Deep reinforcement learning (DRL) has been applied in financial portfolio management to improve returns in changing market conditions. However, unlike most fields where DRL is widely used, the stock market is more volatile and dynamic as it is affected by several factors such as global events and investor sentiment. Therefore, it remains a challenge to construct a DRL-based portfolio management framework with strong return capability, stable training, and generalization ability. This study introduces a new framework utilizing the Memory Instance Gated Transformer (MIGT) for effective portfolio management. By incorporating a novel Gated Instance Attention module, which combines a transformer variant, instance normalization, and a Lite Gate Unit, our approach aims to maximize investment returns while ensuring the learning process's stability and reducing outlier impacts. Tested on the Dow Jones Industrial Average 30, our framework's performance is evaluated against fifteen other strategies using key financial metrics like the cumulative return and risk-return ratios (Sharpe, Sortino, and Omega ratios). The results highlight MIGT's advantage, showcasing at least a 9.75% improvement in cumulative returns and a minimum 2.36% increase in risk-return ratios over competing strategies, marking a significant advancement in DRL for portfolio management.

This paper presents the extension of the track-before-detect based Information Exchange Multi-Bernoulli (IEMB) filter for estimating the set of alive trajectories. We present the filtering recursion, which propagates a multi-Bernoulli density for the set of alive trajectories, and propose a Gaussian implementation based upon the Iterated Posterior Linearisation filter (IPLF). We present simulation results which demonstrate the superior tracking performance of the Trajectory IEMB when compared to a sequential track-building approach using the IEMB filter for sets of targets.

This paper introduces the Stone Soup Astrodynamics Plugin: a plugin for the open-source tracking and state estimation framework to deal with astrodynamics problems. Stone Soup has provided the target tracking and state estimation community with an open, easy-to-deploy framework to develop and assess the performance of different types of trackers. Here, we detail a Stone Soup plugin for astrodynamics which contains useful functions and tools for state estimation in the orbital domain. The plugin also contains wrappers and integrations with popular packages for space domain problems, the European Space Agency's GODOT framework and the Orekit framework. The plugin adopts Stone Soup's goals of testable, trustworthy code, and contains user documentation and use-case examples. In introducing this plugin, we hope to encourage additional adoption and further contributions to the toolkit, as well as invite feedback for future development.

The Rauch-Tung-Striebel (RTS) smoother is an algorithm for computing state estimates in time series using noisy measurements from all time steps. The RTS smoother works by first filtering the state when measurements arrive and then using a backward pass to obtain the smoothed state estimates for all time steps that use measurement information from all time steps as well. The backward pass goes through all time steps for which a filtering estimate were obtained in backward order. We propose a smoother that does the backward pass using only a fraction of the time steps and provides the same results as the conventional RTS smoother for these time steps. This reduces computational complexity and required memory significantly as only data for these interesting time steps need to be stored. We also propose the extension of the reduced sampling-rate smoother for non-linear systems. We show an example application involving position estimation using a state space model that uses a high filtering rate, but where it is suitable to present the final smoothed route with a considerably lower rate. In a second example, we show how the reduced rate smoother works in a nonlinear case.

This paper presents an extended target tracking method to track trains using Distributed Acoustic Sensing (DAS) data. The problem is approached using a measurement likelihood based on a Set of Points on a Rigid Body (SPRB) model applied to a clustered version of the Poisson Multi-Bernoulli Mixture filter. The method efficiently handles asymmetric noise within the set of measurements returned by each train, and proposes a solution to merged measurements appearing at crossings. We use experimental data obtained from trains to show that the proposed algorithm has lower localisation and false target error, leading to better performance in terms generalized optimal sub-pattern assignment (GOSPA) metric.

The Kalman Filter (KF) is a classical algorithm that was developed for estimating a state that evolves in time based on noisy measurements by assuming linear state transition and measurements models. There exist various KF extensions for non-linear situations, but they are not exact and provide different linearization errors. The Iterated Posterior Linearization Filter (IPLF) does the linearizations iteratively to achieve better linearizations. However, it is possible that some measurements cannot be well linearized using the current knowledge, but their linearization may be better after more measurements are available. Thus, we propose an algorithm that can store the older state elements and measurements when their linearization error is high. The resulting algorithm, the Stacked Iterated Posterior Linearization Filter (S-IPLF), is based on linear dynamic models and uses information from multiple time instances to make the linearization of the measurement function. Results show that the proposed algorithm outperforms traditional KF extensions when some of the measurements cannot be well linearized with the current knowledge, but can be when future information is available.

This paper presents a multi-target metric driven approach to sensor management for Bernoulli filtering, in which at most one target of interest is present. The metric used is the generalised optimal sub pattern assignment (GOSPA) metric. We consider the problem of having an agile sensor operating in a surveillance area, tracking objects as they appear from a target birth distribution. Only one target of interest can exist at any given time-step and its single-target density is Gaussian. In this scenario, we have a grid of sensors that we can select from, one at a time using myopic planning. We evaluate the proposed sensor management algorithm via simulations.

This paper presents an efficient implementation of the trajectory Poisson multi-Bernoulli (PMB) filter for multiple extended object tracking (EOT), which directly estimates a set of object trajectories. The trajectory PMB filter propagates a PMB density on the posterior of sets of trajectories through the filtering recursions over time, where the multi-Bernoulli (MB) mixture in the PMB mixture (PMBM) posterior after each update step is approximated as a single MB. The efficient MB approximation is achieved by first running a blocked Gibbs sampler on the joint posterior of the set of trajectories and the measurement association variables. The single-object measurement model is assumed to be a Poisson point process which enables us to parallelize the sampling across all objects and association variables, respectively. Then, samples of object states are utilized to form the approximate MB density via Kullback-Leibler divergence minimization. Simulation results on EOT with known and constant elliptical shapes show that the TPMB implementation using blocked Gibbs sampling outperforms the state-of-the-art TPMB implementation using loopy belief propagation with significantly reduced runtime.

Under the standard multiple target tracking models and a Poisson point process birth model, the Poisson multi-Bernoulli mixture (PMBM) filter provides the closed-form recursion to computing the posterior density over the set of targets. Without approximations, the PMBM computational complexity rapidly rises in time due to the increasing number of data association hypotheses. This paper presents innovative strategies for merging Bernoulli components for the same potential target reducing the number of single-target hypotheses in the PMBM filter, aiming to lower its computational complexity while keeping its performance high. We use several measures to compute the similarity between different Bernoulli components. Simulation results show that the proposed algorithms show performance close to the PMBM filter without Bernoulli merging, as measured by the generalized optimal sub-pattern assignment (GOSPA) metric, with a significantly reduced execution time.

This paper presents the continuous-discrete trajectory probability hypothesis density (CD-TPHD) and the continuous-discrete trajectory cardinality PHD (CD-TCPHD) filter. We consider continuous-time models for target appearance, dynamics and disappearance, which are discretised to obtain the corresponding continuous-discrete models. The CD-TPHD filter propagates a Poisson point process approximation to the posterior (multi-trajectory) density over the set of alive trajectories sampled at the time instants when the measurements have been taken. The CD-TCPHD filter proceeds analogously but propagating a density on an independent and identically distributed (IID) cluster process. An important, novel feature of these filters is that they can infer the time of appearance and the state at appearance time of the trajectories in continuous time, not being constrained to discretised time steps.

This paper presents two multi-Bernoulli filters on sets of trajectories for multiple target tracking. The first filter provides a multi-Bernoulli approximation of the posterior density over the set of alive trajectories at the current time step. The second filter provides a multi-Bernoulli approximation of the posterior density over the set of all trajectories (alive and dead) up to the current time. We also explain the Gaussian implementation of the filters and compare them with other multiple target tracking algorithms in a simulated scenario.

In this paper we introduce spatiotemporal constraints for trajectories, i.e., restrictions that the trajectory must be in some part of the state space (spatial constraint) at some point in time (temporal constraint). Spatiotemporal contraints on trajectories can be used to answer a range of important questions, including, e.g., “where did the person that were in area A at time t, go afterwards?”. We discuss how multiple constraints can be combined into sets of constraints, and we then apply sets of constraints to set of trajectories densities, specifically Poisson Multi-Bernoulli Mixture (PMBM) densities. For Poisson target birth, the exact posterior density is PMBM for both point targets and extended targets. In the paper we show that if the unconstrained set of trajectories density is PMBM, then the constrained density is also PMBM. Examples of constrained trajectory densities motivate and illustrate the key results.

This paper presents a solution for recovering full trajectory information, via the calculation of the posterior of the set of trajectories, from a sequence of multitarget (unlabelled) filtering densities and the multitarget dynamic model. Importantly, the proposed solution opens an avenue of trajectory estimation possibilities for multitarget filters that do not explicitly estimate trajectories. In this paper, we first derive a general multitrajectory forward-backward smoothing equation based on sets of trajectories and the random finite set framework. Then we show how to sample sets of trajectories using backward simulation when the multitarget filtering densities are multi-Bernoulli processes. The proposed approach is demonstrated in a simulation study.

This paper presents the probability hypothesis density (PHD) filter for sets of trajectories: the trajectory probability density (TPHD) filter. The TPHD filter is capable of estimating trajectories in a principled way without requiring to evaluate all measurement-to-target association hypotheses. The TPHD filter is based on recursively obtaining the best Poisson approximation to the multitrajectory filtering density in the sense of minimising the Kullback-Leibler divergence. We also propose a Gaussian mixture implementation of the TPHD recursion. Finally, we include simulation results to show the performance of the proposed algorithm.

The Poisson multi-Bernoulli mixture (PMBM) is an unlabelled multi-target distribution for which the prediction and update are closed. It has a Poisson birth process, and new Bernoulli components are generated on each new measurement as a part of the Bayesian measurement update. The PMBM filter is similar to the multiple hypothesis tracker (MHT), but seemingly does not provide explicit continuity between time steps. This paper considers a recently developed formulation of the multi-target tracking problem as a random finite set (RFS) of trajectories, and derives two trajectory RFS filters, called PMBM trackers. The PMBM trackers efficiently estimate the set of trajectories, and share hypothesis structure with the PMBM filter. By showing that the prediction and update in the PMBM filter can be viewed as an efficient method for calculating the time marginals of the RFS of trajectories, continuity in the same sense as MHT is established for the PMBM filter.

This paper proposes an efficient implementation of the Poisson multi-Bernoulli mixture (PMBM) trajectory filter. The proposed implementation performs track-oriented N-scan pruning to limit complexity, and uses dual decomposition to solve the involved multi-frame assignment problem. In contrast to the existing PMBM filter for sets of targets, the PMBM trajectory filter is based on sets of trajectories which ensures that track continuity is formally maintained. The resulting filter is an efficient and scalable approximation to a Bayes optimal multi-target tracking algorithm, and its performance is compared, in a simulation study, to the PMBM target filter, and the delta generalized labelled multi-Bernoulli filter, in terms of state/trajectory estimation error and computational time.

This paper presents the generalized optimal sub-pattern assignment (GOSPA) metric on the space of finite sets of targets. Compared to the well-established optimal sub-pattern assignment (OSPA) metric, GOSPA is not normalised by the cardinality of the largest set and it penalizes cardinality errors differently, which enables us to express it as an optimisation over assignments instead of permutations. An important consequence of this is that GOSPA allows us to penalize localization errors for detected targets and the errors due to missed and false targets, as indicated by traditional multiple target tracking (MTT) performance measures, in a sound manner. In addition, we extend the GOSPA metric to the space of random finite sets, which is important to evaluate MTT algorithms via simulations in a rigorous way.

Particle filters are a widely used tool to perform Bayesian filtering under nonlinear dynamic and measurement models or non-Gaussian distributions. However, the performance of particle filters plummets when dealing with high-dimensional state spaces. In this paper, we propose a method that makes use of multiple particle filtering to circumvent this difficulty. Multiple particle filters partition the state space and run an individual particle filter for every component. Each particle filter shares information with the rest of the filters to account for the influence of the complete state in the observations collected by sensors. The method considered in this paper uses auxiliary filtering within the MPF framework, outperforming previous algorithms in the literature. The performance of the considered algorithm is tested in a multiple target tracking scenario, with fixed and known number of targets, using a sensor network with a nonlinear measurement model.

In this paper, we evaluate the performance of labelled and unlabelled multi-Bernoulli conjugate priors for multi-target filtering. Filters are compared in two different scenarios with performance assessed using the generalised optimal sub-pattern assignment (GOSPA) metric. The first scenario under consideration is tracking of well-spaced targets. The second scenario is more challenging and considers targets in close proximity, for which filters may suffer from coalescence. We analyse various aspects of the filters in these two scenarios. Though all filters have pros and cons, the Poisson multi-Bernoulli filters arguably provide the best overall performance concerning GOSPA and computational time.