Plug-in problem in discrete GNSS-PIM algorithms

Abstract

The aim of the contributed paper is to find a solution of plug-in problem in Discrete GNSS-PIM algorithms. Global Navigation Satellite Systems-Position Integrity Monitoring(GNSS-PIM) algorithms determine train position and verify its safeness. Plug-in problem has to be solved, when covariance matrix of GNSS positions is unknown and we would like to use its estimate instead. Confidence area for variance components σ1, σ2 and insensitivity region for the test in a given alternative are derivated first as a necessary part of the plug-in problem solution. If the confidence area is a subset of insensitivity region, then the estimate of covariance matrix can be considered as precise enough to be use in the Discrete GNSS-PIM algorithm instead of a real covariance matrix.