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Global Navigation Satellite Systems (GNSS) provide positioning, velocity, and time services for civilian applications. A critical step in the positioning process is the acquisition of visible satellites in the sky. Modern GNSS systems, such as Galileo—developed and maintained by the European Union—utilize a new modulation technique known as Binary Offset Carrier (BOC). However, BOC signals introduce multiple side-peaks in their autocorrelation function, which can lead to significant errors during the acquisition process. In this paper, we propose a novel acquisition method based on higher-order cumulants that effectively eliminates these side-peaks. This method is capable of simultaneously acquiring both conventional ranging signals, such as GPS C/A code, and BOC-modulated signals. The effectiveness of the proposed method is demonstrated through the acquisition of simulated signals, with a comparison to traditional methods. Additionally, we apply the proposed method to real satellite signals to further validate its performance. Our results show that the proposed method successfully suppresses side-peaks, improves acquisition accuracy in weak signal environments, and demonstrates potential for indoor GNSS applications. The study concludes that while the method may increase computational load, its performance in challenging conditions makes it a promising approach for future GNSS receiver designs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In order to deal with the uncertainty of measurement noise, particularly for outlier types of multipath interference and non-line of sight (NLOS) reception, this paper proposes a novel method for processing the navigation states of the Global Positioning System (GPS) that combines the maximum correntropy criterion (MCC) and the interacting multiple model (IMM), with an extended Kalman Filter (EKF). Multipath mitigation is essential for increased positioning accuracy since multipath interference is one of the primary sources of errors. Nonlinear filtering with IMM configuration uses filter structural adaptation. In processing time-varying satellite signal standards for GPS navigation, it offers an alternative for creating the adaptive filter. A collection of switching models built on a method of multiple model estimation can be used to characterize the uncertainty of the noise. Even though most noise in real life is non-Gaussian, time-varying, and of fluctuating strength, the standard EKF operates effectively when the noise is Gaussian. The performance of EKF will drastically decline if the signals appear non-Gaussian. The underlying system disrupted by heavy-tailed, non-Gaussian impulsive sounds could be better since the EKF employs second-order statistical information. The MCC is a method for comparing two random variables based on higher-order signal statistics. The maximum correntropy-extended Kalman filter (MCEKF), which uses the MCC rather than the minimal mean square error (MMSE) as the optimization criterion, is used to enhance performance in non-Gaussian situations. Finally, a performance evaluation will be conducted to compare the effectiveness of the suggested strategy in improving positioning to alternative system designs. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Video surveillance systems are deployed at many places such as airports, train stations, and malls for security and monitoring purposes. However, it is laborious to search for and retrieve persons in multicamera surveillance systems, especially with cluttered backgrounds and appearance variations among multiple cameras. To solve these problems, this paper proposes a person retrieval method that extracts the attributes of a masked image using an instance segmentation module for each object of interest. It uses attributes such as color and type of clothes to describe a person. The proposed person retrieval system involves four steps: (1) using the YOLACT++ model to perform pixelwise person segmentation, (2) conducting appearance-based attribute feature extraction using a multiple convolutional neural network classifier, (3) employing a search engine with a fundamental attribute matching approach, and (4) implementing a video summarization technique to produce a temporal abstraction of retrieved objects. Experimental results show that the proposed retrieval system can achieve effective retrieval performance and provide a quick overview of retrieved content for multicamera surveillance systems. [ABSTRACT FROM AUTHOR]

The goal of this paper is to explore the effect of various parameters on the information geometric structure of the phase-locked loop (PLL) statistics, both transient and stationary. Comprehensive treatment on the behavior of PLL statistics will be given. The behavior of the phase-error statistics of the first-order PLL, in the presence of additive white Gaussian noise (WGN) is investigated through solving the differential equations known as the Fokker–Planck (FP) equation using the implicit Crank–Nicolson finite-difference method. The PLL is one of the most commonly used circuits in electrical engineering. A full knowledge of probability density functions (PDFs) of the phase-error statistics becomes essential in understanding the PLLs. Several illustrative examples are presented to provide profound insights on understanding the PLL statistics both qualitatively and quantitatively. Results covered include the transient and stationary statistics for the nonmodulo-2π probability density function, modulo-2π probability density function, and cycle slipping density function, of the phase error. Various numerical settings of PLL parameters are involved, including the detuning factor and signal-to-noise ratio (SNR). The results presented in this paper elucidate the link between various parameters and the information geometry of the phase-error statistics and form a basis for future investigation on PLL designs. [ABSTRACT FROM AUTHOR]

A robust state estimation technique based on the Huber-based Cubature Kalman Filter (HCKF) is proposed for Global Positioning System (GPS) navigation processing. The Cubature Kalman Filter (CKF) employs a third-degree spherical-radial cubature rule to compute the Gaussian weighted integration, such that the numerical instability induced by round-off errors can be avoided. In GPS navigation, the filter-based estimation of the position and velocity states can be severely degraded due to contaminated measurements caused by outliers or deviation from a Gaussian distribution assumption. For the signals contaminated with non-Gaussian noise or outliers, a robust scheme combining the Huber M-estimation methodology and the CKF framework is beneficial where the Huber M-estimation methodology is used to reformulate the measurement information of the CKF. GPS navigation processing using the HCKF algorithm has been carried out and the performance has been compared to those based on the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and CKF approaches. Simulation and experimental results presented in this paper confirm the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This paper conducts performance evaluation for the ultra-tight integration of Global positioning system (GPS) and inertial navigation system (INS) by use of the fuzzy adaptive strong tracking unscented Kalman filter (FASTUKF). An ultra-tight GPS/INS integration architecture involves fusion of the in-phase and quadrature components from the correlator of the GPS receiver with the INS data. These two components are highly nonlinearly related to the navigation states. The strong tracking unscented Kalman filter (STUKF) is based on the combination of an unscented Kalman filter (UKF) and strong tracking algorithm (STA) to perform the parameter adaptation task for various dynamic characteristics. The STA is basically a nonlinear smoother algorithm that employs suboptimal multiple fading factors, in which the softening factors are involved. In order to resolve the shortcoming in a traditional approach for selecting the softening factor through personal experience or computer simulation, the Fuzzy Logic Adaptive System (FLAS) is incorporated for determining the softening factor, leading to the FASTUKF. Two examples are provided for illustrating the effectiveness of the design and demonstrating effective improvement in navigation estimation accuracy and, therefore, the proposed FASTUKF algorithm can be considered as an alternative approach for designing the ultra tightly coupled GPS/INS integrated navigation system. [ABSTRACT FROM AUTHOR]

This paper presents a sensor fusion method for the Ultra-Tightly Coupled (UTC) Global Positioning System (GPS)/Inertial Navigation System (INS) integrated navigation. The UTC structure, also known as the deep integration, exhibits many advantages, e.g., disturbance and multipath rejection capability, improved tracking capability for dynamic scenarios and weak signals, and reduction of acquisition time. This architecture involves the integration of I (in-phase) and Q (quadrature) components from the correlator of a GPS receiver with the INS data. The Particle Filter (PF) exhibits superior performance as compared to an Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) in state estimation for the nonlinear, non-Gaussian system. To handle the problem of heavy-tailed probability distribution, one of the strategies is to incorporate the UKF into the PF as the proposal distribution, leading to the Unscented Particle Filter (UPF). The combination of an adaptive UPF and Fuzzy Logic Adaptive System (FLAS) is adopted for reducing the number of particles with sufficiently good results. The GPS tracking loops may lose lock due to the signals being weak, subjected to excessive dynamics or completely blocked. One of the principal advantages of the UTC structure is that a Doppler frequency derived from the INS is integrated with the tracking loops to improve the receiver tracking capability. The Doppler frequency shift is calculated and fed to the GPS tracking loops for elimination of the effect of stochastic errors caused by the Doppler frequency. In this paper, several nonlinear filtering approaches, including EKF, UKF, UPF and ‘FLAS assisted UPF’ (FUPF), are adopted for performance comparison for ultra-tight integration of GPS and INS. It is assumed that no outage occurs such that the inertial sensor errors can be properly corrected and accordingly the aiding information is working well. Two examples are provided for performance assessment for the various data fusion methods. The FUPF algorithm with Doppler velocity aiding demonstrates remarkable improvement, especially in the high dynamic environments, in navigation estimation accuracy with reduction of number of particles. [ABSTRACT FROM PUBLISHER]

Divided difference filter (DDF) with quaternion-based dynamic process modeling is applied to global positioning system (GPS) navigation. Using techniques similar to those of the unscented Kalman filter (UKF), the DDF uses divided difference approximations of derivatives based on Stirling’s interpolation formula which results in a similar mean but different posterior covariance compared to the extended Kalman filter (EKF) solutions. The second-order divided difference is obtained from the mean and covariance in second-order polynomial approximation. The quaternion-based dynamic model is adopted for avoiding the singularity problems encountered in the Euler angle method and enhancing the computational efficiency. The proposed method is applied to GPS navigation to increase the navigation estimation accuracy at high-dynamic regions while preserving (without sacrificing) the precision at low-dynamic regions. For the illustrated example, the second-order DDF can deliver about 41–82% accuracy improvement as compared to the EKF. Some properties and performance are assessed and compared to those of the EKF and UKF approaches. [ABSTRACT FROM AUTHOR]