# Towards Improved Inertial Navigation by Reducing Errors Using Deep Learning Methodology
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world. However, GNSS requires direct line-of-sight to four or more satellites for continuous operation, and thus leads to frequent GNSS signal blockages in many areas including indoor buildings, dense urban places, multi-level parking structures, and areas with thick tree-coverage [15; 16]. In most safety critical applications, the INS works in conjunction with a GNSS. Here, the long-term stability of GNSS helps to bound the errors of an INS by using various filtering algorithms [17] (e.g., Complementary Filter [18], Extended Kalman Filter (EKF) [19; 20; 21; 22], and Particle Filter (PF) [23; 24]). MEMS inertial sensors are prone to high noise and large uncertainties in their outputs, such as bias, scale factor, nonorthogonalities, drifts, and noise characteristics, etc., thereby limiting their stand-alone applications [25; 26; 27]. For instance, MEMS gyroscopes are prone to biases, scale factor and misalignment errors, and noises that result in quadratic errors in velocity and cubic errors in the position computations and thus do not allow for extended periods of navigation. These errors build up over time, thereby corrupting the accuracy of the measurements. Here, the deterministic error sources include the bias, scale factor, nonorthogonalities, etc. [28; 29; 30], which are typically removed by specific calibration procedures after experimentation. Stochastic errors occur due to random variations of bias or scale-factor errors over time and are known as bias or scale-factor drifts. There are other arguments that state that bias-scale-factor drift seems to be stochastic due to the lack of observability to disturbance. Drift may also occur because of inherent sensor noise that interferes with the output signals. These errors are nonsymmetric and cannot be compensated by deterministic models. The basic difference between deterministic and stochastic modeling is that in deterministic modeling a relationship must be established between one or more inputs and one or more outputs, whereas in stochastic modeling, there may not be any direct relationship between the inputs and outputs [31; 32; 33; 34; 35]. Currently, many academic research groups and companies are working on alternative navigation methods that can provide reliable and accurate aided inertial navigation within GNSS-denied environments, including fusion algorithms to bind the errors of an INS with radio signals, cameras, star-trackers, and Earth's magnetic field [36; 37; 38]. [PERSON] et al. [39] introduced a dual-model solution for GPS/INS during GPS outages, which integrates with Multiple-Decrease Factor Cubature Kalman filter (MDF-CKF) and Random Forest (RF) that can be used for modeling and compensating the velocity and positioning errors. Compared with traditional Artificial Neural Networks (ANNs), MDF-CKF with Random Forest algorithm dual mode has an overall 34.15% improvement in the position accuracy against conventional CKF. In 2019, [PERSON] et al. [40] introduced an ANN model to estimate Center of Mass-Center of Pressure (CoM-CoP) inclination angle (IA) based on signals using an inertial sensor which included accelerometer, gyroscope, and magnetometer. Then, CoM-CoP IA was calculated to obtain horizontal distance which investigates gait stability. The team applied an ANN and a Long Short-Term Memory (LSTM) to improve the algorithm of CoM-CoP IA by using 3D motion analysis system. Many research groups, including our group, have previously described the use of INS error reduction algorithms by using ANNs, such as Support Vector Machines (SVMs) [40; 41; 42] and deep learning techniques [43; 44; 41] to improve the performance of IMU by reducing its errors which would greatly improve the overall system accuracy and reduce cost when used as part of a sensor-fusion algorithm. Deep learning is a powerful machine learning technology based on ANNs, and expands traditional neural networks to a large scalable network, with a larger number of neurons and hidden layers.