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All Journal International Journal of Electrical and Computer Engineering Indonesian Journal of Electrical Engineering and Computer Science
Ravenny Sandin Nahar
Universiti Teknologi MARA
Computer Science & IT Electrical & Electronics Engineering

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Linear regression models with autoregressive integrated moving average errors for measurements from real time kinematics-global navigation satellite system during dynamic test Kok Mun Ng; Ravenny Sandin Nahar; Mamun IbneReaz
International Journal of Electrical and Computer Engineering (IJECE) Vol 13, No 1: February 2023
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijece.v13i1.pp770-780

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.
Modelling and estimating trajectory points from RTK-GNSS based on an integrated modelling approach Ravenny Sandin Nahar; Kok Mun Ng; Fadhlan Hafizhelmi Kamaruzaman; Noorfadzli Abdul Razak; Juliana Johari
Indonesian Journal of Electrical Engineering and Computer Science Vol 34, No 1: April 2024
Publisher : Institute of Advanced Engineering and Science

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.11591/ijeecs.v34.i1.pp162-172

Abstract

The sparse Gaussian process regression (GPR) has been used to model trajectory data from Real time kinematics-global navigation satellite system (RTK-GNSS). However, upon scrutinizing the model residuals; the sparse GPR model poorly fits the data and exhibits presence of correlated noise. This work attempts to address these issues by proposing an integrated modeling approach called GPR-LR-ARIMA where the sparse GPR was integrated with the linear regression with autoregressive integrated moving average errors (LR-ARIMA) to further enhance the description of the trajectory data. In this integrated approach, the predicted trajectory points from the GPR were further described by the LR-ARIMA. Simulation of the GPR-LR-ARIMA on three sets of trajectory data indicated better model fit, revealed in the normally distributed model residuals and symmetrically distributed scatter plots. Correlated noise was also successfully eliminated by the model. The GPR-LR-ARIMA outperformed both the GPR and LRARIMA by its ability to improve mean-absolute-error in 2-dimension positioning by up to 86%. The GPR-LR-ARIMA contributes to enhancement of positioning accuracy of dynamic GNSS measurements in localization and navigation system with good model fit.
Co-Authors Fadhlan Hafizhelmi Kamaruzaman Juliana Johari Kok Mun Ng Mamun IbneReaz Noorfadzli Abdul Razak