A novel regularization technique which can combine signals from all Global Positioning System (GPS) satellites for a given instant and a given receiver is developed to estimate the vertical total electron content (VTEC) values for the 24-hour period without missing any important features in the temporal domain. The algorithm is based on the minimization of a cost function which also includes a high pass penalty filter. Optional weighting function and sliding window median filter are added to enrich the processing and smoothing of the data. The developed regularized estimation algorithm is applied to GPS data for various locations for the solar maximum week of 23-28 April 2001. The parameter set that is required by the estimation algorithm is chosen optimally using appropriate error functions. This robust and optimum parameter set can be used for all latitudes and for both quiet and disturbed days. It is observed that the estimated TEC values are in general accordance with the TEC estimates from other global ionospheric maps, especially for quiet days and midlatitudes. Owing to its 30 s time resolution, the regularized VTEC estimates from the developed algorithm are very successful in representation and tracking of sudden temporal variations of the ionosphere, especially for high latitudes and during ionospheric disturbances. Copyright 2003 by the American Geophysical Union

[1] Total Electron Content (TEC) constitutes one of the key elements for observing the variable structure of the ionosphere. GPS provides a cost-effective alternative in TEC estimation through earth-based receivers. In this paper, one of the TEC estimation methods, namely Reg-Est, is investigated in detail in terms of its parameters and developed further to include improvements. Reg-Est estimates robust TEC using GPS measurements of 30 s time resolution. The method combines the vertical TEC computed from all the satellites in view over 10°horizon limit in the least squares sense through the minimization of a cost function which also includes a high pass penalty filter. Optional weighting functions and sliding window median filters are added to enrich the processing and smoothing of the data. In this study, the input to the Reg-Est is enlarged to include phase-corrected TEC. The best way of including the instrumental biases is investigated and the algorithm is updated to include the biases in the slant TEC computation. The effect of the thin shell height of the ionosphere in Reg-Est estimates is studied. It is concluded that the Reg-Est algorithm is very robust to the choice of thin shell height. The best weighting function to reduce the multipath effects and to minimize the non-ionospheric noise is selected. The improved Reg-Est algorithm can be used for all latitudes and for both quite and disturbed days of the ionosphere. The Reg-Est TEC are in excellent accordance with the estimates from IGS analysis centers.

[1] In this paper a new algorithm for short-term regularized estimation of vertical total electron content (VTEC) from Global Positioning System (GPS) data is developed. The regularization technique can combine signals, from all GPS satellites for a given instant and a given receiver, for a desired time duration within the 24 hour period without missing any important features in the temporal domain. The algorithm is based on the minimization of a cost function which includes a high pass penalty filter and detrend processing. With an optional weighting function the multipath effects are reduced. A final sliding window median filter is added to enrich the processing and smoothing of the data. The developed regularized estimation algorithm is applied to GPS data for various locations for the solar maximum week of 23-28 April 2001. The parameter set that is required by the estimation algorithm is chosen optimally using appropriate error functions. For this data set the chosen robust and optimum parameters can be used for all latitudes and for both quiet and disturbed days for a minimum of one hour time period. It is observed that the estimated TEC values are in very accordance with the TEC estimates for the 24 hour period. Owing to its 30 s time resolution, the regularized VTEC estimates from the developed algorithm are very successful in representation and tracking of sudden temporal variations of the ionosphere, especially for high latitudes and during ionospheric disturbances.

Regularized estimation of Total Electron Content (Reg-Est) is a novel technique which can combine signals from all the satellites for a given instant and given station and estimate the vertical TEC (VTEC) values for any desired period without missing any important features in the temporal or spatial domain. The preprocessed signals from all the satellites that are received for a certain time period are weighted according to their positions with respect to the local zenith. A two step regularization algorithm combines these signals and provides smooth VTEC estimates for the desired time period which can be as short as half an hour or as long as 24 h. The estimation algorithm is tried on VTEC values obtained from six midlatitude stations for the quiet and disturbed days of October, 2003. Within this period, the same estimation parameter set is used for all stations and time periods. When the regularized estimation results are compared with those from IRI-2001, JPL, CODE, UPC and ESA, best accordance is observed with JPL, UPC and CODE estimates. IRI computations usually provide a better fit for the night values. It is observed that the results from the regularized estimation algorithm are highly accurate in detecting disturbances and irregularities for various time scales and stations.

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