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.