Correct Fix Probability Improvement Method via INS Aiding to Single Epoch RTK System

Abstract

This paper introduces a method that utilizes an Inertial Navigation System (INS) to improve the Probability of Correct Fix (PCF) in a single-epoch Real-Time Kinematic (RTK) system. In the proposed system, only single-epoch GNSS measurements are used to avoid problems caused by cycle slips, and a time-propagated relative vector in the INS is used as a pseudo measurement in addition to the GNSS measurements to obtain an RTK solution with an improved PCF. We mathematically prove that the covariance matrix of an ambiguity float solution is always improved by the addition of prior information of an INS-aided relative vector compared to that of the existing single-epoch RTK. However, the PCF simulation results obtained by using the improved covariance matrix after applying the proposed method show that counter examples with a worse PCF of INS-aided solution than that of a GNSS-only solution may occur due to the characteristics of Z-transformation in the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) method. This study also mathematically proves that the PCF is always improved without a counter example when the original Z matrix calculated from the existing single-epoch RTK is applied. Thus, we propose a new algorithm that does not generate any counter examples, while increasing the PCF significantly based on the proof. Availability simulations were performed for different GNSS measurement noise levels and Inertial Measurement Unit (IMU) sensor grades. The results show that the system availability can be improved after applying the proposed method to the existing single-epoch RTK.