Recently, according to the requirements of some important GPS research subjects in the fields of Geodesy, Geophysics, Space-Physics and navigation in China, we studied systematically how to correcting the effects of the ionosphere on GPS, with high-precision and accuracy. As the parts of the main contributions, the research projects focus mainly on how to improve GPS surveying by reducing ionospheric delay for dual/single frequency kinematic/static users: high accuracy correction of ionospheric delay for single/dual frequency GPS users on the earth and in space, China WAAS ionospheric modeling and the theory and method of monitoring of ionosphere using GPS.
The main contents of this Ph.D paper consist of two parts:
Fisrt part---the outline of research background and the systematic introduction and summarization of the previous research results of this work.
Second part---the main contribution and research results of this paper are focused on as follows:
(1) How to use the measurements of a dual frequency GPS receiver to determine the ionospheric delay correction model for single frequency GPS of a local range;
(2)  How to separate the instrumental biases with the ionospheric delays in GPS observation;
(3) How to establish a large range grid ionosphere model and use the GPS data of Chinese crust movement observation network to investigate the change law of ionospheric TEC of China area;
(4) How to improve the effectiveness of correcting ionospheric delays for WAAS’s users under adverse conditions.
(5) How to establish the basic theory and the corresponding framework of monitoring the stochastic ionospheric disturbance using GPS
(6) How to improve the modelling ability of ionospheric delay according to its diurnal, seasonal, annual variations based on GPS;
(7) How to meet the demand of correcting the ionospheric delay of high-precision orbit determination for low-earth satellite using a single frequency GPS receiver
1 Extracting (local) ionospheric information from GPS data with high-precision
The factors are systematically described and analyzed which limit the precision of using GPS data to extract ionospheric delays. The precision of determining ionospheric delay using GPS is improved based on the further research of the related models and methods. The main achievements of this work include the some aspects as follows:
(1) Based on a simple model with constant number of parameters, which consists of a set of trigonometric series functions, a generalized ionospheric model is constructed whose parameters can be adjusted. Due to the property of selecting the different parameters according to the change law of ionospheric delay, the new model has better availability in the field of the related theoretic research and engineering application. The experimental results show that the model can indicate the characteristic of ionospheric actions, improves further the modeling ability of local ionosphere and may be used to correct efficiently ionospheric delay of the single frequency GPS uses serviced by DGPS.
(2) Different calculating schemes are designed which are used to analyze in detail the characteristics of the effect from instrumental bias (IB) in GPS observations on determining ionospheric delays. IB is different from noise in GPS observations. The experimental results show that the effect of IB is much larger than that of the noise on estimating ionospheic delay, and IB can cause ionospheric delay measurements to include systematic errors of the order of several meters. Therefore, one must significantly take notice of IB and remove its negative effect, and should not casually consider IB as part of noise whenever GPS data are used to fit ionospheric model or to directly calculate ionospheric delay.
(3) Stability of IB is studied with a refined method for separating it from ionospheric delay using multi-day GPS phase-smoothed code data. The experimental results show that, by using averaging of noise with phase-smoothed code observation，the effect of noise on separating IB from ION can be efficiently reduced, and  satellite bias plus receiver bias are relatively stable and may be used to predict the IBs of the next session or even that of the next several days.
(4) A new algorithm about static real time determination of ionospheric delay is presented on the basis of the predicted values of IB and the technique of real time averaging of noise and weighted-adjustment of dual P-code and carrier phase measurements. The preliminary results show that the new method, which is by post-processing phase-smoothed code data to calculate the IB and then with them to predict and to correct the IB of data needed to remove its effects in real time in the next observation periods, has relatively better accuracy and effectiveness in estimating ionospheric delay.  It is very obvious that the scheme can relatively decrease the number of unknown parameters, can efficiently reduce the main negative effect from instrumental bias, and can be easily used to directly and precisely determine ionospheric delay with dual-frequency GPS data. Hence, the method may be considered as an available scheme to determine ionospheric delays for WAAS and many other large range GPS application systems.
2 A method of constructing large range (regional and global) high-precision grid ionospheric model─—the Different Area for Different Stations (DADS) and its application in China
Based on the systematic and further research of the principle and methods of establishing grid ionospheric model (GIM), a new method of establishing a GIM ----- Different Areas for Different Stations (DADS) is investigated which is advantageous for considering the local characters of ionosphere, avoiding the effects of the geometrical construction of GPS reference network on estimating the external precision of the GIM, and improving the precision of calculating model parameters. The above results are used to make a preliminary estimation of the latent precision that can be obtained by establishing a large range high precision grid ionospheric model based on the Chinese crust movement observation network, and to investigate the possibility that the GIM provides high-precision ionospheric correction, and to identify the relevant problems which need to be solved for the planned GPS Wide area Augmentation System (WAAS) of China.
3 A method of efficiently correcting ionospheric delays for WAAS’s users under typical adverse conditions ——the Absolute Plus Relative Scheme (APR-I)
The commonly used WAAS’s DIDC received by single frequency GPS receivers can usually provide the effective correction of  the ionospheric delays for the users under normal conditions and in the fields of calm ionosphere. However, the ionospheric delays cannot be efficiently accounted for during those periods when the WAAS cannot broadcast the DIDC values to users, or when the receivers cannot receive the DIDCs for whatever reason. The ionospheric delay corrections will be less well known in cases when the variations of the ionospheric delays may be very large due to ionospheric disturbances. The above difficulties cannot be avoided to be encountered and must be solved for the WAAS.
For this, a new ionospheric delay correction scheme for single frequency GPS data—the APR-I scheme is proposed which can efficiently address the above problems.
1)      The theoretic basis of constructing the APR-I Scheme
The WAAS can provide high-precision absolute ionospheric delay estimates when it operates properly. Meanwhile, a single frequency GPS receiver serviced by the WAAS can efficiently determine the relative variation of the ionospheric delays between two arbitrary epochs even under adverse conditions if without considering observation noises.
2)      On the APR-I Scheme
Based on a robust recurrence procedure and an efficient combination approach between absolute ionospheric delays and ionospheric relative changes, the APR-I scheme  is present which is an new method of correcting ionospheric delay for single frequency GPS user. The formula of estimating the precision of the APR-I scheme is given. An implementation approach of the APR-I scheme is analyzed as well.
The experimental results discussed above show that the APR-I scheme not only retains the characteristic of high accuracy of the DIDC from the WAAS under normal ionospheric and reception conditions, but also has relatively better correction effectiveness under different abnormal conditions. The implementation of this method need not change the present basic ionospheric delay correction algorithm of the WAAS. In addition, the APR-I method does not impose new demands on receiver hardware, and only requires a few improvements to receiver software. Hence it can be easily used by single frequency GPS users.
4 A new theory of monitoring the random signal —Auto-Covariance Estimation of Variable Samples (ACEVS) and its application in using GPS to monitor the random ionosphere
A new approach for monitoring ionospheric delays is found and developed, based on the characteristic of time series observation of GPS, an investigation of the statistical properties of the estimated auto-covariance of the random ionospheric delay when changing the number of samples in the time series, the development of the related basic theory and the corresponding framework scheme, and the further research of using GPS and the above research results to study ionosphere.
The concrete work is as follows:
1) Studied the Auto-Covariance Estimation of Variable Samples (ACEVS)
From a general mathematical aspect, the basic model of ACEVS is established. The theoretic and approximate solution formulas for ACEVS are derived based on the improvement of theory of white noise and then a test raw of the state of a random signal is established based on ACEVS;
2) Verified and modeled the possibility of using ACEVS to test the change of state of stochastic delays
The possibility of using ACEVS to monitor ionosphere is verified in terms of theory.  Also it is found that the statistical property of ACEVS is sensitive to the change of the random ionospheric delay, on the basis of modeling the characteristics of ACEVS using a dual frequency GPS receiver. The application conditions of using ACEVS to monitor the variation of TEC extracted by GPS data are preliminarily discussed and analyzed as well.
3) Established a preliminary framework scheme of using GPS to monitor the disturbance of random ionospheric delay.
According to ACVES and all other results of the above and the characteristic of the time series observations of GPS, a preliminary framework scheme for monitoring the disturbance of random ionospheric delay using GPS is established. Although this method is proposed for real time monitoring, it can be easily applied to post-processing of GPS data. The framework scheme based on ACVES can be used to design many practical schemes for monitoring ionosphere variation using a (static or kinematic) dual frequency GPS receiver.
5 A new method of modelling ionospheric delay using GPS data ——Ionospheric Eclipse Factor Method (IEFM)
The Ionospheric Eclipse Factor (IEF) and its influence factor (IFF) of Ionospheric Pierce Point (IPP) is present and a simple method of calculating the IEF is also given. By combining the IEF and IFF with the local time t of IPP, a new method of modelling ionospheric delay using GPS data —Ionospheric Eclipse Factor Method (IEFM) is developed. The IEF and its IFF can efficiently combine the different ionospheric models for different seasons according to the diurnal, seasonal and annual variations of ionosphere. The preliminary experimental results show that the correction accuracy of the ionospheric delay modeled by IEFM is very close to that of using the ionosphere- free observation to correct directly the ionospheric delay, that is, the precision of using IEFM to model ionospheric delay for single GPS users seems to has a breakthrough improvement and be similar to that of using the corresponding dual frequency GPS data to correct directly the ionospheric delays. The IEFM also suits to model the ionospheric delays for a kinematic based–single GPS receiver embeded in low-earth satellite with high rapid due to its good ability in distinguishing the daytime and nighttime of the earth ionosphere for an IPP.
6 A new strategy of correcting ionospheric delay for high-precision orbit determination for low-earth satellite using a single frequency GPS receiver ---the APR-II scheme, i.e., Space-based APR scheme
Analyzed the shortcomings of using the previous methods to divide with high accuracy the earth ionosphere into different layers. Used GPS data to model global ionospheric TEC. Established a high precision grid ionospheric model. Discussed the possibility of finding out some local areas whose ionospheric construction and action have relatively better obvious law with respect to the other areas on a global scale. Designed a scheme for combining GPS-grounded data with GPS-spaced data to divide efficiently the ionosphere into some layers.Given the corresponding formula of estimating the precision of the scheme. The preliminary precision estimation and the experimental results show the possibility and property of the above idea of dividing ionosphere into different layers according to application requirement and its implementation scheme. Based on the above research, the APR-II scheme is presented which is a new and combined method of correcting the ionospheric delays of high-precision orbit determination for low-earth satellite using a single frequency GPS receiver. The preliminary experimental results based on two different sets of GPS-grounded data show that the APR-II scheme can provide the effective ionospheric delay correction for high-precision orbit determination for low-earth satellite.