• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.39-51
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• 1994

Some exponential moment inequalities for sub-gaussian random variables are studied in this paper. These inequalities are used to obtain laws of large numbers for random variable and random elements in $L^1(R)$.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.38 no.9
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• pp.624-633
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• 2001

Influence of the grating half-period fluctuation on the normalized coupling coefficient has been studied by an effective index transfer matrix method in quarter wavelength shifted(QWS) DFB lasers. The laser facets are assumed to be perfectly antireflection coated, and the period fluctuation is modeled by two correlated Gaussian random variables. In the presence of the random fluctuation in the grating period, effective normalized coupling coefficient is reduced because the in-phase feedback strength Is weakened. We have shown that the normalized coupling coefficient determined from the side mode spacing is less than the effective coupling coefficient, and the normalized coupling coefficient determined from the mode spacing or spontaneous emission spectrum does not properly represent the feedback strength of the grating.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2331-2334
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• 2003

The basic difference between the EKF(Extended Kalman Filter) and UKF(Unscented Kalman Filter) stems from the manner in which Gaussian random variables(GRV) are represented for propagating through system dynamics. In the EKF, the state distribution is approximated by a GRV, which is then propagated analytically through the first-order linearization of the nonlinear system. This can possibly introduce large errors in the true posterior mean and covariance of the transformed GRV, which may lead to sub-optimal performance and sometimes divergence of the filter. However, the UKF addresses this problem by using a deterministic sampling approach. The state distribution is also approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample points completely capture the true mean and covariance of the GRV, and UKF captures the posterior mean and covariance accurately up to the 2nd order(Taylor series expansion) for any nonlinearity. This paper utilizes the UKF to determine spacecraft orbit when only magnetometer is available. Several catastrophic failures of spacecraft in orbit have been attributed to failures of the spacecraft mission. Recently studies on contingency-major sensor failure cases- have been performed. For mission success, contingency design or plan should be implemented in case of a major sensor failure. Therefore the algorithm presented in this paper can be used for a spacecraft without GPS or contingency design in case of GPS failure.