Error Modeling and Integrity Risk Analysis in SPP

Abstract

With the popularity and development of GNSS, the concept of integrity is proposed in order to ensure the safety of navigation and positioning. In some related fields such as civil aviation and lifesaving, the requirements for the integrity are becoming stricter, making the Integrity Monitoring a hot issue to be solved urgently. However, the existing methods for this problem are theoretically imperfect and the error model used can’t accurately describe the actual error distribution. In this article, we will first present a model for the observation error in single point positioning. Considering that the actual observation errors always have thick tails, a binormal error model has been raised. Next, based on the previous error model, we use the Robust Parameter Estimation (RPE) method based on predicted residual with single iteration to detect and exclude the fault observation values, and then calculate the positioning result. Finally, we derive a method for conservatively estimating the integrity risk in the position by segmenting and magnifying the test-passing domain. The experimental results show that compared with the single normal error model, our binormal error model can describe the actual error distribution better and is conservative in the tail. The RPE method based on predicted residual with single iteration has a good effect of detecting and excluding fault observations and has a small positioning error. When the theoretical risk is less than the risk threshold, the statistical integrity risk obtained from the data is also less than the threshold. In addition, in the case of a worse error distribution with larger fault probability and larger fault error variance, the integrity risk evaluation results are still credible, indicating our method has better robustness.