Search Results (31)

Accurate multi-target filtering is crucial for low-altitude surveillance, where point and group targets often coexist. Poisson multi-Bernoulli mixture (PMBM) filters provide a unified Bayesian framework for the joint filtering of point and group targets under the assumptions of independent target dynamics and standard measurement models. However, in practical scenarios, group targets may generate new targets through member separation, while point targets may produce multiple measurements due to multi-beam sensing and micro-Doppler signatures. These phenomena violate the assumptions of existing PMBM filters and lead to degraded state estimation and target-type inference. To address these challenges, this paper proposes a modified PMBM filter with group target spawning and generalized measurement models for coexisting point and group targets. Specifically, a group-dependent spawning model is incorporated into the prediction step to enable timely detection of newly spawned targets. In addition, a generalized update function is developed to support point-target density updates with measurement sets of arbitrary cardinality, and a measurement-rate-based correction factor is introduced to improve target-type estimation under nonstandard measurement conditions. Furthermore, an efficient Poisson multi-Bernoulli approximation is derived to reduce computational complexity. The effectiveness of the proposed filter is verified through simulation and experimental results. Full article

The manuscript proposes a new non-linear and non-stationary bivariate stochastic model, termed the two-dimensional Gaussian (generalized) Split-BREAK (2D-GSB) process, as a multivariate extension of the univariate GSB framework. The generalization consists in introducing a common threshold mechanism based on the norm of a bivariate innovation vector and a single synchronized Bernoulli indicator which jointly governs regime activation in both components. This structure induces cross-dependent regime shifts and yields a binomial–Gaussian mixture representation of the joint distribution, explicitly linking contemporaneous dependence with a common latent regime mechanism. The fundamental properties of the proposed model are established, with particular emphasis on its asymptotic behavior. Parameter estimation procedure is developed using both the method of moments (MoM) and the empirical characteristic function (ECF) approach, and their performance is evaluated through Monte Carlo simulations. An empirical application to daily crime data illustrates how the proposed framework captures synchronized structural shocks and heavy-tailed features in related crime categories. In comparison with a standard VAR(1) benchmark, the 2D-GSB specification provides a parsimonious yet substantially improved likelihood-based fit, thus offering a theoretically sound framework for analyzing multivariate time series characterized by synchronized regime shifts and heavy-tailed behavior. Full article

To explore how varying viewpoints influence the accuracy of distributed fusion in asynchronous, nonlinear visual-field systems, this study investigates fusion strategies for multi-target tracking. The primary focus is on how different sensor perspectives affect the fusion of nonlinear moving-target data and the spatial segmentation of such targets. We propose a differential-view nonlinear multi-target tracking approach that integrates the Gaussian mixture, jump Markov nonlinear system, and the cardinalized probability hypothesis density (GM-JMNS-CPHD). The method begins by partitioning the observation space based on the boundaries of distinct viewpoints. Next, it applies a combined technique—the TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) and SOS (stochastic outlier selection)—to identify outliers near these boundaries. To achieve accurate detection, the posterior intensity is split into several sub-intensities, followed by reconstructing the multi-Bernoulli cardinality distribution to model the target population in each subregion. The algorithm’s computational complexity remains on par with the standard GM-JMNS-CPHD filter. Simulation results confirm the proposed method’s robustness and accuracy, demonstrating a lower error rate compared to other benchmark algorithms. Full article

Multi-source heterogeneous information fusion based on the Global Navigation Satellite System (GNSS)/Inertial Navigation System (INS)/odometer is an important technical means to solve the problem of navigation and positioning in complex environments. The measurement noise of the GNSS/INS/odometer integrated navigation system is complex and non-stationary; it approximates a Gaussian distribution in an open-sky environment, and it has heavy-tailed properties in the GNSS challenging environment. This work models the measurement noise and one-step prediction as the Gaussian and Student’s t mixture distribution to adjust to different scenarios. The mixture distribution is formulated as the hierarchical Gaussian form by introducing Bernoulli random variables, and the corresponding hierarchical Gaussian state-space model is constructed. Then, the mixing probability of Gaussian and Student’s t distributions could adjust adaptively according to the real-time kinematic solution state. Based on the novel distribution, a robust variational Bayesian Kalman filter is proposed. Finally, two vehicle test cases conducted in GNSS-friendly and challenging environments demonstrate that the proposed robust Kalman filter with the Gaussian–Student’s t mixture distribution can better model heavy-tailed non-Gaussian noise. In challenging environments, the proposed algorithm has position root mean square (RMS) errors of 0.80 m, 0.62 m, and 0.65 m in the north, east, and down directions, respectively. With the assistance of inertial sensors, the positioning gap caused by GNSS outages has been compensated. During seven periods of 60 s simulated GNSS data outages, the RMS position errors in the north, east, and down directions were 0.75 m, 0.30 m, and 0.20 m, respectively. Full article

To address the challenges of the strong randomness and intermittency of wind power generation that affect wind power grid integration, power system scheduling, and the safe and stable operation of the system, an improved Dung Beetle Optimization Algorithm (MSADBO) is proposed to optimize the hyperparameters of the Long Short-Term Memory neural network (LSTM) for ultra-short-term wind power forecasting. By applying Bernoulli mapping for population initialization, the model’s sensitivity to wind power fluctuations is reduced, which accelerates the algorithm’s convergence speed. Incorporating an improved Sine Algorithm (MSA) into the forecasting model for this nonlinear problem significantly improves the position update strategy of the Dung Beetle Optimization Algorithm (DBO), which tends to be overly random and prone to local optima. This enhancement boosts the algorithm’s exploration capabilities both locally and globally, improving the rapid responsiveness of ultra-short-term wind power forecasting. Furthermore, an adaptive Gaussian–Cauchy mixture perturbation is introduced to interfere with individuals, increasing population diversity, escaping local optima, and enabling the continued exploration of other areas of the solution space until the global optimum is ultimately found. By optimizing three hyperparameters of the LSTM using the MSADBO algorithm, the prediction accuracy of the model is greatly enhanced. After simulation validation, taking winter as an example, the MSADBO-LSTM predictive model achieved a reduction in the MAE metric of 40.6% compared to LSTM, 20.12% compared to PSO-LSTM, and 3.82% compared to DBO-LSTM. The MSE decreased by 45.4% compared to LSTM, 40.78% compared to PSO-LSTM, and 16.62% compared to DBO-LSTM. The RMSE was reduced by 26.11% compared to LSTM, 23.05% compared to PSO-LSTM, and 8.69% compared to DBO-LSTM. Finally, the MAPE declined by 79.83% compared to LSTM, 31.88% compared to PSO-LSTM, and 29.62% compared to DBO-LSTM. This indicates that the predictive model can effectively enhance the accuracy of wind power forecasting. Full article

This paper proposes a trajectory multi-Bernoulli filter applied to the superpositional sensor model for multi-target tracking in the presence of unknown measurement noise. This filter can provide a Multi-Bernoulli approximation of the posterior density on a set of alive trajectories at the current time step. We also provide a Gaussian mixture (GM) implementation of this filter, employing a mixture of Gaussian and inverse Wishart distributions to represent the combined state of measurement noise and target information. Subsequently, the variational Bayesian (VB) method is employed to approximate the posterior distribution, ensuring its form remains consistent with the prior distribution. This method is capable of directly generating trajectory estimates and can jointly estimate both multi-object tracking and measurement noise covariance. The performance of this algorithm is verified through simulation. Finally, a computationally more efficient L-scan approximation is provided. The simulation results indicate that the filter can achieve robust tracking performance, adapting to unknown measurement noise. Full article

In practical radar systems, changes in the target aspect toward the radar will result in glint noise disturbances in the measurement data. The glint noise has heavy-tailed characteristics and cannot be perfectly modeled by the Gaussian distribution widely used in conventional tracking algorithms. In this article, we investigate the challenging problem of tracking a time-varying number of maneuvering targets in the context of glint noise with unknown statistics. By assuming a set of models for the possible motion modes of each single-target hypothesis and leveraging the multivariate Laplace distribution to model measurement noise, we propose a robust interacting multi-model multi-Bernoulli mixture filter based on the variational Bayesian method. Within this filter, the unknown noise statistics are adaptively learned while filtering and the predictive likelihood is approximately calculated by means of the variational lower bound. The effectiveness and superiority of our proposed filter is verified via computer simulations. Full article

This paper focuses on the size-dependent free vibration and buckling behaviors of the axially functionally graded (AFG) graphene platelets (GPLs) reinforced nanocomposite microbeams subjected to axially varying loads (AVLs). With various axial grading patterns, the GPL nano-reinforcements are distributed throughout the polymer matrix against microbeam length, and the improved Halpin–Tsai micromechanics model and the rule of mixture are adopted to evaluate the effective material properties. Eigenvalue equations of the microbeams governing the static stability and vibration are derived based on the modified couple stress Euler–Bernoulli beam theory via the state-space method, and are analytically solved with the discrete equilong segment model. The effects of axial distribution patterns, weight fraction, and geometric parameters of GPLs, as well as different types of AVLs, on the size-dependent buckling load and natural frequency are scrutinized in detail. The results show that the synchronized axial distributions of GPLs and AVLs could improve the buckling resistance and natural frequency more powerfully. Full article

Respiratory diseases are among the leading causes of death globally, with the COVID-19 pandemic serving as a prominent example. Issues such as infections affect a large population and, depending on the mode of transmission, can rapidly spread worldwide, impacting thousands of individuals. These diseases manifest in mild and severe forms, with severely affected patients requiring ventilatory support. The air–oxygen blender is a critical component of mechanical ventilators, responsible for mixing air and oxygen in precise proportions to ensure a constant supply. The most commonly used version of this equipment is the analog model, which faces several challenges. These include a lack of precision in adjustments and the inspiratory fraction of oxygen, as well as gas wastage from cylinders as pressure decreases. The research proposes a blender model utilizing only dynamic pressure sensors to calculate oxygen saturation, based on Bernoulli’s equation. The model underwent validation through simulation, revealing a linear relationship between pressures and oxygen saturation up to a mixture outlet pressure of 500 cmH₂O. Beyond this value, the relationship begins to exhibit non-linearities. However, these non-linearities can be mitigated through a calibration algorithm that adjusts the mathematical model. This research represents a relevant advancement in the field, addressing the scarcity of work focused on this essential equipment crucial for saving lives. Full article

A novel Student’s t-based robust Poisson multi-Bernoulli mixture (PMBM) filter is proposed to effectively perform multi-target tracking under heavy-tailed process and measurement noises. To cope with the common scenario where the process and measurement noises possess different heavy-tailed degrees, the proposed filter models this noise as two Student’s t-distributions with different degrees of freedom. Furthermore, this method considers that the scale matrix of the one-step predictive probability density function is unknown and models it as an inverse-Wishart distribution to mitigate the influence of heavy-tailed process noise. A closed-form recursion of the PMBM filter for propagating the approximated Gaussian-based PMBM posterior density is derived by introducing the variational Bayesian approach and a hierarchical Gaussian state-space model. The overall performance improvement is demonstrated through three simulations. Full article

This study addresses the nonlinear forced vibration of a functionally graded (FG) nanobeam subjected to mechanical impact and electromagnetic actuation. Two symmetrical actuators were present in the mechanical model, and their mechanical behaviors were analyzed considering the symmetry in actuation. The model considered the longitudinal–transverse vibration of a simple supported Euler–Bernoulli beam, which accounted for von Kármán geometric nonlinearity, including the first-order strain–displacement relationship. The FG nanobeam was made of a mixture of metals and ceramics, while the volume fraction varied in terms of thickness when a power law function was used. The nonlocal Eringen theory of elasticity was used to study the simple supported Euler–Bernoulli nanobeam. The nonlinear governing equations of the FG nanobeam and the associated boundary conditions were gained using Hamilton’s principle. To truncate the system with an infinite degree of freedom, the coupled longitudinal–transverse governing equations were discretized using the Galerkin–Bubnov approach. The resulting nonlinear, ordinary differential equations, which took into account the curvature of the nanobeam, were studied via the Optimal Auxiliary Functions Method (OAFM). For this complex nonlinear problem, an explicit, analytical, approximate solution was proposed near the primary resonance. The simultaneous effects of the following elements were considered in this paper: the presence of a curved nanobeam; the transversal inertia, which is not neglected in this paper; the mechanical impact; and electromagnetic actuation. The present study proposes a highly accurate analytical solution to the abovementioned conditions. Moreover, in these conditions, the study of local stability was developed using two variable expansion methods, the Jacobian matrix and Routh–Hurwitz criteria, and global stability was studied using the Lyapunov function. Full article

Seasonal autoregressive (SAR) models have many applications in different fields, such as economics and finance. It is well known in the literature that these models are nonlinear in their coefficients and that their Bayesian analysis is complicated. Accordingly, choosing the best subset of these models is a challenging task. Therefore, in this paper, we tackled this problem by introducing a Bayesian method for selecting the most promising subset of the SAR models. In particular, we introduced latent variables for the SAR model lags, assumed model errors to be normally distributed, and adopted and modified the stochastic search variable selection (SSVS) procedure for the SAR models. Thus, we derived full conditional posterior distributions of the SAR model parameters in the closed form, and we then introduced the Gibbs sampler, along with SSVS, to present an efficient algorithm for the Bayesian subset selection of the SAR models. In this work, we employed mixture–normal, inverse gamma, and Bernoulli priors for the SAR model coefficients, variance, and latent variables, respectively. Moreover, we introduced a simulation study and a real-world application to evaluate the accuracy of the proposed algorithm. Full article

In this article, we present a Markov Bernoulli Lomax (MB-L) model, which is obtained by a countable mixture of Markov Bernoulli and Lomax distributions, with decreasing and unimodal hazard rate function (HRF). The new model contains Marshall- Olkin Lomax and Lomax distributions as a special case. The mathematical properties, as behavior of probability density function (PDF), HRF, r^th moments, moment generating function (MGF) and minimum (maximum) Markov-Bernoulli Geometric (MBG) stable are studied. Moreover, the estimates of the model parameters by maximum likelihood are obtained. The maximum likelihood estimation (MLE), bias and mean squared error (MSE) of MB-L parameters are inspected by simulation study. Finally, a MB-L distribution was fitted to the randomly censored and COVID-19 (complete) data. Full article

This paper focuses on the problem of joint detection, tracking, and classification (JDTC) for multiple extended objects (EOs) within a Poisson multi-Bernoulli (MB) mixture (PMBM) filter, where an EO is described as an ellipse, and the ellipse is modeled by a random matrix. The EOs are classified according to the size information of the ellipse. Usually, detection, tracking, and classification are processed step-by-step. However, step-by-step processing ignores the coupling relationship between detection, tracking, and classification, resulting in information loss. In fact, detection, tracking, and classification affect each other, and JDTC is expected to be beneficial for achieving better overall performance. In the multi-target tracking problem based on RFS, the overall performance of the PMBM filter satisfying the conjugate priors has been verified to be superior to other filters. Specifically, the PMBM filter propagates multiple MB simultaneously during iterative updates and model the distribution of hitherto undetected EOs. At present, the PMBM filter is only applied to multiple extended objects tracking problem. Therefore, we consider using the PMBM filter to solve the JDTC problem of multiple EOs and further improve JDTC performance. Furthermore, the closed-form implementation based on the product of a gamma Gaussian inverse Wishart (GGIW) and class probability mass function (PMF) is proposed. The details of parameters calculation in the implementation process and the derivation of class PMF are presented in this paper. Simulation experiments verify that the proposed algorithm, named the JDTC-PMBM-GGIW filter, performs well in comparison to the existing JDTC strategies for multiple extended objects. Full article

This study provides a solution for multiple group/extended target tracking with an arbitrary shape. Many tracking approaches for extended/group targets have been proposed. However, these approaches make assumptions about the target shape, which have limitations in practical applications. To address this problem, in this work, an extended/group target tracking algorithm based on B-spline is proposed. Specifically, the extension of an extended or a group target was modeled as a spatial probability distribution characterized by the control points of a B-spline function that was then jointly propagated with the measurement rate model and kinematic component model over time using the Poisson multi-Bernoulli mixture (PMBM) filter framework. In addition, an amplitude-aided measurement partitioning approach is proposed to improve the accuracy caused by distance-based approaches. The simulation results demonstrate that the extension, shape and orientation of targets can be estimated better by the proposed algorithm, even if the shape changes. The tracking performance is also improved by about 10% and 13% compared to the other two algorithms. Full article