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The probability hypothesis density (PHD) and Poisson multi-Bernoulli (PMB) filters are two popular set-type multi-object filters. Motivated by the fact that the multi-object filtering density after each update step in the PHD filter is a PMB without approximation, in this paper we present a multi-object smoother involving PHD forward filtering and PMB backward smoothing. This is achieved by first running the PHD filtering recursion in the forward pass and extracting the PMB filtering densities after each update step before the Poisson Point Process approximation, which is inherent in the PHD filter update. Then in the backward pass we apply backward simulation for sets of trajectories to the extracted PMB filtering densities. We call the resulting multi-object smoother hybrid PHD-PMB trajectory smoother. Notably, the hybrid PHD-PMB trajectory smoother can provide smoothed trajectory estimates for the PHD filter without labeling or tagging, which is not possible for existing PHD smoothers. Also, compared to the trajectory PHD filter, which can only estimate alive trajectories, the hybrid PHD-PMB trajectory smoother enables the estimation of the set of all trajectories. Simulation results demonstrate that the hybrid PHD-PMB trajectory smoother outperforms the PHD filter in terms of both state and cardinality estimates, and the trajectory PHD filter in terms of false detections., Comment: 2024 IEEE International conference on multisensor fusion and integration (MFI 2024). arXiv admin note: text overlap with arXiv:2206.08112

In the rapidly evolving field of 3D reconstruction, 3D Gaussian Splatting (3DGS) and 2D Gaussian Splatting (2DGS) represent significant advancements. Although 2DGS compresses 3D Gaussian primitives into 2D Gaussian surfels to effectively enhance mesh extraction quality, this compression can potentially lead to a decrease in rendering quality. Additionally, unreliable densification processes and the calculation of depth through the accumulation of opacity can compromise the detail of mesh extraction. To address this issue, we introduce MVG-Splatting, a solution guided by Multi-View considerations. Specifically, we integrate an optimized method for calculating normals, which, combined with image gradients, helps rectify inconsistencies in the original depth computations. Additionally, utilizing projection strategies akin to those in Multi-View Stereo (MVS), we propose an adaptive quantile-based method that dynamically determines the level of additional densification guided by depth maps, from coarse to fine detail. Experimental evidence demonstrates that our method not only resolves the issues of rendering quality degradation caused by depth discrepancies but also facilitates direct mesh extraction from dense Gaussian point clouds using the Marching Cubes algorithm. This approach significantly enhances the overall fidelity and accuracy of the 3D reconstruction process, ensuring that both the geometric details and visual quality., Comment: https://mvgsplatting.github.io

Simultaneous localization and mapping (SLAM) methods need to both solve the data association (DA) problem and the joint estimation of the sensor trajectory and the map, conditioned on a DA. In this paper, we propose a novel integrated approach to solve both the DA problem and the batch SLAM problem simultaneously, combining random finite set (RFS) theory and the graph-based SLAM approach. A sampling method based on the Poisson multi-Bernoulli mixture (PMBM) density is designed for dealing with the DA uncertainty, and a graph-based SLAM solver is applied for the conditional SLAM problem. In the end, a post-processing approach is applied to merge SLAM results from different iterations. Using synthetic data, it is demonstrated that the proposed SLAM approach achieves performance close to the posterior Cram\'er-Rao bound, and outperforms state-of-the-art RFS-based SLAM filters in high clutter and high process noise scenarios.

Niobium carbide (NbC) is a high-field Type II superconductor with a critical temperature ($T_C$) of 11.1 K, just above that of pure Nb ($T_C = 9$ K). Downsizing NbC to the nanoparticle scale introduces significant alterations in its critical field and/or the superconducting temperature. Here we report on superconducting NbC nanoparticles with $T_C \approx$ 10 K synthesized by laser ablation in acetone, using the lens-target distance (laser fluence) and centrifugation as control parameters of the particle size. X-ray diffraction analyses certified the cubic NbC phase and electron microscopy images revealed spherical particles with average size near 8 nm, with no apparent size dependence on fluence. Besides, magnetization curves exhibited magnetic loops featuring a saturation magnetization around $10^{-3} \mu_B$/molecule along with a small and typical superconducting loop for all investigated samples. We also observed a suppression of the diamagnetic behavior below $T_C$ upon decreasing laser fluence. Moreover, all samples exhibited a weak electron spin resonance (ESR) Curie-like signal at $g\approx2.0$ probably associated with localized defects in the particle's surface. The intriguing coexistence of superconductivity and magnetism in nanoparticles has recently garnered significant research attention. This complex scenario and unique properties are due to the substantial increase of surface-to-volume ratio in these superconducting NbC nanoparticles and further investigation would be crucial to unveil novel material properties and shed new light on our understanding of the superconducting phenomenon in this new morphology.

This paper considers a batch solution to the multi-object tracking problem based on sets of trajectories. Specifically, we present two offline implementations of the trajectory Poisson multi-Bernoulli mixture (TPMBM) filter for batch data based on Markov chain Monte Carlo (MCMC) sampling of the data association hypotheses. In contrast to online TPMBM implementations, the proposed offline implementations solve a large-scale, multi-scan data association problem across the entire time interval of interest, and therefore they can fully exploit all the measurement information available. Furthermore, by leveraging the efficient hypothesis structure of TPMBM filters, the proposed implementations compare favorably with other MCMC-based multi-object tracking algorithms. Simulation results show that the TPMBM implementation using the Metropolis-Hastings algorithm presents state-of-the-art multiple trajectory estimation performance., Comment: Accepted for publication in IEEE Transactions on Aerospace and Electronic Systems. MATLAB implementation available at https://github.com/yuhsuansia/Batch-TPMBM-using-MCMC-sampling

In this work the explicit solution of the electronic plasma diffusion with radiation reaction force, under the action of an exponential decay external electric field is given. The electron dynamics is described by a classical generalized Langevin equation characterized by an Ornstein-Uhlenbeck-type friction memory kernel, with an effective memory time which accounts for the effective thermal interaction between the electron and its surroundings (thermal collisions between electrons + radiation reaction force). The incident electric field exerts an electric force on the electron, which in turn can induce an additional damping to the braking radiation force, allowing a delay in the electron characteristic time. This fact allows that the effective memory time be finite and positive, and as a consequence, obtaining physically admissible solutions of the stochastic Abraham-Lorentz-like equation. It is shown that the diffusion process is quasi-Markovian which includes the radiation effects., Comment: 16 pages, 8 figures

This paper proposes a metric to measure the dissimilarity between graphs that may have a different number of nodes. The proposed metric extends the generalised optimal subpattern assignment (GOSPA) metric, which is a metric for sets, to graphs. The proposed graph GOSPA metric includes costs associated with node attribute errors for properly assigned nodes, missed and false nodes and edge mismatches between graphs. The computation of this metric is based on finding the optimal assignments between nodes in the two graphs, with the possibility of leaving some of the nodes unassigned. We also propose a lower bound for the metric, which is also a metric for graphs and is computable in polynomial time using linear programming. The metric is first derived for undirected unweighted graphs and it is then extended to directed and weighted graphs. The properties of the metric are demonstrated via simulated and empirical datasets., Comment: Accepted in IEEE Transactions on Signal Processing. The code is available at https://github.com/JinhaoGu/The-graph-GOSPA-metric

This paper proposes a multi-object tracking (MOT) algorithm for traffic monitoring using a drone equipped with optical and thermal cameras. Object detections on the images are obtained using a neural network for each type of camera. The cameras are modelled as direction-of-arrival (DOA) sensors. Each DOA detection follows a von-Mises Fisher distribution, whose mean direction is obtain by projecting a vehicle position on the ground to the camera. We then use the trajectory Poisson multi-Bernoulli mixture filter (TPMBM), which is a Bayesian MOT algorithm, to optimally estimate the set of vehicle trajectories. We have also developed a parameter estimation algorithm for the measurement model. We have tested the accuracy of the resulting TPMBM filter in synthetic and experimental data sets., Comment: accepted in IEEE Transactions on Vehicular Technology

Belief propagation (BP) is a useful probabilistic inference algorithm for efficiently computing approximate marginal probability densities of random variables. However, in its standard form, BP is only applicable to the vector-type random variables with a fixed and known number of vector elements, while certain applications rely on RFSs with an unknown number of vector elements. In this paper, we develop BP rules for factor graphs defined on sequences of RFSs where each RFS has an unknown number of elements, with the intention of deriving novel inference methods for RFSs. Furthermore, we show that vector-type BP is a special case of set-type BP, where each RFS follows the Bernoulli process. To demonstrate the validity of developed set-type BP, we apply it to the PMB filter for SLAM, which naturally leads to new set-type BP-mapping, SLAM, multi-target tracking, and simultaneous localization and tracking filters. Finally, we explore the relationships between the vector-type BP and the proposed set-type BP PMB-SLAM implementations and show a performance gain of the proposed set-type BP PMB-SLAM filter in comparison with the vector-type BP-SLAM filter., Comment: 17 pages, 7 figures

Recently, the implementation of plasmonic nanoantennas has opened new possibilities to investigate the nanoscale dynamics of individual biomolecules in living cell. However, studies have yet been restricted to single molecular species as the narrow wavelength resonance of gold-based nanostructures precludes the simultaneous interrogation of different fluorescently labeled molecules. Here we exploited broadband aluminum-based nanoantennas carved at the apex of near-field probes to resolve nanoscale-dynamic molecular interactions on intact living cell membranes. Through multicolor excitation, we simultaneously recorded fluorescence fluctuations of dual-color labeled transmembrane receptors known to form nanoclusters in living cells. Fluorescence cross-correlation studies revealed transient interactions between individual receptors in regions of ~60 nm. Moreover, the high signal-to-background ratio provided by the antenna illumination allowed us to directly detect fluorescent bursts arising from the passage of individual receptors underneath the antenna. Remarkably, by reducing the illumination volume below the characteristic receptor nanocluster sizes, we resolved molecular diffusion within nanoclusters and distinguished it from nanocluster diffusion. Spatiotemporal characterization of transient interactions between molecules is crucial to understand how they communicate with each other to regulate cell function. Our work demonstrates the potential of broadband photonic antennas to study multi-molecular events and interactions in living cell membranes with unprecedented spatiotemporal resolution.

This paper presents a mathematical formulation to perform temporal parallelisation of continuous-time optimal control problems, which are solved via the Hamilton--Jacobi--Bellman (HJB) equation. We divide the time interval of the control problem into sub-intervals, and define a control problem in each sub-interval, conditioned on the start and end states, leading to conditional value functions for the sub-intervals. By defining an associative operator as the minimisation of the sum of conditional value functions, we obtain the elements and associative operators for a parallel associative scan operation. This allows for solving the optimal control problem on the whole time interval in parallel in logarithmic time complexity in the number of sub-intervals. We derive the HJB-type of backward and forward equations for the conditional value functions and solve them in closed form for linear quadratic problems. We also discuss other numerical methods for computing the conditional value functions and present closed form solutions for selected special cases. The computational advantages of the proposed parallel methods are demonstrated via simulations run on a multi-core central processing unit and a graphics processing unit.

This paper shows that the Poisson multi-Bernoulli mixture (PMBM) density is a multi-target conjugate prior for general target-generated measurement distributions and arbitrary clutter distributions. That is, for this multi-target measurement model and the standard multi-target dynamic model with Poisson birth model, the predicted and filtering densities are PMBMs. We derive the corresponding PMBM filtering recursion. Based on this result, we implement a PMBM filter for point-target measurement models and negative binomial clutter density in which data association hypotheses with high weights are chosen via Gibbs sampling. We also implement an extended target PMBM filter with clutter that is the union of Poisson-distributed clutter and a finite number of independent clutter sources. Simulation results show the benefits of the proposed filters to deal with non-standard clutter., Comment: Matlab code available at https://github.com/Agarciafernandez/MTT and https://github.com/yuhsuansia/Extented-target-PMBM-filter-independent-clutter-sources

This paper develops a general trajectory probability hypothesis density (TPHD) filter, which uses a general density for target-generated measurements and is able to estimate trajectories of coexisting point and extended targets. First, we provide a derivation of this general TPHD filter based on finding the best Poisson posterior approximation by minimizing the Kullback-Leibler divergence, without using probability generating functionals. Second, we adopt an efficient implementation of this filter, where Gaussian densities correspond to point targets and Gamma Gaussian Inverse Wishart densities for extended targets. The L-scan approximation is also proposed as a simplified version to mitigate the huge computational cost. Simulation and experimental results show that the proposed filter is able to classify targets correctly and obtain accurate trajectory estimation.

A novel MIMO homogeneous Super-Twisting Algorithm is proposed in this paper for nonlinear systems with relative degree one, having a time and state-varying uncertain control matrix. The uncertainty is represented by a constant but unknown left matrix factor. Sufficient conditions for stability with full-matrix control gains are established, in contrast to the usual scalar gains. For this a smooth Lyapunov function, based on a passivity interpretation, is used. Moreover, continuous and homogeneous approximations of the classical discontinuous Super-Twisting algorithm are obtained, using a unified analysis method.

In this paper, we propose a Poisson multi-Bernoulli (PMB) filter for extended object tracking (EOT), which directly estimates the set of object trajectories, using belief propagation (BP). The proposed filter propagates a PMB density on the posterior of sets of trajectories through the filtering recursions over time, where the PMB mixture (PMBM) posterior after the update step is approximated as a PMB. The efficient PMB approximation relies on several important theoretical contributions. First, we present a PMBM conjugate prior on the posterior of sets of trajectories for a generalized measurement model, in which each object generates an independent set of measurements. The PMBM density is a conjugate prior in the sense that both the prediction and the update steps preserve the PMBM form of the density. Second, we present a factor graph representation of the joint posterior of the PMBM set of trajectories and association variables for the Poisson spatial measurement model. Importantly, leveraging the PMBM conjugacy and the factor graph formulation enables an elegant treatment on undetected objects via a Poisson point process and efficient inference on sets of trajectories using BP, where the approximate marginal densities in the PMB approximation can be obtained without enumeration of different data association hypotheses. To achieve this, we present a particle-based implementation of the proposed filter, where smoothed trajectory estimates, if desired, can be obtained via single-object particle smoothing methods, and its performance for EOT with ellipsoidal shapes is evaluated in a simulation study., Comment: Accepted for publication in IEEE Transactions on Aerospace and Electronic Systems. MATLAB implementation available at https://github.com/yuhsuansia/Trajectory-PMB-EOT-BP

This paper provides a comparative analysis between the adaptive birth model used in the labelled random finite set literature and the track initiation in the Poisson multi-Bernoulli mixture (PMBM) filter, with point-target models. The PMBM track initiation is obtained via Bayes' rule applied on the predicted PMBM density, and creates one Bernoulli component for each received measurement, representing that this measurement may be clutter or a detection from a new target. Adaptive birth mimics this procedure by creating a Bernoulli component for each measurement using a different rule to determine the probability of existence and a user-defined single-target density. This paper first provides an analysis of the differences that arise in track initiation based on isolated measurements. Then, it shows that adaptive birth underestimates the number of objects present in the surveillance area under common modelling assumptions. Finally, we provide numerical simulations to further illustrate the differences., Comment: Matlab implementations of PMBM filters can be found at https://github.com/Agarciafernandez/MTT and https://github.com/yuhsuansia

This paper presents a general solution for computing the multi-object posterior for sets of trajectories from a sequence of multi-object (unlabelled) filtering densities and a multi-object dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multi-object filters that do not explicitly estimate trajectories. In this paper, we first derive a general multi-trajectory backward smoothing equation based on random finite sets of trajectories. Then we show how to sample sets of trajectories using backward simulation for Poisson multi-Bernoulli filtering densities, and develop a tractable implementation based on ranked assignment. The performance of the resulting multi-trajectory particle smoothers is evaluated in a simulation study, and the results demonstrate that they have superior performance in comparison to several state-of-the-art multi-object filters and smoothers., Comment: Accepted for publication in IEEE Transactions on Signal Processing

This paper proposes a clustering and merging approach for the Poisson multi-Bernoulli mixture (PMBM) filter to lower its computational complexity and make it suitable for multiple target tracking with a high number of targets. We define a measurement-driven clustering algorithm to reduce the data association problem into several subproblems, and we provide the derivation of the resulting clustered PMBM posterior density via Kullback-Leibler divergence minimisation. Furthermore, we investigate different strategies to reduce the number of single target hypotheses by approximating the posterior via merging and inter-track swapping of Bernoulli components. We evaluate the performance of the proposed algorithm on simulated tracking scenarios with more than one thousand targets., Comment: 17 pages, 11 figures, journal paper

Single molecule detection has revolutionised the fields of chemistry and biology by offering powerful ways to study individual molecules under different scenarios. Nanophotonic structures, including plasmonic antennas, significantly overcome the concentration limit at which single molecule events can be observed, enabling their detection at concentrations that are relevant to biological and chemical processes. Although antennas can be fabricated in large arrays, probing dynamic events requires high temporal resolution, which is best achieved by serial antenna interrogation. Unfortunately, this precludes the simultaneous recording from multiple antennas at different sample locations, and is time consuming, resulting in poor statistics and low-throughput data acquisition, abating the true potential of arrays. Here we exploit arrays of antenna-in-box nanostructures in combination with sCMOS readout to interrogate nanoscale volumes from 225 antennas simultaneously. Recording at 1 kHz allowed multiplexed dynamic measurements from 50 nanoantennas simultaneously with a temporal resolution dictated by the camera framerate and the photons emitted per molecule during a single passage. We demonstrate the capability for high-throughput arrayed detection of single molecule dynamics at the nanoscale in the membrane of living cells, and determine the axial location of membrane molecular components with 1 nm accuracy and temporal resolution below 1 ms., Comment: 19 pages, 4 figures

This paper considers the problem of robust iterative Bayesian smoothing in nonlinear state-space models with additive noise using Gaussian approximations. Iterative methods are known to improve smoothed estimates but are not guaranteed to converge, motivating the development of more robust versions of the algorithms. The aim of this article is to present Levenberg-Marquardt (LM) and line-search extensions of the classical iterated extended Kalman smoother (IEKS) as well as the iterated posterior linearisation smoother (IPLS). The IEKS has previously been shown to be equivalent to the Gauss-Newton (GN) method. We derive a similar GN interpretation for the IPLS. Furthermore, we show that an LM extension for both iterative methods can be achieved with a simple modification of the smoothing iterations, enabling algorithms with efficient implementations. Our numerical experiments show the importance of robust methods, in particular for the IEKS-based smoothers. The computationally expensive IPLS-based smoothers are naturally robust but can still benefit from further regularisation.

This paper proposes a Poisson multi-Bernoulli mixture (PMBM) filter on the space of sets of tree trajectories for multiple target tracking with spawning targets. A tree trajectory contains all trajectory information of a target and its descendants, which appear due to the spawning process. Each tree contains a set of branches, where each branch has trajectory information of a target or one of the descendants and its genealogy. For the standard dynamic and measurement models with multi-Bernoulli spawning, the posterior is a PMBM density, with each Bernoulli having information on a potential tree trajectory. To enable a computationally efficient implementation, we derive an approximate PMBM filter in which each Bernoulli tree trajectory has multi-Bernoulli branches, obtained by minimising the Kullback-Leibler divergence. The resulting filter improves tracking performance of state-of-the-art algorithms in a simulated scenario., Comment: Matlab code can be found at https://github.com/Agarciafernandez

This paper proposes a metric for sets of trajectories to evaluate multi-object tracking algorithms that includes time-weighted costs for localisation errors of properly detected targets, for false targets, missed targets and track switches. The proposed metric extends the metric in [1] by including weights to the costs associated to different time steps. The time-weighted costs increase the flexibility of the metric [1] to fit more applications and user preferences. We first introduce a metric based on multi-dimensional assignments, and then its linear programming relaxation, which is computable in polynomial time and is also a metric. The metrics can also be extended to metrics on random finite sets of trajectories to evaluate and rank algorithms across different scenarios, each with a ground truth set of trajectories., Comment: Matlab code available at https://github.com/Agarciafernandez/MTT (Trajectory metric folder)

This paper presents an analysis on sensor management using a cost function based on a multi-target metric, in particular, the optimal subpattern-assignment (OSPA) metric, the unnormalised OSPA (UOSPA) metric and the generalised OSPA (GOSPA) metric (\alpha=2). We consider the problem of managing an array of sensors, where each sensor is able to observe a region of the surveillance area, not covered by other sensors, with a given sensing cost. We look at the case in which there are far-away, independent potential targets, at maximum one per sensor region. In this set-up, the optimal action using GOSPA is taken for each sensor independently, as we may expect. On the contrary, as a consequence of the spooky effect at a distance in optimal OSPA/UOSPA estimation, the optimal actions for different sensors using OSPA and UOSPA are entangled., Comment: This paper received the 2nd best paper award at the 24th International Conference on Information Fusion. A presentation on the GOSPA metric can be found at https://www.youtube.com/watch?v=M79GTTytvCM

Network intrusion detection systems (NIDS) are one of many solutions that make up a computer security system. Several machine learning-based NIDS have been proposed in recent years, but most of them were developed and evaluated under the assumption that the training context is similar to the test context. In real networks, this assumption is false, given the emergence of new attacks and variants of known attacks. To deal with this reality, the open set recognition field, which is the most general task of recognizing classes not seen during training in any domain, began to gain importance in NIDS research. Yet, existing solutions are often bounded to high temporal complexities and performance bottlenecks. In this work, we propose an algorithm to be used in NIDS that performs open set recognition. Our proposal is an adaptation of the single-class Energy-based Flow Classifier (EFC), which proved to be an algorithm with strong generalization capability and low computational cost. The new version of EFC correctly classifies not only known attacks, but also unknown ones, and differs from other proposals from the literature by presenting a single layer with low temporal complexity. Our proposal was evaluated against well-established multi-class algorithms and as an open set classifier. It proved to be an accurate classifier in both evaluations, similar to the state of the art. As a conclusion of our work, we consider EFC a promising algorithm to be used in NIDS for its high performance and applicability in real networks.

This paper derives the optimal Bayesian processing of an out-of-sequence (OOS) set of measurements in continuous-time for multiple target tracking. We consider a multi-target system modelled in continuous time that is discretised at the time steps when we receive the measurements, which are distributed according to the standard point target model. All information about this system at the sampled time steps is provided by the posterior density on the set of all trajectories. This density can be computed via the continuous-discrete trajectory Poisson multi-Bernoulli mixture (TPMBM) filter. When we receive an OOS measurement, the optimal Bayesian processing performs a retrodiction step that adds trajectory information at the OOS measurement time stamp followed by an update step. After the OOS measurement update, the posterior remains in TPMBM form. We also provide a computationally lighter alternative based on a trajectory Poisson multi-Bernoulli filter. The effectiveness of the two approaches to handle OOS measurements is evaluated via simulations., Comment: Matlab files can be found at https://github.com/Agarciafernandez/MTT