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2 TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2 2013

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Stability Tests of Positive Fractional Continuous-time Linear Systems with Delays

Kaczorek T.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2013

Vol. 7, no. 2

211--215

Necessary and sufficient conditions for the asymptotic stability of positive fractional continuoustime linear systems with many delays are established. It is shown that: 1) the asymptotic stability of the positive fractional system is independent of their delays, 2) the checking of the asymptotic stability of the positive fractional systems with delays can be reduced to checking of the asymptotic stability of positive standard linear systems without delays.

Modeling of Ionospheric Delay for SBAS Using Spherical Harmonics Functions

Han D., Yun H., Kee C.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

2013

Vol. 7, no. 2

205--209

In SBAS (satellite‐based augmentation system), it is important to estimate ionospheric delay accurately to guarantee userʹs accuracy and integrity. Grid based ionospheric models are generally used to estimate ionospheric delay for SBAS. In grid based model, SBAS broadcasts vertical ionospheric delays at the grid point, and users get their ionospheric delay by interpolating those values. Ionospheric model based on spherical harmonics function is another method to estimate ionospheric delay. This is a function based approach and spherical harmonics function is a 2‐D fourier series, containing the product of latitude dependent associated Legendre functions and the sum of the longitude dependent sine and cosine terms. Using ionospheric delay measurements, coefficients for each spherical harmonics functions are estimated. If these coefficients are known, user can reconstruct ionospheric delay. In this paper, we consider the spherical harmonics based model and propose a ionospheric delay estimation strategy for SBAS that can be used to mitigate ionospheric delay estimation error, especially in storm condition. First, coefficients are estimated under initial order and degree. Then residual errors for each measurement are modeled by higher order and degree terms, then coefficients for these terms are estimated. Because SBAS message capacity is limited, in normal condition, initial order terms are only used to estimate ionospheric delay. If ionospheric storm is detected and there is need to mitigate the error, higher order terms are also used and error can be decreased. To compare the accuracy of spherical harmonics based model with grid based model, some post‐processing test results are presented. Raw observation data is obtained from RINEX format and the root mean square(RMS) and max value of residual errors are presented.