• Proceedings of the Korean Institute of Navigation and Port Research Conference
• /
• v.1
• /
• pp.133-138
• /
• 2006

Singular value decomposition (SDV) approach is applied to the observability analysis of GPS/INS in this paper. A measure of observability for a subspace is introduced. It indicates the minimum size of perturbation in the information matrix that makes the subspace unobservable. It is shown that the measure has direct connections with observability of systems, error covariance, and singular structure of the information matrix. The observability measure given in this paper is applicable to the multi-input/multi-output time-varying systems. An example on the observability analysis of GPS/INS is given. The measure of observability is confirmed to be less sensitive to system model perturbation. It is also shown that the estimation error for the vertical component of gyro bias can be considered unobservable for small initial error covariance for a constant velocity horizontal motion.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.6
• /
• pp.647-655
• /
• 1999

For linear time-varying systems described by the triple (A(t),B(t),C(t)) where A(t),B(t),C(t) are the system, the input, and the output matrices, respectively, we propose concepts for measures of modal and gross controllability /observability. We introduce a differential algebraic eigenbvalue theory for linear time-varying systems to calculate the PD-eigenvalues and left and right PD-eigenvectors of the system matrix A(t) which will be used to derive the concepts for the measures. The time-dependent angle between the left PD-eigenvectors of the system matrix A(t) and the columns of the input matrix B(t), and the magnitude of the each element of the input matrix B(t) are used to propose the modal controllability measure. Similarly, the time-dependent angle between the right PD-eigenvectors of the system matrix A(t) and the rows of the output matrix C(t) are used to propose the madal observability measure. Gross measure of controllability of a mode from all inputs and its gross measure of observability in all outputs for the linear time-varying systems are also proposed. Numerical examples are presented to illustrate the proposed concepts.

• Journal of the Korean Society for Precision Engineering
• /
• v.14 no.4
• /
• pp.64-71
• /
• 1997

Objective of calibration is to find out the accurate kinematic relationships between robot joint angles and the position of the end-effector by estimating accurate model parameters defining the kinematic function. Estimating the model parameters requires measurement of the end-effector position at a number of different robot configurations. This paper studies the implication of measurement configurations in robot calibration. For selecting appropriate measurement configurations in robot calibration, an index is defined to measure the observability of the model parameters with respect to a set of robot configurations. It is found that, as the observability index of the selected measurement configurations increase the attribution of the position errors to the parameter errors becomes dominant while the effects of the measurement and unmodeled errors are less significant; consequently better estimation of parameter errors is expected. To demonstrate the implication of the observability measure in robot calibration, computer simulations are performed and their results are discussed.

• Proceedings of the KIEE Conference
• /
• 1996.07b
• /
• pp.1002-1004
• /
• 1996

In this paper, presented are the results of observability analysis for the vehicle maneuver during In-Flight Alignment of SDINS. The target system for observability analysis is 10th order one. Three trajectories for IFA are considered. To analyze the observability of the time varying system, correlation coefficient is used and to measure the degree of observability of the given system, simulation is carried out using covariance matrix. The results of simulation show that trajectories which are having continuous changes in attitude and acceleration of system is superior to straight trajectory in correcting navigation errors.

• Transactions of the Korean Society of Machine Tool Engineers
• /
• v.17 no.4
• /
• pp.8-14
• /
• 2008

This paper aims at finding out dominant robot configurations with maximal position errors, which can be attributed to the parameter errors, by using Monte-Carlo simulation for error analysis of a 3-axis SCARA(Selective Compliance Assembly Robot Arm) type robot. In particular, the Monte-Carlo simulation is used for virtually measuring on the position errors, instead of physical measurement. In order to measure the observability of the model parameters with respect to a set of robot configurations, we propose the observability index which is defined as the product of singular values for error propagation matrices. Thus the index can be used for discriminating dominant robot configurations from a set of simulated ones in conjunction with standard deviation of positional errors, This paper analyzed error by robot positional error.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.29 no.6 s.237
• /
• pp.795-803
• /
• 2005

This paper studies the observability of calibration system with a measurement operator. The calibration system needs a simple digital indicator to measure the mobile table movements with respect to the MC coordinate. However, it yields the concern about the poor parameter observability due to measuring only a part of the movements. We uses the QR-decomposition to find the optimal calibration configurations maximizing the linear independence of rows of an observation matrix. The number of identifiable parameter is examined by the rank of the observation matrix, which represents the parameter observability. The method is applied to a 6-axis MC with parallel tilting table and the calibration results are presented. These results verify that all necessary kinematic parameters are observable and the calibration system has robustness to the noise using optimal calibration configurations.

• Proceedings of the KSME Conference
• /
• 2003.11a
• /
• pp.1512-1517
• /
• 2003

This paper presents the calibration for the parallel typed tilting table. The calibration system needs only simple sensing device which is a digital indicator to measure the orientation of a table. The calibration algorithm is developed by a measurement operator. It eliminates the concern about the poor parameter observability due to a large number of parameters of parallel-mechanism. This paper uses the QR-decomposition to find the optimal calibration configurations maximizing the linear independence of rows of a observation matrix. The number of identifiable parameters is examined by the rank of the observation matrix, which represents the parameter observability. The method is applied to a Parallel-typed Tilting Table and all the necessary kinematic parameters are identifiable.

• 제어로봇시스템학회:학술대회논문집
• /
• 1990.10a
• /
• pp.469-474
• /
• 1990

The implementation of modern guidance law derived from optimal control theory requires accurate current states of target, for example, position, velocity and acceleration etc. But there is no sensors that measure the target states directly. So they are estimated from measurable data. For atmospheric missile engagement, direct application of the modern guidance laws may result In deterioration of Intercept performance because of poor observability associated with angles only-measurements by passive seeker and homing geometry. In this paper, a trajectory modulation method called "adaptive Intermittent maneuvers" is added to the modern guidance law, so the observability is enhanced and, consequently, improved the intercept performance. The estimation algorithm called "modified gain pseudo-measurement filter" is used for tracking filter. It is assumed that the passive seeker measure the angles between line of sight and Inertial frame. The Monte-Carlo simulation for realistic air-to-air Intercept scenario are conducted to demonstrate the effectiveness of intermittent maneuvers.ermittent maneuvers.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.11
• /
• pp.1621-1628
• /
• 2004

This paper proposes a design methodology for the robust observer using the eigenstructure assignment in multi-output systems so that the observer is less sensitive to the ill-conditioning factors such as unknown initial estimation error, modeling error and measurement bias in transient and steady-state observer performance. The robustness of the observer can be achieved by selecting the desired eigenvector matrix to have a small condition number that guarantees the small upper bound of the estimation error. So the left singular vectors of the unitary matrix spanned by space of the achievable eigenvectors are selected as a desired eigenvectors. Also, this paper proposes how to select the desired eigenvector based on the measure of observability and designs the observer with small gain. An example of a spindle drive system is simulated to validate the robustness to the ill-conditioning factors in the observer performance.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2008.04a
• /
• pp.63-70
• /
• 2008

In this paper, we propose a bearing redundant coordinates and decoupled PD controller for 5-axes active magnetic bearing system, which consists of two bearing parts such as three-pole hybrid active magnetic bearing for stabilize the radial direction and ring-type permanent magnetic bearing stabilizing in axial and tilting motion. Based on derived system equation with decoupled control scheme, we conduct the modal analysis and measure of modal controllability and observability.