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

Abstract

<span lang="EN-US">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.</span>

Overbounding Ifree errors based on bayesian Gaussian mixture model for ground-based augmentation system

“…where, 𝛼 0 is a concentration parameter, the value of mixing coefficient is near to zero and Γ(x) is a Gamma function. The mean and covariance matrix are sampled through the (13), 𝑃(𝜇 𝑗 |𝛾 𝑗 ) = 𝑁 (𝜇 𝑗 |𝛽 0 (𝜂 0 𝛾 𝑗 ) −1 ) 𝑊(𝛾 𝑗 |𝑣 0 , 𝜎 0 ), Hence, the processes involved in Bayesian GMM generation for every observation are presented in ( 14), ( 15), ( 16) and (17),…”

“…In the recent years, it is seen that over-bounding relies on localization for defining its location and pose which subsequently aids the path planning and navigation processes [16]. The localization techniques such as cooperative positioning, field measure from sensors and range-based techniques are developed to attain high-level positioning accuracy [17]. However, the sensors deployed in this localization system generate measurement errors like single-point solution in GPS and offset drifts in the inertia sensors [18].…”

Modelling and estimating trajectory points from RTK-GNSS based on an integrated modelling approach

“…Step 1 to 4 indicates the methods of modeling the fully independent conditional (FIC) sparse GPR as explained in [28] whereas step 5 to 8 depicts the LR-ARIMA modelling adopted from [30]. In step 1 to 4, FIC sparse GPR model is trained using the rover trajectory data to predict improved trajectory x-y coordinate points.…”

“…The aim of this work is to improve model fitting and positioning accuracy of dynamic trajectory data described by the sparse GPR models [28]. We proposed an integrated model approach using both sparse GPR and Linear regression with autoregressive moving average errors (LR-ARIMA) models that were developed by Nahar et al [28] and Ng et al [30] respectively to describe dynamic trajectory data. ARIMA error models could further describe the un-modelled errors in the residuals of the GPR with better correlation in the model based on time series method [30]- [34].…”

“…We proposed an integrated model approach using both sparse GPR and Linear regression with autoregressive moving average errors (LR-ARIMA) models that were developed by Nahar et al [28] and Ng et al [30] respectively to describe dynamic trajectory data. ARIMA error models could further describe the un-modelled errors in the residuals of the GPR with better correlation in the model based on time series method [30]- [34]. The predicted outputs from the sparse GPR are fed into the LR-ARIMA, forming an integrated two-stage model named as GPR-LR-ARIMA.…”