Allocating the weight to each local density is essential in generalized covariance intersection (GCI) fusion. However, such a problem has not been fully addressed in the existing literature and still remains an open issue. In this paper, we propose a deep learning enhanced framework that dynamically optimizes GCI fusion weights by leveraging sensor node dependent local variables, resulting in the GCINet for fusion of probability density functions (PDFs). The key innovation lies in the employment of contextual based variables (e.g., measurement noise) as input to a neural network, which is trained by minimizing a suitably defined cost function. The proposed approach eliminates the need for manual weight tuning and overcomes the limitations of traditional optimization-based methods reliant on, e.g., Shannon entropy or Chernoff information. Application of proposed GCINet to distributed extended object tracking (EOT) application is discussed. Simulation results show that the proposed GCINet achieves superior accuracy compared to GCI fusion under equal as well as heuristically designed fusion weights.

This paper presents the consensus iterated posterior linearisation filter (IPLF) for distributed state estimation. The consensus IPLF algorithm is based on a measurement model described by its conditional mean and covariance given the state, and performs iterated statistical linear regressions of the measurements with respect to the current approximation of the posterior to improve estimation performance. Three variants of the algorithm are presented based on the type of consensus that is used: consensus on information, consensus on measurements, and hybrid consensus on measurements and information. Simulation results show the benefits of the proposed algorithm in distributed state estimation.

This paper presents an approach for 2-dimensional extended object tracking (EOT). The extended object (EO) is represented as a superellipse characterized by kinematic and shape states, with the latter uniquely specified in terms of four parameters. An approximated measurement model is proposed accounting for the fact that the measurements can be generated from any position inside or on the contour of the EO. Then, EOT is performed by iteratively estimating the kinematic state via a Kalman filter, while the posterior of the shape state is represented and propagated in particle filter form due to the strong nonlinearity of the resulting shape measurement model. Simulation results are provided to assess the performance of the proposed method.

In this article, we propose a novel approach to distributed joint detection, tracking, and classification (D-JDTC) of multiple targets by means of a multisensor network. The proposed approach relies on labeled multi-Bernoulli (LMB) random finite set modeling of the multisensor state, and consists of two main tasks, that is, local filtering in each individual node and data fusion among multiple nodes. For local filtering, the LMB filter is extended to JDTC by augmenting the target state to incorporate class and mode information. Further, the well-known generalized covariance intersection and recently developed minimum information loss fusion paradigms are exploited for data fusion among sensors. The effectiveness of the resulting algorithm, called D-JDTC-LMB, is assessed via simulation experiments.

Passive location and tracking of radio emitters is of great research value in civilian and defense applications. Among the existing methods, localization based on received signal strength indicator (RSSI) has been widely used due to its advantages in terms of low cost and easy implementation. However, most RSSI-based localization methods rely on the assumption that the emitter has been detected. Moreover, the emitter signal is supposed to propagate with the simplified path-loss model in which the shadow effects caused by obstacles are not considered. As a result, there are still gaps between the aforementioned methods and practical applications. In this paper, we consider the combined path-loss and shadowing model, which has been empirically confirmed in both outdoor and indoor radio propagation environments. Joint detection and tracking of an emitter is proposed by modeling the state of the emitter as Bernoulli random finite set, characterized by an existence probability and a spatial probability density function. Compared to existing studies, this paper works upon more practically appealing signal propagation model, and achieves better performance in real-time emitter detection and tracking. Moreover, the proposed method also provides explicit estimates of the unknown shadowing-related parameters, which can be adopted in further applications such as spectrum cartography and radio map construction. The feasibility of the proposed method is assessed via simulation experiments.

In this work a new class of filters, called Lambda:Omicron Multiplicative Error Model (L:OMEM), is introduced with the aim to efficiently address tracking of maneuvering extended objects. In this context, two main challenges have to be tackled: (1) the tracked object moves with unknown time-varying speed and turning rate; (2) the tracked object can produce a large amount of measurements. Closed-form formulas and a novel method to reduce extended object tracking to a conventional point object tracking problem are derived, so that the novel filter results into an accurate and computationally cheap algorithm. Numerical simulations are presented to validate the effectiveness of the proposed approach, where the L:OMEM filter is compared to state-of-the-art filters for extended objects.

Target state estimation with Doppler-only sensors has attracted a lot of attention due to its wide potential applications in target localization and tracking. While existing Doppler-only tracking methods rely on the assumption that Doppler sensors have been correctly registered, in many practical cases there can be significant registration errors which imply measurement biases and thus performance degradation in target state estimation. Motivated by this issue, the present paper addresses the problem of jointly estimating target state and sensor biases based on Doppler-only measurements. The proposed method consists of two phases, i.e., (1) raw estimation of the target state without considering sensor biases, followed by (2) a bias compensation step that relies on linearization of the measurement function and joint estimation of target state-sensor biases via a least square method. The Cramer-Rao lower bound (CRLB) in estimating sensor biases is evaluated and the performance of the proposed method is also assessed via simulations.

An event-triggered consensus filter is proposed in this letter for state estimation in distributed sensor networks based on the hybrid consensus on measurement and consensus on information scheme. For bandwidth reduction and energy saving, an event-triggered transmission strategy is developed in which each node selectively transmits only the most relevant data so as to reduce data transmission while preserving the filtering performance. Two different transmission tests are performed in parallel, respectively on the prior and on the likelihood information pair, to evaluate the information loss (measured in terms of Kullback-Leibler divergence) that would be incurred if the current values were replaced by the predicted ones according to the last transmitted data. Simulation results on a distributed target tracking case-study demonstrate outperformance of the proposed filter with respect to conventional triggered filters.

An adaptive consensus filter for sensor networks with unknown process and measurement noise statistics is proposed in this letter. The variational Bayes(VB) approach is exploited to get local estimates of unknown noise covariances with prior inverse Wishart distributions. A distributed averaging approach on exponential-class densities is applied for consensus on the natural parameters of the unknown predicted error covariance. Consensus on measurements is performed in parallel and the two consensus outcomes are fused. Simulation results demonstrate the effectiveness of the proposed adaptive consensus filter compared to conventional, non-adaptive, consensus filters.

This article addressessimultaneous localization and mapping(SLAM) viaprobability hypothesis density(PHD) filtering. The resulting approach, named PHD-SLAM, has demonstrated its effectiveness, especially when measurements provided by the sensors onboard the vehicle are highly contaminated by missdetections and clutter. However, since theproposal distribution(PD) of standard PHD-SLAM does not take into account most recently received measurements, a huge amount of particles are typically needed in order to achieve satisfactory performance. In this article, a new PD, which aims to approximate the vehicle pose posterior, is proposed for PHD-SLAM. The resulting algorithm, named PHD-SLAM 2.0, allows for drastically reducing the number of particles, and hence, the computational burden, while preserving the SLAM performance. The computational complexity of PHD-SLAM 2.0 is analyzed, and its performance is assessed via both simulated and real-data experiments.

5G is expected to enable simultaneous vehicle localization and environment mapping (SLAM). Furthermore, vehicular networks will be covered with 5G small cells, wherein the map information is collected at each base station (BS) and then fused so as to promote the overall performance of SLAM. In 5G multi-cell SLAM, there are challenges such as the unknown number of targets, uncertainty regarding the association between the targets and the measurements, unknown types of targets, as well as map management among BSs. To address those challenges, we propose a new method for 5G multi-cell SLAM which comprises a joint cubature Kalman filter and multi-model probability hypothesis density, and a map fusion routine. Simulation results demonstrate that the proposed method solves the aforementioned challenges and also improves vehicle state and map estimates.

The linear opinion pool (LinOP) provides a potential solution to the problem of information fusion. However, the LinOP cannot be directly applied to multi-object fusion since the resulting fused multi-object density, in general, no longer belongs to the same family of the local ones, thus it cannot be utilized as prior information for the next recursion in Bayesian multi-object filtering. In this letter, by showing that the LinOP is actually the one that leads to minimum information loss (MIL), we propose to find the fused multi-object density that has the same form as the local ones and, at the same time, leads to MIL. The performance of MIL fusion is then compared with the one of the well-known generalized covariance intersection (GCI) fusion via simulations.

This article addresses fully distributed multirobot (multivehicle) simultaneous localization and mapping (SLAM). More specifically, a multivehicle scenario is considered, wherein a team of vehicles explore the scene of interest in order to cooperatively construct the map of the environment by locally updating and exchanging map information in a neighborwise fashion. To this end, a random-set-based local SLAM approach is undertaken at each vehicle by regarding the map as a random finite set and updating the first-order moment, called probability hypothesis density (PHD), of its multiobject density. Consensus on map PHDs is adopted in order to spread the map information through the team of vehicles also taking into account the different and time-varying fields of view of the team members. The convergence of the consensus strategy is analyzed theoretically, and the effectiveness of the proposed approach is assessed on both simulated and experimental datasets. The complexity and scalability of the proposed approach are also analyzed both theoretically and experimentally.

5G millimeter wave (mmWave) signals can enable accurate positioning in vehicular networks when the base station and vehicles are equipped with large antenna arrays. However, radio-based positioning suffers from multipath signals generated by different types of objects in the physical environment. Multipath can be turned into a benefit, by building up a radio map (comprising the number of objects, object type, and object state) and using this map to exploit all available signal paths for positioning. We propose a new method for cooperative vehicle positioning and mapping of the radio environment, comprising a multiple-model probability hypothesis density filter and a map fusion routine, which is able to consider different types of objects and different fields of views. Simulation results demonstrate the performance of the proposed method.

This paper focuses on reducing communication bandwidth and, consequently, energy consumption in the context of distributed target detection and tracking over a peer-to-peer sensor network. A consensus Bernoulli filter with event-triggered communication is developed by enforcing each node to transmit its local information to the neighbors only when a suitable measure of discrepancy between the current local posterior and the one predictable from the last transmission exceeds a preset threshold. Two information-theoretic criteria, i.e. Kullback-Leibler divergence and Hellinger distance, are adopted in order to measure the discrepancy between random finite set densities. The performance of the proposed event-triggered consensus Bernoulli filter is evaluated through simulation experiments.

A key issue in multi-sensor surveillance is the capability to surveil a much larger region than the field-of-view (FoV) of any individual sensor by exploiting cooperation among sensor nodes. Whenever a centralized or distributed information fusion approach is undertaken, this goal cannot be achieved unless a suitable fusion approach is devised. This paper proposes a novel approach for dealing with different FoVs within the context of Generalized Covariance Intersection (GCI) fusion. The approach can be used to perform multi-object tracking on both a centralized and a distributed peer-to-peer sensor network. Simulation experiments on realistic tracking scenarios demonstrate the effectiveness of the proposed solution.

This letter proposes analytical expressions for the fusion of certain classes of labeled multiobject densities via Kullback-Leibler averaging. Specifically, we provide analytical fusion rules for the labeled multi-Bernoulli and marginalized δ-generalized labeled multi-Bernoulli families of labeled multiobject densities. Information fusion via Kullback-Leibler averaging ensures immunity to double counting of information and is essential to the development of effective multiagent multiobject estimation.

In this paper, consensus-based Kalman filtering is extended to deal with the problem of joint target tracking and sensor self-localization in a distributed wireless sensor network. The average weighted Kullback-Leibler divergence, which is a function of the unknown drift parameters, is employed as the cost to measure the discrepancy between the fused posterior distribution and the local distribution at each sensor. Further, a reasonable approximation of the cost is proposed and an online technique is introduced to minimize the approximated cost function with respect to the drift parameters stored in each node. The remarkable features of the proposed algorithm are that it needs no additional data exchanges, slightly increased memory space and computational load comparable to the standard consensus-based Kalman filter. Finally, the effectiveness of the proposed algorithm is demonstrated through simulation experiments on both a tree network and a network with cycles as well as for both linear and nonlinear sensors.

This paper addresses 6-DOF (degree-of-freedom) tactile localization, i.e., the pose estimation of tridimensional objects using tactile measurements. This estimation problem is fundamental for the operation of autonomous robots that are often required to manipulate and grasp objects whose pose is a priori unknown. The nature of tactile measurements, the strict time requirements for real-time operation, and the multimodality of the involved probability distributions pose remarkable challenges and call for advanced nonlinear filtering techniques. Following a Bayesian approach, this paper proposes a novel and effective algorithm, named memory unscented particle filter (MUPF), which solves 6-DOF localization recursively in real time by only exploiting contact point measurements. The MUPF combines a modified particle filter that incorporates a sliding memory of past measurements to better handle multimodal distributions, along with the unscented Kalman filter that moves the particles toward regions of the search space that are more likely with the measurements. The performance of the proposed MUPF algorithm has been assessed both in simulation and on a real robotic system equipped with tactile sensors (i.e., the iCub humanoid robot). The experiments show that the algorithm provides accurate and reliable localization even with a low number of particles and, hence, is compatible with real-time requirements.

A novel consensus approach to networked nonlinear filtering is introduced. The proposed approach is based on the idea of carrying out in parallel a consensus on likelihoods and a consensus on prior probability distributions and then combine the outcomes with a suitable weighting factor. Simulation experiments concerning a target tracking case-study show that the proposed consensus-based nonlinear filter can be convenient when only a few consensus iterations per sampling interval can be afforded.

This issue marks the first anniversary issue of IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS after it changed its name from IEEE TRANSACTIONS ON NEURAL NETWORKS. I am happy to report that we had a great year! The number of new submissions in a year exceeded 1,000 for the first time in the history of TNN/TNNLS. IEEE TNN had a very successful development for 22 years from 1990 to 2011, and we have good reasons to believe that IEEE TNNLS will have many more years of successful growth.

Moving-horizon (MH) state estimation is addressed for nonlinear discrete-time systems affected by bounded noises acting on system and measurement equations by minimizing a sliding-window least-squares cost function. Such a problem is solved by searching for suboptimal solutions for which a certain error is allowed in the minimization of the cost function. Nonlinear parameterized approximating functions such as feedforward neural networks are employed for the purpose of design. Thanks to the offline optimization of the parameters, the resulting MH estimation scheme requires a reduced online computational effort. Simulation results are presented to show the effectiveness of the proposed approach in comparison with other estimation techniques.