can be alternative for TRN, when a fast convergence of navigation solution is needed.