This paper addresses distributed multi-target tracking (DMTT) in spatially unregistered sensor networks, which necessitates the joint estimation of multi-target states and inter-sensor spatial registration (SR) parameters. To this end, we propose a computationally efficient DMTT algorithm within the probability hypothesis density (PHD) filtering framework. Specifically, by exploiting geometric average (GA) fusion, we develop a recursive SR estimation scheme referred to as PHD-GA-SR. An exponential Gaussian mixture (exp-GM) implementation is further derived for the SR posterior, while the local single-target probability density functions are represented by GMs. In addition, Kullback-Leibler divergence bounded pruning and maximum a posteriori estimate are investigated, and the computational complexity of the proposed approach is analyzed. Simulation results demonstrate that the proposed PHD-GA-SR achieves a favorable trade-off between estimation accuracy and computational efficiency in both static and dynamic unregistered sensor network scenarios.

Target tracking entails the estimation of the evolution of the target state over time, namely the target trajectory. Classical state-space modeling approaches, which focus on estimating discrete-time point states, exhibit notable limitations in accurately representing long-term trajectory trends and in dealing with model mismatch in scenarios with complex maneuvers. Different from the classical state space model, our series of studies, including this paper, model the collection of the target state overtime as a stochastic process (SP) that is further decomposed into a deterministic part which represents the trend of the trajectory and a residual SP representing the residual fitting error. Subsequently, the tracking problem is formulated as a learning task regarding the trajectory SP for which a key part is to estimate a trajectory function of time (T-FoT) best fitting the measurements in time series. For this purpose, we consider the polynomial fitting and address the regularized polynomial T-FoT optimization employing two distinct regularization strategies on the order of the polynomial, seeking trade-off between the accuracy and simplicity. One solves the problem by grid searching in a narrow, bounded range that is proven containing the optimal result while the other adopts l0 norm regularization for which a hybrid Newton solver is designed. Simulation results obtained in both single and multiple maneuvering target scenarios demonstrate the effectiveness of our approaches.

In the realm of target tracking, performance evaluation plays a pivotal role in the design, comparison, and analysis of trackers. Compared with the traditional trajectory composed of a finite set of point estimates obtained by a tracker at the discrete measurement time instants, the trajectory that our series of studies pursued is given by a curve function of time (FoT). This approach takes root in modeling the states of the target in times series as a stochastic process (SP) and the trajectory FoT (T-FoT) represents the deterministic part of this SP. The T-FoT provides the complete information of the movement of the target over time and can be used to infer the state corresponding to arbitrary time, not only at the measurement time. However, there are no metrics available for comparing and evaluating the T-FoT. To address this lacuna, this paper, as the first part of a series of companion papers, proposes a metric denominated as the spatio-temporal-aligned trajectory integral distance (Star-ID). The Star-ID associates and aligns the estimated and actual trajectories in the spatio-temporal domain and distinguishes between the time-aligned and unaligned segments in calculating false alarm, miss-detection and localization errors. The effectiveness of the Star-ID and its time-averaged measure is validated through theoretical analysis, sanity test and simulation of single target or multiple target tracking.

In the presence of outliers or non-Gaussian noise in linear estimator design, lightweight Kalman filters (KFs) suffer from severe vulnerability, whereas robust Gaussian mixture filters (GMFs) incur much higher computational costs. To reconcile the robustness of the estimation with resource constraints, this letter investigates a distributed heterogeneous fusion architecture integrating GMFs with KFs. For this multimodal KF-GMF fusion case, we prove the robustness superiority of the arithmetic average (AA) fusion in comparison to the geometric average (GA) fusion. Furthermore, to resolve the mode conflict caused by anomalous outliers in the KF nodes, a graph-centrality-based anomaly isolation mechanism is proposed. By mapping the statistical consistency of fused Gaussian components into a weighted topological graph, this mechanism utilizes a node strength criterion to identify and eliminate disturbance-induced, topologically isolated modes/components with theoretical guarantees. Simulations demonstrate that the proposed KF-GMF AA fusion approach significantly outperforms the GA fusion in terms of tracking accuracy and convergence.

HEV, primarily known for its waterborne transmission, is increasingly recognized for its zoonotic potential, raising public health concerns for individuals in close contact with animals or animal products. This study aims to evaluate the seroprevalence of Hepatitis E Virus (HEV) among slaughterhouse workers in Saudi Arabia and compare it to a control group of blood donors, emphasizing potential occupational risks and associated factors.This comparative cross-sectional study included 239 slaughterhouse workers (study group) and 250 blood donors (control group). HEV IgG antibodies were detected using an in-house ELISA. Sociodemographic data, occupational exposure duration, and animal contact details were analyzed.The HEV seroprevalence was significantly higher in slaughterhouse workers (49.7%) compared to blood donors (22.1%) (p < 0.0001). Age and duration of occupational exposure were strongly predictive of HEV infection, with workers exposed for over one year showing higher odds of seropositivity. Geographic region and type of animal contact showed no significant associations.The findings suggest that prolonged occupational exposure to animals demonstrated increased the risk of HEV infection among slaughterhouse workers. Public health interventions, including improved hygiene measures, health screenings, and potential vaccination, could mitigate the risk of HEV transmission in high-exposure occupations.

In nonlinear systems, system inputs play a critical role in achieving control objectives, yet they are highly susceptible to noise during measurement and execution. Ignoring input noise can cause the standard particle filter (SPF) algorithm to produce biased estimates. To address this issue, this study begins by analyzing how input noise contributes to the deviation in the SPF at first. A novel particle filter (PF) then is proposed, designed to be robust against noisy inputs by incorporating information from both process noise and input noise. This approach constructs a new importance density. Drawing inspiration from Gibbs sampling, the method hierarchically and independently samples input and state variables from the new importance density, which accounts for both input and state randomness. The input random variable is eliminated through Monte Carlo independent resampling of the two variables, yielding the final state estimate. To validate the proposed method, three comparative experiments were conducted, evaluating the SPF, the combined particle filter (CPF), and the auxiliary particle filter (APF) algorithms. The results demonstrate that the new PF outperforms SPF in handling nonlinear, non- Gaussian systems with noisy inputs and effectively mitigates deviations caused by input noise.

Complex target environments present characteristics of saturation, high speed, and high maneuverability, posing increasingly challenging demands for target tracking. In this context, traditional phased-array radar (PAR) faces the dilemma of limited tracking resources and filter model mismatch. To address these issues, this paper proposes a heterogeneous time resource arrangement (HTRA) and refined tracking (RT) method. Firstly, to mitigate the impact of maneuvering model mismatch, we modify the traditional strong tracking filter by considering the effect of different measurements on the correction of the maneuvering model, and formulate the RT method as an optimization problem according to the residual consistency criterion. Then, to properly allocate and arrange limited time resources, by defining a multidimensional time resource vector, we adopt the posterior estimate covariance from RT as a performance metric, and design a performance-driven HTRA framework to achieve time assignment under model mismatch conditions. Simulation results demonstrate that, compared to traditional approaches, the joint HTRA and RT strategy significantly enhance the tracking performance of complex targets within a given time resource budget.

To address the critical data loss problem in multichannel radar systems in complex electromagnetic environments, we propose a subspace-aligned tensor completion framework that effectively incorporates auxiliary information from a physically plausible source, thereby providing a correlated yet distinct observation of the same target scene. To overcome the limitations of existing methods in dealing with low-rank multi-dimensional data and severe data loss, a Tucker decomposition-based joint optimization framework is proposed that simultaneously enforces low-rankness of the three-dimensional observation tensor via weighted nuclear norm regularization, integrates preprocessed auxiliary radar tensors as reconstruction priors, and establishes a factor matrix alignment mechanism to enhance structural consistency. Theoretically, we establish an upper bound on the recovery error with four components: low-rank optimization error, primary auxiliary tensor deviation, subspace alignment error, and observation noise. Simulations verify that our method consistently outperforms both standard low-rank completion techniques and naive fusion approaches across various observation ratios. Notably, the empirical error strictly complies with the derived theoretical bound, validating the efficacy of our integrated framework, which combines auxiliary information guidance with subspace alignment.

This paper addresses the challenging state estimation problem in real-world systems characterized by nonlinearities and time-varying measurement noise. Data-driven approaches like KalmanNet, while enhancing state estimation for nonlinear systems, struggle to adapt to changing noise environments. To overcome these limitations, this paper proposes a noise-parameter adaptive KalmanNet state estimation method that combines the strengths of both model-driven and data-driven paradigms, enabling adaptive state estimation in dynamic environments with time-varying measurement noise. Specifically, the proposed method leverages data-trained networks to extract the state transition characteristics of nonlinear systems and designs a dual model and data driven state estimation framework. This framework decouples the prior state error covariance from Kalman gain computation. Furthermore, an online adaptive estimation strategy incorporating Bayesian inference is introduced to estimate time-varying measurement noise, thereby improving the robustness and adaptability of the model's state estimation performance in dynamic scenarios.

To solve the target tracking problem with little a-priori information about the target dynamics, our series of studies, including this paper as the third part, propose a continuous-time trajectory estimation approach (dubbed targeting track) based on the stochastic process (SP) theory and a deterministic-stochastic decomposition framework. Specifically, we decompose the learning of the trajectory SP into two sequential stages: the first fits the deterministic trend of the trajectory using a curve function of time, while the second estimates the residual stochastic component through learning either a Gaussian process (GP) or Student's-$t$ process (StP). The former has been addressed in the companion paper and the latter is the focus of this paper. This leads to a data-driven tracking approach that produces the continuous-time trajectory with minimal prior knowledge of the target dynamics. Notably, our approach models the temporal correlations of the state sequence and of measurement noise using separate GP or StP. It does not only take advantage of the smooth trend of the target but also makes use of the long-term temporal correlation of both the data and the model fitting error. Although the GP admits an exact closed-form expression for the linear system, approximations have to be adopted for StP modeling. Simulations in four maneuvering target tracking scenarios have demonstrated its effectiveness and superiority in comparison with existing approaches.

Recently, it has been validated that the arithmetic average (AA) fusion exhibits robust theoretical properties and demonstrates significant practical efficacy in multi-sensor multi-target tracking contexts. The fusion density in question may pertain to either the single-target probability density function (PDF) or the multi-target probability hypothesis density (PHD) function. In this study, we extend the applicability of AA fusion from the conventional PDF/PHD fusion to the domain of trajectory fusion. In this context, the spatiotemporal trajectory is modeled as stochastic processes (SPs) with mean function represented as a curve function of time (FoT). Specifically, we explore the Gaussian process and the Student’s t process within this letter. This extension substantially broadens the scope of the existing AA fusion methodology. Nonetheless, it introduces novel challenges, particularly in preserving fusion closure and addressing practical implementation requirements. This letter analyzes these challenges and proposes preliminary solutions. Simulation studies are also provided.

This paper, the fourth part of a series of papers on the arithmetic average (AA) density fusion approach and its application for target tracking, addresses the intricate challenge of distributed heterogeneous multisensor multitarget tracking, where each inter-connected sensor operates a probability hypothesis density (PHD) filter, a multiple Bernoulli (MB) filter or a labeled MB (LMB) filter and they cooperate with each other via information fusion. Earlier papers in this series have proven that the proper AA fusion of these filters is all exactly built on averaging their respective unlabeled/labeled PHDs. Based on this finding, two PHD-AA fusion approaches are proposed via variational minimization of the upper bound of the Kullback-Leibler divergence between the local and multi-filter averaged PHDs subject to cardinality consensus based on the Gaussian mixture implementation, enabling heterogeneous filter cooperation. One focuses solely on fitting the weights of the local Gaussian components (L-GCs), while the other simultaneously fits all the parameters of the L-GCs at each sensor, both seeking average consensus on the unlabeled PHD, irrespective of the specific posterior form of the local filters. For the distributed peer-to-peer communication, both the classic consensus and flooding paradigms have been investigated. Simulations have demonstrated the effectiveness and flexibility of the proposed approaches in both homogeneous and heterogeneous scenarios.

We address the multisensor multitarget tracking problem based on a hierarchical sensor network. In this setup, there is a fusion center, several cluster heads, and many sensors. Each sensor runs a Gaussian mixture probability hypothesis density (PHD) filter. The sensors send their locally calculated Gaussian components to the local cluster head in the presence of false data injection (FDI) and denial-of-service (DoS) attackers. We propose a hybrid PHD averaging fusion framework that consists of two parts: one uses the arithmetic average (AA) fusion to compensate for information shortage due to DoS and the other uses the geometric average (GA) fusion to suppress false information due to FDI. By integrating the respective zero forcing and avoiding behaviors of the two average fusion approaches, our proposed hybrid fusion scheme is proven resilient to both FDI and DoS attacks. Experimental results illustrate that our proposed algorithm can provide reliable tracking performance against FDI and DoS attacks.

In this paper, the heterogeneous fusion of the Kalman and Student’s t filters is considered in the context of distributed filter fusion for target tracking. This problem is involved in a multi-sensor tracking scenario where each sensor runs either a Kalman or Student’s t filter and they cooperate with each other via fusing the posterior density in a peer-to-peer fashion. This type of heterogeneous fusion has never been investigated before without closed-form solution. What is more, these sensors/filters are inherently correlated with each other to an unknown degree which raises a significant challenge for robust fusion. To address these challenges, both the arithmetic and geometric average fusion approaches are extended based on the appreciated moment matching strategies, in order to maintain the Gaussian or Student’s $\boldsymbol{t}$ distribution of the local posterior. The effectiveness and robustness of the proposed methods are verified through simulations which have demonstrated the superiority of arithmetic average fusion method over covariance intersection fusion and augmented measurement fusion.

The rapid development of the deep learning technology has provided novel, data-driven solutions to the classic maneuvering target tracking problems. Based on the celebrated interactive multiple model (IMM) approach, this paper proposes a deep learning state fusion target tracking algorithm, termed IMM-LSTM, which combines the advantages of the IMM algorithm and long short-term memory (LSTM) network. The algorithm assigns a separate target motion model for each of the LSTM trackers that are run in parallel. Further on, an LSTM-based classifier is employed to determine the weights for each motion model of the target and the final estimate is given by the weighted average of the estimates of these individual trackers. Simulation results have shown that our algorithm yields better tracking accuracy and robustness in scenarios where the a-priori target information is deficient.

BACKGROUND:HEV is endemic in several Middle Eastern countries including Saudi Arabia, which hosts the annual pilgrimage for Muslims from around the world. One of the Hajj rituals is the sacrifice of animals, including camels, cows, goats, and sheep. HEV Zoonosis is established in swine and other suspected species, including deer, rabbits, dromedary, and Bactrian camels. HEV was identified in small, domesticized animals like goats, cows, sheep, and horses. We previously investigated HEV seroprevalence in Camels. This study aimed to evaluate HEV seroprevalence in other highly consumed ruminants in Saudi Arabia, namely cows, sheep, and goats. METHODS:Sera from cows (n = 47), goats (n = 56), and sheep (n = 67) were analyzed for the presence of HEV-IgG by using in-house developed ELISA assays. RESULTS:The highest seroprevalence was found in sheep (62.7%), followed by cows (38.3%), and then goats (14.3%), with a p-value of < 0.001. No other demographic characteristics of the animals were significantly correlated with the HEV seroprevalence. CONCLUSIONS:This study provides baseline data as the first study on the seroprevalence of HEV in ruminant animals in Saudi Arabia. The high seroprevalence found in sheep and cows must be further investigated for the potential zoonotic HEV transmission to humans. Further studies are needed to investigate the active viremia in these animal species through nucleic acid detection and sequencing to provide data on the circulating HEV genotypes among the targeted animal species. The detection of HEV in different animal products, such as milk, liver, and others, also remains an important study area to consider.

This paper addresses the intractable track matching problem involved in multi-sensor multi-target tracking using the labeled multi-Bernoulli filters. Unlike the unlabeled density defined in the common state space, the labeled multi-target density is defined in the joint state and label space, where the label contains time-series/history information of the underlying track. To measure the similarity between labeled densities (individual tracks) that is required for inter-sensor track matching and fusion, one has to account for the divergences in both state and label spaces. The challenge, however, arises from the lack of a proper metric to measure the label difference. It requires considering the entire trajectory of the track, encompassing the whole-life information from the birth of the track to the present. In this paper, we provide a solution of comparing and matching labels based on the whole-life time-series state distributions of the labels/tracks, by extending the common divergences like the Cauchy-Schwarz and Kullback-Leibler from distributions at a single time-instant to those over time-series. Representative scenarios are considered for illustration.

As a fundamental information fusion approach, the arithmetic average (AA) fusion has recently been investigated for various random finite set (RFS) filter fusion in the context of multi-sensor multi-target tracking. It is not a straightforward extension of the ordinary density-AA fusion to the RFS distribution but has to preserve the form of the fusing multi-target density. In this work, we first propose a statistical concept, probability hypothesis density (PHD) consistency, and explain how it can be achieved by the PHD-AA fusion and lead to more accurate and robust detection and localization of the present targets. This forms a both theoretically sound and technically meaningful reason for performing inter-filter PHD AA-fusion/consensus, while preserving the form of the fusing RFS filter. Then, we derive and analyze the proper AA fusion formulations for most existing unlabeled/labeled RFS filters basing on the (labeled) PHD-AA/consistency. These derivations are theoretically unified, exact, need no approximation and greatly enable heterogenous unlabeled and labeled RFS density fusion which is separately demonstrated in two consequent companion papers.