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We propose a fully Bayesian approach to wideband, or broadband, direction-of-arrival (DoA) estimation and signal detection. Unlike previous works in wideband DoA estimation and detection, where the signals were modeled in the time-frequency domain, we directly model the time-domain representation and treat the non-causal part of the source signal as latent variables. Furthermore, our Bayesian model allows for closed-form marginalization of the latent source signals by leveraging conjugacy. To further speed up computation, we exploit the sparse ``stripe matrix structure'' of the considered system, which stems from the circulant matrix representation of linear time-invariant (LTI) systems. This drastically reduces the time complexity of computing the likelihood from $\mathcal{O}(N^3 k^3)$ to $\mathcal{O}(N k^3)$, where $N$ is the number of samples received by the array and $k$ is the number of sources. These computational improvements allow for efficient posterior inference through reversible jump Markov chain Monte Carlo (RJMCMC). We use the non-reversible extension of RJMCMC (NRJMCMC), which often achieves lower autocorrelation and faster convergence than the conventional reversible variant. Detection, estimation, and reconstruction of the latent source signals can then all be performed in a fully Bayesian manner through the samples drawn using NRJMCMC. We evaluate the detection performance of the procedure by comparing against generalized likelihood ratio testing (GLRT) and information criteria.

Sequential Monte Carlo Squared (SMC$^2$) is a Bayesian method which can infer the states and parameters of non-linear, non-Gaussian state-space models. The standard random-walk proposal in SMC$^2$ faces challenges, particularly with high-dimensional parameter spaces. This study outlines a novel approach by harnessing first-order gradients derived from a Common Random Numbers - Particle Filter (CRN-PF) using PyTorch. The resulting gradients can be leveraged within a Langevin proposal without accept/reject. Including Langevin dynamics within the proposal can result in a higher effective sample size and more accurate parameter estimates when compared with the random-walk. The resulting algorithm is parallelized on distributed memory using Message Passing Interface (MPI) and runs in $\mathcal{O}(\log_2N)$ time complexity. Utilizing 64 computational cores we obtain a 51x speed-up when compared to a single core. A GitHub link is given which provides access to the code., Comment: 8 pages, 3 images. Accepted to 2024 IEEE International Conference on Multisensor Fusion and Integration (MFI 2024). https://mfi2024.org/. arXiv admin note: text overlap with arXiv:2311.12973

Calibrating statistical models using Bayesian inference often requires both accurate and timely estimates of parameters of interest. Particle Markov Chain Monte Carlo (p-MCMC) and Sequential Monte Carlo Squared (SMC$^2$) are two methods that use an unbiased estimate of the log-likelihood obtained from a particle filter (PF) to evaluate the target distribution. P-MCMC constructs a single Markov chain which is sequential by nature so cannot be readily parallelized using Distributed Memory (DM) architectures. This is in contrast to SMC$^2$ which includes processes, such as importance sampling, that are described as \textit{embarrassingly parallel}. However, difficulties arise when attempting to parallelize resampling. None-the-less, the choice of backward kernel, recycling scheme and compatibility with DM architectures makes SMC$^2$ an attractive option when compared with p-MCMC. In this paper, we present an SMC$^2$ framework that includes the following features: an optimal (in terms of time complexity) $\mathcal{O}(\log_2N)$ parallelization for DM architectures, an approximately optimal (in terms of accuracy) backward kernel, and an efficient recycling scheme. On a cluster of $128$ DM processors, the results on a biomedical application show that SMC$^2$ achieves up to a $70\times$ speed-up vs its sequential implementation. It is also more accurate and roughly $54\times$ faster than p-MCMC. A GitHub link is given which provides access to the code., Comment: 8 pages, 6 figures, accepted to Combined SDF and MFI Conference 2023 conference

This paper is concerned with sensor management for target search and track using the generalised optimal subpattern assignment (GOSPA) metric. Utilising the GOSPA metric to predict future system performance is computationally challenging, because of the need to account for uncertainties within the scenario, notably the number of targets, the locations of targets, and the measurements generated by the targets subsequent to performing sensing actions. In this paper, efficient sample-based techniques are developed to calculate the predicted mean square GOSPA metric. These techniques allow for missed detections and false alarms, and thereby enable the metric to be exploited in scenarios more complex than those previously considered. Furthermore, the GOSPA methodology is extended to perform non-myopic (i.e. multi-step) sensor management via the development of a Bellman-type recursion that optimises a conditional GOSPA-based metric. Simulations for scenarios with missed detections, false alarms, and planning horizons of up to three time steps demonstrate the approach, in particular showing that optimal plans align with an intuitive understanding of how taking into account the opportunity to make future observations should influence the current action. It is concluded that the GOSPA-based, non-myopic search and track algorithm offers a powerful mechanism for sensor management., Comment: The paper has been accepted for publication in IEEE Transactions on Aerospace and Electronic Systems, DOI 10.1109/TAES.2023.3324908

Bayesian Decision Trees (DTs) are generally considered a more advanced and accurate model than a regular Decision Tree (DT) because they can handle complex and uncertain data. Existing work on Bayesian DTs uses Markov Chain Monte Carlo (MCMC) with an accept-reject mechanism and sample using naive proposals to proceed to the next iteration, which can be slow because of the burn-in time needed. We can reduce the burn-in period by proposing a more sophisticated way of sampling or by designing a different numerical Bayesian approach. In this paper, we propose a replacement of the MCMC with an inherently parallel algorithm, the Sequential Monte Carlo (SMC), and a more effective sampling strategy inspired by the Evolutionary Algorithms (EA). Experiments show that SMC combined with the EA can produce more accurate results compared to MCMC in 100 times fewer iterations., Comment: arXiv admin note: text overlap with arXiv:2301.09090

This paper explores the effect of three-dimensional rotations on two-qubit Bell states and proposes a Bayesian method for the estimation of the parameters of the rotation. We use a particle filter to estimate the parameters of the rotation from a sequence of Bell state measurements and we demonstrate that the resultant improvement over the optimal single qubit case approaches the $\sqrt{2}$ factor that is consistent with the Heisenberg limit. We also demonstrate how the accuracy of the estimation method is a function of the purity of mixed states., Comment: 9 pages, 5 figures

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Existing work on Bayesian decision trees uses MCMC. Unfortunately, this can be slow, especially when considering large volumes of data. It is hard to parallelise the accept-reject component of the MCMC. None-the-less, we propose two methods for exploiting parallelism in the MCMC: in the first, we replace the MCMC with another numerical Bayesian approach, the Sequential Monte Carlo (SMC) sampler, which has the appealing property that it is an inherently parallel algorithm; in the second, we consider data partitioning. Both methods use multi-core processing with a HighPerformance Computing (HPC) resource. We test the two methods in various study settings to determine which method is the most beneficial for each test case. Experiments show that data partitioning has limited utility in the settings we consider and that the use of the SMC sampler can improve run-time (compared to the sequential implementation) by up to a factor of 343.

Imaging methods based on array signal processing often require a fixed propagation speed of the medium, or speed of sound (SoS) for methods based on acoustic signals. The resolution of the images formed using these methods is strongly affected by the assumed SoS, which, due to multipath, nonlinear propagation, and non-uniform mediums, is challenging at best to select. In this letter, we propose a Bayesian approach to marginalize the influence of the SoS on beamformers for imaging. We adapt Bayesian direction-of-arrival estimation to an imaging setting and integrate a popular minimum variance beamformer over the posterior of the SoS. To solve the Bayesian integral efficiently, we use numerical Gauss quadrature. We apply our beamforming approach to shallow water sonar imaging where multipath and nonlinear propagation is abundant. We compare against the minimum variance distortionless response (MVDR) beamformer and demonstrate that its Bayesian counterpart achieves improved range and azimuthal resolution while effectively suppressing multipath artifacts.

Social media's growing popularity raises concerns around children's online safety. Interactions between minors and adults with predatory intentions is a particularly grave concern. Research into online sexual grooming has often relied on domain experts to manually annotate conversations, limiting both scale and scope. In this work, we test how well-automated methods can detect conversational behaviors and replace an expert human annotator. Informed by psychological theories of online grooming, we label $6772$ chat messages sent by child-sex offenders with one of eleven predatory behaviors. We train bag-of-words and natural language inference models to classify each behavior, and show that the best performing models classify behaviors in a manner that is consistent, but not on-par, with human annotation.

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

State-space models have been widely used to model the dynamics of communicable diseases in populations of interest by fitting to time-series data. Particle filters have enabled these models to incorporate stochasticity and so can better reflect the true nature of population behaviours. Relevant parameters such as the spread of the disease, $R_t$, and recovery rates can be inferred using Particle MCMC. The standard method uses a Metropolis-Hastings random-walk proposal which can struggle to reach the stationary distribution in a reasonable time when there are multiple parameters. In this paper we obtain full Bayesian parameter estimations using gradient information and the No U-Turn Sampler (NUTS) when proposing new parameters of stochastic non-linear Susceptible-Exposed-Infected-Recovered (SEIR) and SIR models. Although NUTS makes more than one target evaluation per iteration, we show that it can provide more accurate estimates in a shorter run time than Metropolis-Hastings., Comment: FUSION 2022: 25th International Conference on Information Fusion (FUSION 2022), 8 Pages, 16 images

This paper proposes a position fixing method for autonomous navigation using partial gravity gradient solutions from cold atom interferometers. Cold atom quantum sensors can provide ultra-precise measurements of inertial quantities, such as acceleration and rotation rates. However, we investigate the use of pairs of cold atom interferometers to measure the local gravity gradient and to provide position information by referencing these measurements against a suitable database. Simulating the motion of a vehicle, we use partial gravity gradient measurements to reduce the positional drift associated with inertial navigation systems. Using standard open source global gravity databases, we show stable navigation solutions for trajectories of over 1000km., Comment: 10 pages, 6 figures

Quantum state estimation, based on the numerical integration of stochastic master equations (SMEs), provides estimates for the evolution of quantum systems subject to continuous weak measurements. The approach is similar to classical state estimation methods in that the quantum trajectories produced by solving the SME are conditioned on continuous classical measurement signals. In this paper, we explore the use of classical state estimation for a candidate quantum system, one based on an experimentally realisable system: a material object undergoing continuous feedback cooling in an optical trap. In particular, we demonstrate that classical tracking methods based on particle filters can be used to track quantum states, and are particularly useful for higher temperature regimes where quantum state estimation becomes computationally demanding., Comment: 8 pages, 5 figures. Conference paper

The emergence of the novel coronavirus (COVID-19) has generated a need to quickly and accurately assemble up-to-date information related to its spread. While it is possible to use deaths to provide a reliable information feed, the latency of data derived from deaths is significant. Confirmed cases derived from positive test results potentially provide a lower latency data feed. However, the sampling of those tested varies with time and the reason for testing is often not recorded. Hospital admissions typically occur around 1-2 weeks after infection and can be considered out of date in relation to the time of initial infection. The extent to which these issues are problematic is likely to vary over time and between countries. We use a machine learning algorithm for natural language processing, trained in multiple languages, to identify symptomatic individuals derived from social media and, in particular Twitter, in real-time. We then use an extended SEIRD epidemiological model to fuse combinations of low-latency feeds, including the symptomatic counts from Twitter, with death data to estimate parameters of the model and nowcast the number of people in each compartment. The model is implemented in the probabilistic programming language Stan and uses a bespoke numerical integrator. We present results showing that using specific low-latency data feeds along with death data provides more consistent and accurate forecasts of COVID-19 related deaths than using death data alone., Comment: This research was presented at the Joint Statistical Meetings (JSM) 2021: Statistics, Data, and the Stories They Tell and subsequently published as part of the proceedings. 13 pages, 4 tables, 4 images

It has been widely documented that the sampling and resampling steps in particle filters cannot be differentiated. The {\itshape reparameterisation trick} was introduced to allow the sampling step to be reformulated into a differentiable function. We extend the {\itshape reparameterisation trick} to include the stochastic input to resampling therefore limiting the discontinuities in the gradient calculation after this step. Knowing the gradients of the prior and likelihood allows us to run particle Markov Chain Monte Carlo (p-MCMC) and use the No-U-Turn Sampler (NUTS) as the proposal when estimating parameters. We compare the Metropolis-adjusted Langevin algorithm (MALA), Hamiltonian Monte Carlo with different number of steps and NUTS. We consider two state-space models and show that NUTS improves the mixing of the Markov chain and can produce more accurate results in less computational time., Comment: 35 pages, 10 figures

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

Markov Chain Monte Carlo (MCMC) is a powerful method for drawing samples from non-standard probability distributions and is utilized across many fields and disciplines. Methods such as Metropolis-Adjusted Langevin (MALA) and Hamiltonian Monte Carlo (HMC), which use gradient information to explore the target distribution, are popular variants of MCMC. The Sequential Monte Carlo (SMC) sampler is an alternative sampling method which, unlike MCMC, can readily utilise parallel computing architectures and also has tuning parameters not available to MCMC. One such parameter is the L-kernel which can be used to minimise the variance of the estimates from an SMC sampler. In this letter, we show how the proposal used in the No-U-Turn Sampler (NUTS), an advanced variant of HMC, can be incorporated into an SMC sampler to improve the efficiency of the exploration of the target space. We also show how the SMC sampler can be optimized using both a near-optimal L-kernel and a Hamiltonian proposal, Comment: This work has been submitted to the IEEE for possible publication

Many real-world problems require one to estimate parameters of interest, in a Bayesian framework, from data that are collected sequentially in time. Conventional methods for sampling from posterior distributions, such as {Markov Chain Monte Carlo} can not efficiently address such problems as they do not take advantage of the data's sequential structure. To this end, sequential methods which seek to update the posterior distribution whenever a new collection of data become available are often used to solve these types of problems. Two popular choices of sequential method are the Ensemble Kalman filter (EnKF) and the sequential Monte Carlo sampler (SMCS). While EnKF only computes a Gaussian approximation of the posterior distribution, SMCS can draw samples directly from the posterior. Its performance, however, depends critically upon the kernels that are used. In this work, we present a method that constructs the kernels of SMCS using an EnKF formulation, and we demonstrate the performance of the method with numerical examples.

By facilitating the generation of samples from arbitrary probability distributions, Markov Chain Monte Carlo (MCMC) is, arguably, \emph{the} tool for the evaluation of Bayesian inference problems that yield non-standard posterior distributions. In recent years, however, it has become apparent that Sequential Monte Carlo (SMC) samplers have the potential to outperform MCMC in a number of ways. SMC samplers are better suited to highly parallel computing architectures and also feature various tuning parameters that are not available to MCMC. One such parameter - the `L-kernel' - is a user-defined probability distribution that can be used to influence the efficiency of the sampler. In the current paper, the authors explain how to derive an expression for the L-kernel that minimises the variance of the estimates realised by an SMC sampler. Various approximation methods are then proposed to aid implementation of the proposed L-kernel. The improved performance of the resulting algorithm is demonstrated in multiple scenarios. For the examples shown in the current paper, the use of an approximately optimum L-kernel has reduced the variance of the SMC estimates by up to 99 % while also reducing the number of times that resampling was required by between 65 % and 70 %. Python code and code tests accompanying this manuscript are available through the Github repository \url{https://github.com/plgreenLIRU/SMC_approx_optL}., Comment: 29 pages, 14 figures

This paper studies the reliability of a real-world learning-enabled system, which conducts dynamic vehicle tracking based on a high-resolution wide-area motion imagery input. The system consists of multiple neural network components -- to process the imagery inputs -- and multiple symbolic (Kalman filter) components -- to analyse the processed information for vehicle tracking. It is known that neural networks suffer from adversarial examples, which make them lack robustness. However, it is unclear if and how the adversarial examples over learning components can affect the overall system-level reliability. By integrating a coverage-guided neural network testing tool, DeepConcolic, with the vehicle tracking system, we found that (1) the overall system can be resilient to some adversarial examples thanks to the existence of other components, and (2) the overall system presents an extra level of uncertainty which cannot be determined by analysing the deep learning components only. This research suggests the need for novel verification and validation methods for learning-enabled systems.

Pixel-based Global Motion Estimation (GME) 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 letter, we propose a parameterised student-t cost function that can interpolate between two cost functions that are amongst the most widely in image registration problems, the L2 norm and the Cauchy-Lorentzian function. We also propose a parameter estimation method that helps to find the best parameters for the proposed cost function. Experiments prove that the proposed approach can estimate global motion accurately relative to the existing cost functions without demanding a higher computational cost.

This paper proposes an approach to detect moving objects in Wide Area Motion Imagery (WAMI), in which the objects are both small and well separated. Identifying the objects only using foreground appearance is difficult since a $100-$pixel vehicle is hard to distinguish from objects comprising the background. Our approach is based on background subtraction as an efficient and unsupervised method that is able to output the shape of objects. In order to reliably detect low contrast and small objects, we configure the background subtraction to extract foreground regions that might be objects of interest. While this dramatically increases the number of false alarms, a Convolutional Neural Network (CNN) considering both spatial and temporal information is then trained to reject the false alarms. In areas with heavy traffic, the background subtraction yields merged detections. To reduce the complexity of multi-target tracker needed, we train another CNN to predict the positions of multiple moving objects in an area. Our approach shows competitive detection performance on smaller objects relative to the state-of-the-art. We adopt a GM-PHD filter to associate detections over time and analyse the resulting performance., Comment: Accepted for publication in 22nd International Conference on Information Fusion (FUSION 2019)

Markov Chain Monte Carlo (MCMC) is a well-established family of algorithms which are primarily used in Bayesian statistics to sample from a target distribution when direct sampling is challenging. Single instances of MCMC methods are widely considered hard to parallelise in a problem-agnostic fashion and hence, unsuitable to meet both constraints of high accuracy and high throughput. Sequential Monte Carlo (SMC) Samplers can address the same problem, but are parallelisable: they share with Particle Filters the same key tasks and bottleneck. Although a rich literature already exists on MCMC methods, SMC Samplers are relatively underexplored, such that no parallel implementation is currently available. In this paper, we first propose a parallel MPI version of the SMC Sampler, including an optimised implementation of the bottleneck, and then compare it with single-core Metropolis-Hastings. The goal is to show that SMC Samplers may be a promising alternative to MCMC methods with high potential for future improvements. We demonstrate that a basic SMC Sampler with 512 cores is up to 85 times faster or up to 8 times more accurate than Metropolis-Hastings.

This paper investigates the problem of aerial vehicle recognition using a text-guided deep convolutional neural network classifier. The network receives an aerial image and a desired class, and makes a yes or no output by matching the image and the textual description of the desired class. We train and test our model on a synthetic aerial dataset and our desired classes consist of the combination of the class types and colors of the vehicles. This strategy helps when considering more classes in testing than in training., Comment: This paper has been accepted in the National Aerospace Electronics Conference (NAECON) 2018 and would be indexed in IEEE

The development, benchmarking and validation of aerial Persistent Surveillance (PS) algorithms requires access to specialist Wide Area Aerial Surveillance (WAAS) datasets. Such datasets are difficult to obtain and are often extremely large both in spatial resolution and temporal duration. This paper outlines an approach to the simulation of complex urban environments and demonstrates the viability of using this approach for the generation of simulated sensor data, corresponding to the use of wide area imaging systems for surveillance and reconnaissance applications. This provides a cost-effective method to generate datasets for vehicle tracking algorithms and anomaly detection methods. The system fuses the Simulation of Urban Mobility (SUMO) traffic simulator with a MATLAB controller and an image generator to create scenes containing uninterrupted door-to-door journeys across large areas of the urban environment. This `pattern-of-life' approach provides three-dimensional visual information with natural movement and traffic flows. This can then be used to provide simulated sensor measurements (e.g. visual band and infrared video imagery) and automatic access to ground-truth data for the evaluation of multi-target tracking systems., Comment: v1 (Accepted for publication in Simulation Modelling Practice and Theory)

We discuss a general method of model selection from experimentally recorded time-trace data. This method can be used to distinguish between quantum and classical dynamical models. It can be used in post-selection as well as for real-time analysis, and offers an alternative to statistical tests based on state-reconstruction methods. We examine the conditions that optimize quantum hypothesis testing, maximizing one's ability to discriminate between classical and quantum models. We set upper limits on the temperature and lower limits on the measurement efficiencies required to explore these differences, using a novel experiment in levitated optomechanical systems as an example., Comment: 9 pages, 1 figure. Accepted for publication in Physical Review A (Rapid Communication)

This paper proposes an efficient method for the simultaneous estimation of the state of a quantum system and the classical parameters that govern its evolution. This hybrid approach benefits from efficient numerical methods for the integration of stochastic master equations for the quantum system, and efficient parameter estimation methods from classical signal processing. The classical techniques use Sequential Monte Carlo (SMC) methods, which aim to optimize the selection of points within the parameter space, conditioned by the measurement data obtained. We illustrate these methods using a specific example, an SMC sampler applied to a nonlinear system, the Duffing oscillator, where the evolution of the quantum state of the oscillator and three Hamiltonian parameters are estimated simultaneously., Comment: 11 pages, 5 figures, accepted for publication in Phys Rev A

Particle filtering is a numerical Bayesian technique that has great potential for solving sequential estimation problems involving non-linear and non-Gaussian models. Since the estimation accuracy achieved by particle filters improves as the number of particles increases, it is natural to consider as many particles as possible. MapReduce is a generic programming model that makes it possible to scale a wide variety of algorithms to Big data. However, despite the application of particle filters across many domains, little attention has been devoted to implementing particle filters using MapReduce. In this paper, we describe an implementation of a particle filter using MapReduce. We focus on a component that what would otherwise be a bottleneck to parallel execution, the resampling component. We devise a new implementation of this component, which requires no approximations, has $O\left(N\right)$ spatial complexity and deterministic $O\left(\left(\log N\right)^2\right)$ time complexity. Results demonstrate the utility of this new component and culminate in consideration of a particle filter with $2^{24}$ particles being distributed across $512$ processor cores., Comment: 31 pages, 16 figures

This work proposes a novel method through which local information about the target density can be used to construct an efficient importance sampler. The backbone of the proposed method is the Incremental Mixture Importance Sampling (IMIS) algorithm of Raftery and Bao (2010), which builds a mixture importance distribution incrementally, by positioning new mixture components where the importance density lacks mass, relative to the target. The key innovation proposed here is that the mixture components used by IMIS are local approximations to the target density. In particular, their mean vectors and covariance matrices are constructed by numerically solving certain differential equations, whose solution depends on the gradient field of the target log-density. The new sampler has a number of advantages: a) it provides an extremely parsimonious parametrization of the mixture importance density, whose configuration effectively depends only on the shape of the target and on a single free parameter representing pseudo-time; b) it scales well with the dimensionality of the target; c) it can deal with targets that are not log- concave. The performance of the proposed approach is demonstrated on a synthetic non-Gaussian multimodal density, defined on up to eighty dimensions, and on a Bayesian logistic regression model, using the Sonar data-set. The Julia code implementing the importance sampler proposed here can be found at https:/github.com/mfasiolo/LIMIS.

This paper presents an efficient method for estimating the probability of conflict between air traffic within a block of airspace. Autonomous Sense-and-Avoid is an essential safety feature to enable Unmanned Air Systems to operate alongside other (manned or unmanned) air traffic. The ability to estimate probability of conflict between traffic is an essential part of Sense-and-Avoid. Such probabilities are typically very low. Evaluating low probabilities using naive Direct Monte Carlo generates a significant computational load. This paper applies a technique called Subset Simulation. The small failure probabilities are computed as a product of larger conditional failure probabilities, reducing the computational load whilst improving the accuracy of the probability estimates. The reduction in the number of samples required can be one or more orders of magnitude. The utility of the approach is demonstrated by modeling a series of conflicting and potentially conflicting scenarios based on the standard Rules of the Air., Comment: Submitted to IEEE Transactions on Aerospace and Electronic Systems

A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to nonlinear filtering problems. They do so by defining a continuum of densities between the prior probability density and the posterior, i.e. the filtering density. Building on these methods' successes, we propose a novel filter. The new filter aims to address the shortcomings of sequential Monte Carlo methods when applied to important nonlinear high-dimensional filtering problems. The novel filter uses equally weighted samples, each of which is associated with a local solution of the Fokker-Planck equation. This hybrid of Monte Carlo and local parametric approximation gives rise to a global approximation of the filtering density of interest. We show that, when compared with state-of-the-art methods, the Gaussian-mixture implementation of the new filtering technique, which we call Stochastic Particle Flow, has utility in the context of benchmark nonlinear high-dimensional filtering problems. In addition, we extend the original particle flow filters for tackling multi-target multi-sensor tracking problems to enable a comparison with the new filter., Comment: 79 pages