Linear regression models with autoregressive integrated moving average errors for measurements from real time kinematics-global navigation satellite system during dynamic test

Abstract

The autoregressive integrated moving average (ARIMA) method has been used to model global navigation satellite systems (GNSS) measurement errors. Most ARIMA error models describe time series data of static GNSS receivers. Its application for modeling of GNSS under dynamic tests is not evident. In this paper, we aim to describe real time kinematic-GNSS (RTK-GNSS) errors during dynamic tests using linear regression with ARIMA errors to establish a proof of concept via simulation that measurement errors along a trajectory logged by the RTK-GNSS can be “filtered”, which will result in improved positioning accuracy. Three sets of trajectory data of an RTK-GNSS logged in a multipath location were collected. Preliminary analysis on the data reveals the inability of the RTK-GNSS to achieve fixed integer solution most of the time, along with the presence of correlated noise in the error residuals. The best linear regression models with ARIMA errors for each data set were identified using the Akaike information criterion (AIC). The models were implemented via simulations to predict improved coordinate points. Evaluation on model residuals using autocorrelation, partial correlation, scatter plot, quantile-quantile (QQ) plot and histogram indicated that the models fitted the data well. Mean absolute errors were improved by up to 57.35% using the developed models.