Impact of Wrong Ambiguity Fixing on GNSS Positioning

Abstract

Global Navigation Satellite System (GNSS) has been developed in recent several decades, which provides a new technique for timing, positioning and navigation. And GNSS positioning is a basic service to us, both in daily life and scientific research. During high-precise positioning, ambiguity resolution is a key factor that has a huge influence on the accuracy of the result. And the wrong fixing is themain source of lose of accuracy, so many methods of test are proposed to validate the fixing result. We are interested in the performance of solutions that have been labeled as wrong fixing, and want to check if those wrong fixings should be excluded or accepted during estimation.
At firstwe introduce the basic model and challenges of ambiguity fixing, aswell as the widely usedmethod integer least squares and Z-transformation. Some previous research of distribution of fixed solution also enables us to compute the bounds of baseline residual. Then we focus on an example to do some pre-research, and find out the main research question - how to accept wrong fixing during estimation and the impact under different scenarios or estimation methods. We use a simulation-basedmethod to do the research but the
measurements are generated based on the real ephemeris in certain day.
After giving the double difference measurement model based on code and phase with respect to single or dual frequencies, in short baseline scenario, we define some parameters 1-norm, infinity-norm, weighted 2-norm, and good/bad performance of wrong fixings that might be useful for analysis. And some detailed information in chosen epochs are shown with multiple figures and we derive those which are helpful, such as infinity-normratio. Then we develop 4 validation methods, Infinity-normratio detection (RD),Weighted 2-norm detection (WD), 1-norm baseline residual detection (BD1) and Infinity-norm baseline residual detection (BDi), to check if we could recognize wrong fixings with good performance from all wrong fixings.
We also compute some statistics, such as the success rate of detection, the rate of misdiagnose, and the rate of participation to see whether our validation methods are effective or not. The histogram of wrong fixing or correct fixing corresponds the existed research of distribution well. And the time series analysis also proves the reliability of our validation methods, although there exist some errors due to the small sample size of simulations.
We also apply the multi-epoch least squares and Kalman filter to see the influence of fixing success rate, standard deviation of horizontal residuals, residual bounds and performance of wrong fixings. We find that there are obvious improvements on all of them. An extra experiment is designed to see the impact of atmospheric delays and the results show that it is really different from short baseline scenarios and we need to find more proper threshold to make sure our validation methods work.
Finally, we could draw a conclusion that it is possible to find out wrong fixings that could be accepted, but the threshold for each validation method should be adaptive for different scenarios and Kalman filter is very reliable, with which the wrong fixing is always likely to be excluded during the estimation.