###### Abstract  
An approach based on Artificial Neural Networks is proposed in this paper to improve the localisation accuracy of Inertial Navigation Systems (INS)/Global Navigation Satellite System (GNSS) based aided navigation during the absence of GNSS signals. The INS can be used to continuously position autonomous vehicles during GNSS signal losses around urban canyons, bridges, tunnels and trees, however, it suffers from unbounded exponential error drifts cascaded over time during the multiple integrations of the accelerometer and gyroscope measurements to position. More so, the error drift is characterised by a pattern dependent on time. This paper proposes several efficient neural network-based solutions to estimate the error drifts using Recurrent Neural Networks, such as the Input Delay Neural Network (IDNN), Long Short-Term Memory (LSTM), Vanilla Recurrent Neural Network (vRNN), and Gated Recurrent Unit (GRU). In contrast to previous papers published in literature, which focused on travel routes that do not take complex driving scenarios into consideration, this paper investigates the performance of the proposed methods on challenging scenarios, such as hard brake, roundabouts, sharp cornering, successive left and right turns and quick changes in vehicular acceleration across numerous test sequences. The results obtained show that the Neural Network-based approaches are able to provide up to 89.55% improvement on the INS displacement estimation and 93.35% on the INS orientation rate estimation. Keywords:INS; GPS outage; autonomous vehicle navigation; inertial navigation; deep learning; neural networks +
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the position of the vehicle in the absence of the GNSS signal needed for positioning and correction. Traditionally, Kalman filters are used in modelling the error between the Global Positioning System (GPS) and INS positions [6; 7; 8]. However, they have limitations when modelling highly non-linear dependencies, stochastic relationships and non-Gaussian noise measurements [6]. Over the years, other methods based on artificial intelligence have been proposed by a number of researchers to learn the error-drift within the sensors' measurements [9; 10; 11; 12; 13; 14]. The use of the sigma pi neural network on the positioning problem was explored by [PERSON] et al. in Reference [15]. [PERSON] et al. investigated the use of the Input Delay Neural Network (IDNN) to model the INS/GPS positional error [6]. A Multi-Layer Feed-Forward Neural Network (MFNN) was applied in Reference [16] on a single point positioning INS/GPS integrated architecture. Reference [17] employed the MFNN on an integrated tactical grade INS and a Differential GPS architecture for a better position estimation solution. More so, Recurrent Neural Networks, which are distinguishable from other neural networks due to their ability to make nodal connections in temporal sequences, have been proven to model the time-dependent error drift of the INS more accurately compared to other neural network techniques [18]. In Reference [19], [PERSON] et al. compared the performance of the Long Short-Term Memory (LSTM) algorithm to the Multi-Layer Perceptron (MLP) and showed the superiority of the LSTM over the MLP. Similarly, in Reference [1], [PERSON] et al. investigated the performance of the LSTM algorithm for high data rate positioning and compared it to other techniques, such as the IDNN, MLP and Kalman filter. Nevertheless, we observe that despite the number of techniques investigated on the INS/GPS error drift modelling, there lacks an investigation into the performances of the techniques on complex driving scenarios and environments experienced in everyday driving. Such scenarios range from hard brakes on regular, wet, or muddy roads to sharp cornering scenarios, heavy traffic, roundabouts, etc. We thus set out to investigate the performances of neural network-based approaches on such complex driving environments and show that these scenarios prove rather more challenging for the INS.