Consider an array receiving unknown wideband signals from an unknown number of sources k. Wideband signals can occupy arbitrarily wide bandwidths, rendering demodulation-based approaches inapplicable, a common situation in settings involving acoustic signals. Here, we aim to determine k given N noisy array-valued measurements, a task known as the "detection problem," for which Bayesian model comparison is a common approach. To render Bayesian inference tractable, it is typically necessary to marginalize the source signals. Unfortunately, for wideband signals, naive marginalization has an unaffordable time complexity of 𝒪(N^3 k^3). As a result, fully Bayesian signal detection has yet to be demonstrated in wideband settings. In this work, we propose a wideband signal model that allows for computationally tractable marginalization of the source signals. We begin from the canonical model of linear time-invariant (LTI) signal propagation, which is then augmented into a circular convolution, all without loss of generality. This allows for efficient computation in the frequency domain, where the resulting linear system admits a decomposition into a sparse matrix we refer to as a stripe matrix decomposition. Exploiting this sparsity pattern reduces the time complexity of computing the marginal likelihood to 𝒪(N k^3). These computational improvements enable efficient posterior inference via reversible-jump Markov chain Monte Carlo (RJMCMC). In this work, we use the non-reversible extension of RJMCMC (NRJMCMC), which often achieves lower autocorrelation and faster convergence than RJMCMC. Detection of the latent source signals can then be performed in a fully Bayesian manner using samples drawn by NRJMCMC. We evaluate our procedure by comparing it against generalized likelihood ratio testing (GLRT) and information criteria.

While typical online estimation methods can estimate the multiparameter dynamics of many systems, they may not be sufficient for a system with highly noisy measurement and rapid detection rate. In this paper, we create a hybrid estimation method by augmenting the sequential Monte Carlo (SMC) sampler, an online estimation method with an offline technique known as the time-batch estimation technique. By continuously monitoring the system, we may divide signals into batches and average them into an averaged trajectory. The system dynamics is then evolved with batch-averaged Kraus maps, for which we derive a highly efficient approximation. To facilitate the adoption of our algorithm, we present a modular derivation of the SMC methods and showcase our algorithm as an explicit example. We then implement our algorithm on the measurement signals obtained from superconducting-qubit experiments under two types of measurement setting: a fluorescence measurement and a dispersive z-measurement. The algorithm's hyperparameter values are chosen from independent numerical simulation, while the accuracy of our estimation is validated by a signal reconstruction method. Our results show that, for the fluorescence case, our algorithm can estimate the system's parameters better than the standard calibration method, and, for the dispersive case, our estimation is capable of finding an unexpected jump in parameter values that the standard calibration method could not find.

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.

Imagine a polygon-shaped platform P and only one static spotlight outside P; which direction should the spotlight face to light most of P? This problem occurs in maximising the visibility, as well as in limiting the uncertainty in localisation problems. More formally, we define the following maximum cover problem: “Given a convex polygon P and a Field Of View (FOV) with a given centre and inner angle ϕ ; find the direction (an angle of rotation θ ) of the FOV such that the intersection between the FOV and P has the maximum area”. In this paper, we provide the theoretical foundation for the analysis of the maximum cover with a rotating field of view. Since the optimal solution is a real number, we develop an algorithm that approximates the direction of the field of view, with precision ε , and complexity 𝒪(n(logn+(logε)/ϕ )) .

This paper deals with the problem of tracking a specific target moving through a complex urban environment using cooperative airborne imaging sensors. We demonstrate algorithms to maintain a line of sight to the target where possible and adapts to occlusions, and other sensor limitations, as the vehicle moves through a complex urban environment. This work exploits an advanced simulation capability, built around Unreal Engine 5, that can generate realistic video data which is used to test and to stress tracking algorithms whilst providing ground truth data for true targets and for collateral entities.

Passive towed array sonar systems play an essential role in submarine situational awareness. However, the detection and localisation of sound-emitting objects is a more challenging task compared to their active counterparts due to a lack of immediate range information. By making manoeuvres and changing the bearings at multiple positions, a passive sonar can localise and track the source of the sound. Reinforcement learning is the process of learning an optimal strategy to guide an agent’s actions towards optimising its cumulative reward for a given task. This work evaluates an agent’s ability to control a passive towed array sonar system for optimal source localisation and tracking in the underwater environment, using collision avoidance as a practical example application.

Multi-view pedestrian tracking has frequently been used to cope with the challenges of occlusion and limited fields-of-view in single-view tracking. However, there are few end-to-end methods in this field. Many existing algorithms detect pedestrians in individual views, cluster projected detections in a top view and then track them. The others track pedestrians in individual views and then associate the projected tracklets in a top view. In this paper, an end-to-end framework is proposed for multi-view tracking, in which both multi-view and temporal aggregations of feature maps are applied. The multi-view aggregation projects the per-view feature maps to a top view, uses a transformer encoder to output encoded feature maps and then uses a CNN to calculate a pedestrian occupancy map. The temporal aggregation uses another CNN to estimate position offsets from the encoded feature maps in consecutive frames. Our experiments have demonstrated that this end-to-end framework outperforms the state-of-the-art online algorithms for multi-view pedestrian tracking.

We propose a method to jointly optimize placement of a sonobuoy field and selection of appropriate active sonar waveforms in a complex undersea environment, using deep reinforcement learning. To this end, we develop a custom simulation environment and train an online algorithm that uses updated information as sonobuoys are placed and sonar measurements made. The approach may be termed multiple bistatic, though it shares features with multistatic approaches. We develop benchmarks using conventional fixed sonobuoy placement patterns together with fixed composite sonar pulse trains and present results that show our new approach can outperform the best conventional combination of fixed placement pattern and pulse train.

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 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.

This paper presents a new approach to finding optimal patterns for the placement of fields of sonobuoys in a complex undersea environment. We model the problem as a biobjective one, where the aim is to minimise both sensor placement time and uncertainty over target localisation. Both objectives may be important in time-critical localisation scenarios and our approach allows an operator to choose between different optimal solutions, favouring lower placement time or lower localisation uncertainty as operational circumstances require. We develop a two-phase algorithm, where an offline multiobjective evolutionary phase finds initial Pareto-non-dominated solutions to a static problem and then an online multiobjective reinforcement learning phase finds improved solutions using updated information. We find that the evolutionary algorithm improves significantly on standard grid patterns and that the reinforcement learning algorithm improves further on the evolutionary phase. The number of sonobuoys required may also be reduced.

In this paper, we present a geometric framework for the passive localisation of static emitters. The objective is to localise the position of the emitters in a given area by centralised coordination of mobile passive sensors. This framework uses only the geometry of the problem to minimise the maximal bounds of the emitters' locations without using a belief or probability distribution. This geometric approach provides effective boundaries on the emitters' position. It can also be useful in evaluating different decision-making strategies for coordinating mobile passive sensors and complementing statistical methods during the initialisation process. The effectiveness of the geometric approach is shown by designing and evaluating a greedy decision-making strategy, where a sensor selects its future position by minimising the maximum uncertainty on its next measurement using one of the global objective functions. Finally, we analyse and discuss the emergent behaviour and robustness of the proposed algorithms.

This paper concerns the application of information fusion and Bernoulli filtering to a maritime surveillance scenario. Sensor data was recorded during live trials featuring a static Leonardo Osprey maritime surveillance active electronic scan array (AESA) radar observing a cooperative rigid inflatable boat (RIB) target deployed in the Firth of Forth estuary north of Edinburgh, UK. The RIB was equipped with a global positioning system (GPS) and an automatic identification system (AIS) recording geodetic position over time, where the collected data is fused to generate ground truth. A multi-target joint detection and tracking (MTJDT) algorithm is used to both detect and track the RIB target from post-processed radar and AIS data whilst ignoring other information regarding objects and sources of interference. Generalised optimal sub-pattern assignment (GOSPA) and receiver operating characteristic (ROC) analysis are used to evaluate target detection, localisation, and cardinality performance quantification. Results suggest conventional data processing and the proposed tracking algorithm achieve reasonable detection and tracking performance under the assumption that the ground truth well-represents the RIB position without knowledge of error statistics, but track divergence and discontinuities occur due to radar obscuration by buildings, data inaccuracies and clutter.

We present a new approach to finding optimal patterns for the placement of fields of sonobuoys in a complex undersea environment. The problem is modelled as a biobjective one, where the aim is to both minimize uncertainty over target localization and minimize sensor placement time. We develop a two-phase algorithm, where an offline multiobjective evolutionary phase finds initial Pareto-nondominated solutions to a static problem, and then an online multiobjective reinforcement learning phase finds improved solutions using updated information. Initial results show that our approach generates significant improvements over standard grid patterns.

This paper develops optimal procedures for point estimation with Bernoulli filters. These filters are of interest to radar and sonar surveillance because they are designed for stochastic targets that can enter and exit the surveillance region at random instances. Because of this property they are not served by the minimum mean square estimator, which is the most widely used approach to optimal point estimation. Instead of the squared error loss, this paper proposes an application-oriented loss function that is compatible with Bernoulli filters, and it develops two significant practical estimators: the minimum probability of error estimate (which is based on the rule of ideal observer), and the minimum mean operational loss estimate (which models a simple defence scenario).

Quantum sensors based on atom interferometers can provide measurements of inertial quantities with unprecedented accuracy and precision. It has been suggested that this sea change in sensing could provide an inertial navigation capability that is comparable with current satellite based navigation systems. However, the accuracy of sensor measurements is not the only factor that limits the accuracy of inertial navigation systems. In this paper, we explore the fundamental limits to inertial navigation, and explain how quantum inertial sensors could be used to alleviate some of the problems encountered in current classical inertial navigation systems, but not to solve the fundamental instability inherent in inertial navigation methods.

This paper examines the use of Poisson multi-Bernoulli mixture (PMBM) filters with realistic signal propagation models for tracking of targets with active sonar systems. In particular, the paper considers application of BELLHOP simulation to model the spatial dependence of the target probability of detection. The intention is to develop practical approaches to the problem of accurately representing sonar propagation within an advanced tracking filter.

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 1000 km.

This paper is concerned with the implementation of track-before-detect (TkBD) algorithms for a range of single-target multi-sensor scenarios with only intermittently visible targets. Visible targets generate measurements from sensors characterised by data rate and clutter density. Bernoulli filters implementing multiple hypothesis tracking (MHT) strategies are deployed to infer both the target location and existence probability. Various Bernoulli filter configurations are compared, including integrated probabilistic data association filters (IPDAF) and integrated expected likelihood particle filters (IELPF) using both prior and Gaussian mixture proposal distributions for the latter. Performance is evaluated against the clutter density in scenarios featuring one low data rate active sensor or two sensors, complimenting the former with a high data rate passive sensor with opposing measurement resolutions. The performance measures used are the area under the receiver operating characteristic (ROC) curve, localisation root mean squared error (RMSE) compared with the posterior Cramér-Rao lower bound (PCRLB), and computation time. Simulation results show that Kalman filters provide an effective solution at low computational expense in less cluttered and comparatively easy scenarios, whereas particle filters implementing Gaussian mixture proposal distributions provide performance benefits relative to computational costs as scenarios become more cluttered and comparatively challenging.

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.