Several machine learning (ML) methodologies are gaining popularity as artificial intelligence (AI) becomes increasingly prevalent. An artificial neural network (ANN) may be used as a “black-box” modeling strategy without the need for a detailed system physical model. It is more reasonable to solely use the input and output data to explain the system’s actions. ANNs have been extensively researched, as artificial intelligence has progressed to enhance navigation performance. In some circumstances, the Global Navigation Satellite System (GNSS) can offer consistent and dependable navigational options. A key advancement in contemporary navigation is the fusion of the GNSS and inertial navigation system (INS). Numerous strategies have been put out recently to increase the accuracy for jamming, GNSS-prohibited environments, the integration of GNSS/INS or other technologies by means of a Kalman filter as well as to solve the signal blockage issue in metropolitan areas. A neural-network-based fusion approach is suggested to address GNSS outages. The overview, inquiry, observation, and performance evaluation of the present integrated navigation systems are the primary objectives of the review. The important findings in ANN research for use in navigation systems are reviewed. Reviews of numerous studies that have been conducted to investigate, simulate, and integrate navigation systems in order to produce accurate and dependable navigation solutions are offered.

Global Positioning System (GPS) positioning accuracy is strongly affected by inaccurate noise modeling and non-Gaussian pseudorange measurement errors, including heavy-tailed disturbances and abnormal outliers caused by multipath propagation and signal degradation. Conventional extended Kalman filters (EKFs) generally assume Gaussian measurement noise with fixed covariance matrices, which limits their robustness under degraded measurement conditions. This study proposes a Student-t robust quantum-behaved particle swarm optimization-based extended Kalman filter (ST-QPSO-EKF) for adaptive GPS state estimation. The proposed framework combines quantum-behaved particle swarm optimization (QPSO) with a Student-t-based robust measurement update, where the process-noise scaling factor, measurement-noise scaling factor, and Student-t degrees-of-freedom parameter are jointly optimized. The optimized parameters are obtained through an offline calibration stage and subsequently applied in the recursive GPS filtering process. A nonlinear GPS navigation simulation was conducted using Gaussian, Student-t heavy-tailed, and outlier-contaminated pseudorange measurement scenarios. The proposed method was compared with conventional EKF, QPSO-EKF, and Student-t EKF using 20 independent Monte Carlo realizations. The results demonstrate that QPSO-EKF provides improved accuracy under nominal Gaussian conditions, whereas ST-QPSO-EKF achieves superior performance under non-Gaussian measurement environments. Under Student-t heavy-tailed noise, ST-QPSO-EKF reduced the position RMSE to 3.814 m, while under outlier-contaminated noise it achieved a position RMSE of 3.952 m, outperforming the other compared methods. In addition, the proposed method maintained comparable online computational cost because the QPSO optimization was performed offline. The results indicate that jointly optimizing covariance parameters and Student-t robustness provides an effective strategy for improving GPS positioning reliability under complex pseudorange measurement conditions.