Error Analysis was my major independent work related to the GPS geodesy.

For my second (after the mantle convection) research topic at MIT, I carried out an error analysis for the geodetic measurements in the Tien-Shan region of Central Asia taken during field experiments in the summers of 1992 and 1993. This network includes a big range in length of baselines (from 270 m to 600 km) and variety of altitudes and geometric location of sites, as well as a large number of Block-I and Block-II satellites visible simultaneously. The data richness of the experiment allowed to carry out many computer simulated experiments and provided good statistical results.

Analyzing an error spectrum of the GPS phase measurements, I consider low and high frequency noise components separately.

I found that long wavelength signal in the post-fit residuals can be mostly explained by insufficiently resolved ray delay caused by heterogeneity of atmosphere, temporal as well as spatial. As I have shown, stochastically estimated multiple atmospheric delays at zenith allow to account for daily periodical changes in atmosphere, if they are repeated at least every two hours. I have completed the estimation of the multiple zenith delay for the period of significant atmosphere changes: from the beginning of thunder storm to the quiet weather. I found that actual delay can differ from single zenith estimation by 2 cm during quiet weather and be as big as 4 cm during significant changes (thunder storm). Analyzing the LC double-differenced post-fit residuals and calculated baseline coordinates, I have shown that introduction of the multiple atmosphere delay estimation improves the post-fits essentially, but changes the position of sites significantly, even beyond their formal errors. I analyzed the temporal and spatial characteristics of the residual low frequency signal of the post-fits and suggest that its source is azimuthal asymmetry of the atmosphere, which causes the delay up to 1 cm of the rays coming from the low elevation satellites. This effect is seen as long wavelength structure of small amplitude on the span of double differenced LC post-fits. I believe that introduction of additional stochastically estimated parameters around the horizon at time and place of arising/sating satellites will allow to account for the error in the solution.

I have shown that high frequency errors can be described as combination of gaussian white noise and first order Gauss-Markov process. To recognize their statistical characteristics I completed the analysis of 643 sets of LC double-differenced post-fit residuals and their auto-correlation functions. I believe that consistent interpretation of the high frequency errors has to consider combination of gaussian white noise with covariance of 5 mm and first order Gauss-Markov process with correlation time 180 sec and standard deviation 8 mm. Time correlated noise will affect the single-day solution and covariance matrix of the coordinates as well as the multi-day solution, which uses Kalman filter.

This research has shown many unresolved yet problems in the error interpretation of the GPS data analysis. Although the introduction of the multiple estimation of the atmosphere delay at zenith promises to change (probably improve) the position of stations significantly, before run new solution it will be interesting to resolve the strange lengthening of the baselines as well as azimuthal asymmetry of the atmosphere. Also, I am eager to see how the estimated values for relative positioning and its statistical characteristics change with suggested adjustments in low and high frequency noise estimation; how all of these affect the global multi-session solution, weighted and normalized rms analysis, and, finally, the estimated site velocities.