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.

In this paper, we provide geometric insights with visualization into the multivariate Gaussian distribution and its entropy and mutual information. In order to develop the multivariate Gaussian distribution with entropy and mutual information, several significant methodologies are presented through the discussion, supported by illustrations, both technically and statistically. The paper examines broad measurements of structure for the Gaussian distributions, which show that they can be described in terms of the information theory between the given covariance matrix and correlated random variables (in terms of relative entropy). The content obtained allows readers to better perceive concepts, comprehend techniques, and properly execute software programs for future study on the topic’s science and implementations. It also helps readers grasp the themes’ fundamental concepts to study the application of multivariate sets of data in Gaussian distribution. The simulation results also convey the behavior of different elliptical interpretations based on the multivariate Gaussian distribution with entropy for real-world applications in our daily lives, including information coding, nonlinear signal detection, etc. Involving the relative entropy and mutual information as well as the potential correlated covariance analysis, a wide range of information is addressed, including basic application concerns as well as clinical diagnostics to detect the multi-disease effects.

Multiple forms of interference and noise that impact the receiver’s capacity to receive and interpret satellite signals, and consequently the preciseness of positioning and navigation, may be present during the processing of Global Positioning System (GPS) navigation. The non-Gaussian noise predominates in the signal owing to the fluctuating character of both natural and artificial electromagnetic interference, and the algorithm based on the minimum mean-square error (MMSE) criterion performs well when assuming Gaussian noise, but drops when assuming non-Gaussian noise. The maximum correntropy criteria (MCC) adaptive filtering technique efficiently reduces pulse noise and has adequate performance in heavy-tailed noise, which addresses the issue of filter performance caused by the presence of non-Gaussian or heavy-tailed unusual noise values in the localizing measurement noise. The adaptive kernel bandwidth (AKB) technique employed in this paper applies the calculated adaptive variables to generate the kernel function matrix, in which the adaptive factor can modify the size of the kernel width across a reasonably appropriate spectrum, substituting the fixed kernel width for the conventional MCC to enhance the performance. The conventional maximum correntropy criterion-based extended Kalman filter (MCCEKF) algorithm’s performance is significantly impacted by the value of the kernel width, and there are certain predetermined conditions in the selection based on experience. The MCCEKF with a fixed adaptive kernel bandwidth (MCCEKF-AKB) has several advantages due to its novel concept and computational simplicity, and gives a qualitative solution for the study of random structures for generalized noise. Additionally, it can effectively achieve the robust state estimation of outliers with anomalous values while guaranteeing the accuracy of the filtering.

This paper provides a useful supplement note for implementing the Kalman filters. The material presented in this work points out several significant highlights with emphasis on performance evaluation and consistency validation between the discrete Kalman filter (DKF) and the continuous Kalman filter (CKF). Several important issues are delivered through comprehensive exposition accompanied by supporting examples, both qualitatively and quantitatively for implementing the Kalman filter algorithms. The lesson learned assists the readers to capture the basic principles of the topic and enables the readers to better interpret the theory, understand the algorithms, and correctly implement the computer codes for further study on the theory and applications of the topic. A wide spectrum of content is covered from theoretical to implementation aspects, where the DKF and CKF along with the theoretical error covariance check based on Riccati and Lyapunov equations are involved. Consistency check of performance between discrete and continuous Kalman filters enables readers to assure correctness on implementing and coding for the algorithm. The tutorial-based exposition presented in this article involves the materials from a practical usage perspective that can provide profound insights into the topic with an appropriate understanding of the stochastic process and system theory.

One technique that is widely used in various fields, including nonlinear target tracking, is the extended Kalman filter (EKF). The well-known minimum mean square error (MMSE) criterion, which performs magnificently under the assumption of Gaussian noise, is the optimization criterion that is frequently employed in EKF. Further, if the noises are loud (or heavy-tailed), its performance can drastically suffer. To overcome the problem, this paper suggests a new technique for maximum correntropy EKF with nonlinear regression (MCCEKF-NR) by using the maximum correntropy criterion (MCC) instead of the MMSE criterion to calculate the effectiveness and vitality. The preliminary estimates of the state and covariance matrix in MCKF are provided via the state mean vector and covariance matrix propagation equations, just like in the conventional Kalman filter. In addition, a newly designed fixed-point technique is used to update the posterior estimates of each filter in a regression model. To show the practicality of the proposed strategy, we propose an effective implementation for positioning enhancement in GPS navigation and radar measurement systems.