The low latitude tropical ionosphere has been investigated by various researchers using Global Positioning System (GPS). Presently for many civil aviation applications, the ionospheric modeling of the tropical region has gained importance, in particular for flight safety. Since ionosphere is dispersive in nature, dual frequency (L1 = 1575.42 MHz and L2 = 1227.60 MHz) GPS observations can be used to obtain Ionospheric Total Electron Content (TEC). Since TEC varies with local time and geomagnetic latitude, an Ionospheric Modeling Technique using spatial linear approximation of vertical TEC over receiver station has been implemented following Sardon et al. The effects of all the systematic errors due to the satellite plus the receiver (SPR) instrumental biases can reach upto several nanoseconds. (1 TEC is 1016 electrons/m2, 1 ns = 2.86 TEC and 1 TEC = 0.16 m). Hence, to have an accurate estimation of ionospheric TEC, the instrumental biases must also be estimated. This thesis describes a heuristic adaptive Kalman Filtering scheme developed to estimate the TEC, the constants in the linearisation scheme, as well as the above total instrumental biases. The Kalman filter implementation is basically an optimization problem of minimizing the Cost Function J based on the difference between the model output and the measurement, called as the ‘innovation’, scaled by its covariance. In order to obtain the best possible results using the Kalman Filter approach, it is essential to provide appropriate values for the initial state, process and measurement noise covariances (P0, Q and R) respectively, which in general may not be known. Usually manual tuning of the filter parameter is carried out without using the above cost function J! The filter estimates can be highly sensitive to the above chosen statistics and thus these will have to be estimated carefully. Hence, we have utilized the Adaptive Kalman Filtering procedure of Myers and Tapley extended by Gemson and Ananthasayanam. The minimization is carried out by simultaneously estimating the above statistics and the unknown parameters, which include the TEC and the instrumental bias. In addition, A Constant Gain Kalman Filter approach using Genetic Algorithm (GA) has also been developed for the above requirement. It is observed that the steady state gains in KF and AKF approaches are in good match with the constant gains obtained from Genetic Algorithm. Using the above Adaptive Kalman Filtering technique and Constant Gain Kalman Filter approach, vertical TEC values and SPR biases have been estimated from the IGS receiver observations stationed at ISTRAC/ISRO, Bangalore, India. A diurnal TEC variation over Bangalore for a period of one year for 2003 and January 2004 is estimated and reported in this thesis. This approach has also been applied to study the behaviour of the ionosphere over low latitude IGS station at Fortaleza, Brazil data during the great magnetic storm on the 15th July 2000 and the results were found to be consistent with the results of Basu et al. In addition, Using Constant Kalman filter, the TEC enhancement over Indian region has been estimated for the October 2003 Ionospheric storm, and the results were found to be consistent with the reported results in the literature.