Particle filters are essential for state estimation in non-linear and non-Gaussian systems, with performance hinging on effective proposal distributions. This paper presents the implementation of Kalman Filter and No-U-Turn Sampler (NUTS) proposals within the Stone Soup Python framework. The Kalman Filter proposal offers computational efficiency for structured systems, while NUTS enables robust exploration of complex, highdimensional distributions. Benchmark evaluations demonstrate the complementary strengths of these methods, enhancing Stone Soup's capabilities for diverse state estimation challenges.

Markov chain Monte Carlo (MCMC) methods are a powerful but computationally expensive way of performing nonparametric Bayesian inference. MCMC proposals which utilise gradients, such as Hamiltonian Monte Carlo (HMC), can better explore the parameter space of interest if the additional hyperparameters are chosen well. The No-U-Turn Sampler (NUTS) is a variant of HMC which is extremely effective at selecting these hyper-parameters but is slow to run and is not suited to GPU architectures. An alternative to NUTS, Change in the Estimator of the Expected Square HMC (ChEES-HMC) was shown not only to run faster than NUTS on GPU but also sample from posteriors more efficiently. Sequential Monte Carlo (SMC) samplers are another sampling method which instead output weighted samples from the posterior. They are very amenable to parallelisation and therefore being run on GPUs while having additional flexibility in their choice of proposal over MCMC. We incorporate (ChEES-HMC) as a proposal into SMC samplers and demonstrate competitive but faster performance than NUTS on a number of tasks.

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.

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.

In this paper, we discuss the derivations, implementations and performance of target tracking algorithms for a single-target single-sensor system estimating the state, covariance and existence probability of a target. Given the target exists, we simulate measurements of the target with a given probability of detection, along with false measurements (clutter) parametrised by a clutter density. We evaluate the performance of the algorithms by computing the area under Receiver Operating Characteristic (ROC) curves against a range of clutter density values. We give particular attention to the effectiveness of correctly inferring the presence or absence of the target. We select the Integrated Probabilistic Data Association Filter (IPDAF) and the Integrated Expected Likelihood Particle Filter (IELPF) algorithms, with the IELPF implementing a near-optimal proposal which uses the current scan of measurements as well as a prior proposal for comparison. Simulation results indicate the performance of the IPDAF exceeds that of the preexisting particle filter implementing a prior proposal, but a novel particle filter using a near-optimal proposal and a modest number of particles outperforms the IPDAF.

In this paper we describe a Sequential Monte Carlo (SMC) sampler that performs joint tracking and destination estimation of a target traveling along a known road network, as its journey progresses. The destination estimation is based on a simplistic model of driver intent, which assumes no prior knowledge of the history of visited destinations. The proposed algorithm is capable of refining the distribution of destinations that can be inferred from an incoming stream of position estimates. We compare the performance achieved by the proposed algorithm with a mainstay Particle Filter, demonstrating how the later suffers greatly from sample impoverishment, therefore necessitating an ever increasing number of particles as the number of possible destinations increases, while showcasing that the issue is significantly mitigated by the proposed SMC Sampler.

Pixel-based image alignment has always struggled to simultaneously reject outliers, avoid local minima and run quickly. There are many robust cost functions that perform well in terms of rejecting outliers, but they can yield unstable results during long image sequences as a result of their inability to adjust to changes in image content. In this paper, we propose a parameterised student-t cost function that can interpolate between two cost functions that are amongst the most widely used ones in image alignment problems, the L2 norm (quadratic function) and the Cauchy-Lorentzian function. We also propose a parameter estimation method that helps to find optimal parameters for the proposed cost function for a video. Experiments prove that the proposed approach can estimate the alignment variable accurately relative to the existing cost functions without demanding a higher computational cost.

Ahstract-This paper considers the problem of tracking a manoeuvring target when some of the measurements are delayed by the time taken to propagate through some medium. We are especially interested in bearing-only measurements, since it is possible to extract range information by fusing measurements which have negligible propagation delay (such as from electrooptical sensors) and measurements which have a propagation delay proportional to the range to the target (such as from acoustic sensors). This requires us to handle measurements which appear out of sequence, and with emission times unknown to the tracker. Unlike previous approaches, a particle filter is used, which handles out-of-sequence measurements by storing a history of hypothesised target states and measurement emission times for each particle. This allows new target states and times to be inserted into the trajectory of each target by interpolating between adjacent states in the history.

Manifold embedding techniques have properties that render them attractive candidates to learn a compact and general representation of a three dimensional spatial object. In turn this representation can be used for object recognition through classification. This paper presents a comparative study of several supervised spectral embedding techniques and their relationship with the feature space used to describe the exemplars which act as inputs to an embedding procedure. By concentrating on this aspect, we are able to highlight preferential combinations between feature description and embedding, and we formulate recommendations on the use of such methods for fusing multiple views of an object to recognize it under variable poses.

This paper compares the tracking performance that can be achieved when using a nonlinear drag model for a helicopter, a constant drag motion model, and a baseline constant acceleration model. A particle filter is used for state estimation to address problems associated with nonlinear drag and nonlinear measurements of helicopter pose. We demonstrate that the inclusion of this nonlinear kinematic effect provides improved tracking performance for a manoeuvring target.

This paper proposes an improvement to FastSLAM. The approach is applicable when the dynamic model describing the motion of the camera has linear sub-structure. The core novelty of the proposed algorithm is to separate the consideration of the camera's dynamic model into two sub-models without constraining the two sub-models to have independent noise processes. In contrast to commonly-used FastSLAM algorithms, which use a particle filter to consider both these sub-models, a particle filter is used for one sub-model and a Kalman filter for the other. This tactic is Rao-Blackwellisation and is the same as that which underpins the development of FastSLAM, but where the focus was only on exploiting near-linear sub-structure related to the state of the landmarks. Comparisons with Unscented FastSLAM 2.0 indicate that the new approach improves estimation accuracy. Comparisons with cutting-edge SLAM algorithms also reflect the competitive nature of this approach as a solution to navigation problems. Future work will improve the processing of features and consider multi-sensor data input.

An assignment problem is considered with the constraint that the same hypothesis cannot be applied to more than one object. We desire efficiency without approximation. Multiple target tracking methods such as the joint probabilistic association filter (JPDAF) motivate us. Methods of solving this assignment problem involving enumerating all possible joint assignments is infeasible except for small problems. A recent approach circumvents this combinatorial explosion by representing the structure of the target hypotheses in a `net' which exploits redundancy in an ordered list of objects us to describe the problem. Here, we generalize this approach to process the objects in a tree structure this exploits conditional independence between subsets of the objects. This gives a substantial computational saving and allows us to consider scenarios which were previously impractical. In particular, we show the feasibility of using an exact JPDAF implementation to track 400 targets

This paper describes the integration of a particle filter and a continuous version of the transferable belief model. The output from the particle filter is used as input to the transferable belief model. The transferable belief model's continuous nature allows for the prior knowledge over the classification space to be incorporated within the system. Classification of objects is demonstrated within the paper and compared to the more classical Bayesian classification routine. This is the first time that such an approach has been taken to jointly classify and track targets. We show that there is a great deal of flexibility built into the continuous transferable belief model and in our comparison with a Bayesian classifier, we show that our novel approach offers a more robust classification output that is less influenced by noise