ABSTRACT. In this work, estimators for platform pose and landmark maps for visual-inertial data are analysed. It is shown that the full, non-linear, visual-inertial problem has a conditionally linear substructure in the 2D case which can be exploited for efficient solutions, e.g., Block Coordinate Descent (BCD). It is also shown that the measurement noise from the non-linear model becomes parameter dependent resulting in biased estimates if that fact is ignored. However, the bias can be accounted for using the Iteratively Reweighted Least Squares (IRLS) method. In the 3D case the conditionally linear substructure is not separable. However, it can be shown that the Jacobian of the non-linear substructure can be calculated recursively resulting in an efficient solution. A simple simulated 2D visual-inertial example is used to illustrate the theoretical results.

ABSTRACT. We present a novel quaternion-based inertial orientation estimation filter. Inclination drift from gyroscope strapdown integration is corrected from specific force measurements that are low-pass filtered in an almost-inertial frame to effectively compensate for instantaneous accelerations and decelerations. Heading drift is corrected via a scalar heading offset. The resulting decoupled state representation provides simultaneous 6D and 9D orientation estimation. We systematically evaluated the method on a rich orientation estimation benchmark dataset and show that the proposed method clearly outperforms three of the currently most commonly adopted and accurate inertial orientation estimation filters. The filter is available as open-source software, and its parameters are tuned to work well for a wide range of movements and application scenarios. Our fundamentally different filtering approach with a decoupled state representation and novel inclination correction resulted in a new level of accuracy, with a 41% improvement of the total orientation error and doubling the inclination accuracy. This facilitates new and exciting high-precision applications in the field of inertial motion tracking.

ABSTRACT. In this paper, a simultaneous localization and mapping (SLAM) algorithm for tracking the motion of a pedestrian with a foot-mounted inertial measurement unit (IMU) is proposed. The algorithm uses two maps, namely, a motion map and a magnetic field map. The motion map captures typical motion patterns of pedestrians in buildings that are constrained by e.g. corridors and doors. The magnetic map models local magnetic field anomalies in the environment using a Gaussian process (GP) model and uses them as position information. These maps are used in a Rao-Blackwellized particle filter (RBPF) to correct the pedestrian position and orientation estimates from the pedestrian dead-reckoning (PDR). The PDR is computed using an extended Kalman filter with zero-velocity updates (ZUPT-EKF). The algorithm is validated using real experimental sequences and the results show the efficacy of the algorithm in localizing pedestrians in indoor environments.

ABSTRACT. This paper is concerned with discrete time Kalman-type filtering with state transition and measurement noises that may be non-additive or non-linearly transformed. More specifically, we extend the iterative estimation algorithm Posterior Linearization Filter (PLF) for estimation with this kind of noises. The approach solves the prediction and update step simultaneously, which allows to use the PLF iterations to improve the estimation in the non-linear state transition model. The proposed algorithm also produces single step fixed-lag smoothing estimates. We show in examples how the proposed approach can be used with non-Gaussian state transition noises and nonlinearly transformed state transition noises.

ABSTRACT. Tracking a kinematic chain model with inertial sensors and magnetometers using a Bayesian Filter approach typically one magnetometer per segment is used to compensate for a global heading drift. In this work we present a study showing that heading information can be propagated from one segment to neighboring segments in a kinematic chain. In particular we elaborate on recent theoretical results and observe that the absolute orientation of all segments in a kinematic chain can be estimated drift-free with only sparse sources of heading information. Our study consists of two parts. The first part is based on a simulated manipulator consisting of three segments. The second one includes the lower body (seven segments) of subjects performing walking trials. Here the inertial sensor data was generated using position and rotation tracking data from a marker-based optical reference system. We show that under certain circumstances the inclusion of a single source of heading information is enough to capture even under disturbances the absolute orientation of the remaining segments drift-free.

ABSTRACT. Power outages pose meaningful economic and social impacts on communities around the world. However, society's increasing reliance on electricity reduces the tolerance for power outages and consequently highlights the need to enhance the power grid resilience against natural hazards. For example, power lines based on cable-stayed towers must take special care to avoid cable loosening or foundation settlement, leading to tower collapse and cascading power failures. Our work uses a data fusion strategy to improve the inference quality of faulty or noisy sensors in remote monitoring. Machine Learning (ML) models based on Feedforward Neural Networks (FNN) and Principal Component Analysis (PCA) are used to predict expected values based on correlated sensor data. Our experiments compare the data fusion approaches with the ground truth values of inclination and cable tension. We show that the strategies with PCA and FNN and only with FNN reduced the Mean Absolute Percentage Error (MAPE) for cable tension estimation by 54% and 65% on average, respectively, with a corresponding error reduction of 37% and 54% on average for tower displacement estimation.

ABSTRACT. This paper considers a camera calibration problem using a discretized drone trajectory recorded by an accurate GPS. The challenge is that the GPS receiver and camera are not time synchronized (there is an unknown time offset between the two systems). The problem is formulated as an estimation problem to estimate the parameter vector consisting of the three camera orientation angles and the time offset. The estimation is based on the camera measurements and the discretized GPS trajectory. The maximum likelihood (ML) estimator using the Iterated Least Squares (ILS) algorithm is developed. It can estimate the parameter vector in continuous space using discretized GPS information. Simulation tests are conducted on three drone trajectories. The estimation accuracy achieves the CRLB, and thus it is statistically efficient. The results are further analyzed from the point of view of real impact: the calibration error (residual biases) should not be significant compared to the camera measurement error (noise standard deviation). The most suitable drone trajectory is therefore recommended among the three. Its calibration errors are smaller than one sixth of the measurement error.

ABSTRACT. The usage of light detection and ranging sensors (LiDARs) has grown rapidly in recent years. The ability to directly capture 3D point clouds is a big advantage compared to other visual systems like cameras. One disadvantage is that uncertainty information is difficult to obtain for these systems, although this information is crucial for the decisions based on the measurements. This becomes even more important, when LiDARs are used in conjunction with other sensors in multi-sensor systems (MSS). The sensor data fusion with different sensors requires an extrinsic calibration, which describes the transformation between the LiDAR frame and the body frame platform. This can be done utilizing object space information measured by the LiDAR, which is used to infer the origin of the sensor frame based on reference geometries. This process can be used to additionally determine intrinsic parameters of the sensor. Possible intrinsic parameters are corrections for the distance measurements or approximations for the uncertainty of the measurement elements. In this work, the determination of extrinsic and intrinsic parameters is combined for the first time with the approximation of a stochastic model for a multi-beam LiDAR. This is demonstrated on a real-data set of a Velodyne VLP-16, for which the transformation parameters between sensor frame and body frame are determined. Additionally, an distance offset is determined and the variance components are estimated to establish a better approximation for the stochastic model. The impact of the calibration field and choice of position within this calibration field are shown and discussed. The results are evaluated in a separate experiment using a kinematic MSS.

ABSTRACT. In this paper, we assess the performance of our real-world multi-camera traffic surveillance system along a segment of the A9 Autobahn north of Munich. Its principal component is a Labeled Multi-Bernoulli based tracking module that sequentially fuses the detection data from parallel camera processing pipelines. We present a systematic investigation of the system's characteristic failure modes that lead to a degradation of its performance. To this end, we assess state of the art metrics and performance measures in regard to their suitability for flagging unwanted behavior or failures in real-world multi-object tracking systems. Our analysis is structured into three levels of abstraction: target-level, time-step-level, and track-level. These abstraction levels allow us to systematically approach the analysis from different perspectives and to direct the focus on recurring errors and systemic deficiencies. In particular, the track-level analysis proved to be the most expedient approach since it drew our attention to system challenges like occlusions and other time-correlated detection errors. It further identified the system bias introduced by the adoption of class-dependent object extents. Our analysis is intended to guide the future development effort of our system and to serve as a basis for investigations and improvements of similar systems.

ABSTRACT. When a target is not maneuvering, the residuals from the NCV Kalman filter are independent, zero mean, and Gaussian. When the target maneuvers, the residuals are no longer independent, unbiased or Gaussian. A chi-squared (χ2) test is a common method to detect maneuvering targets, however, the sign information between consecutive residuals is lost by the calculation of the χ2 statistic. In this work, two methods that inherently use the sign information (the bias resulting from filter mismatch) are explored for the purpose of detecting weak maneuvers. First, a recursion is developed to compute the full cross correlation for an arbitrary number of residuals under the hypothesis that the target is maneuvering. This result is compared in a hypothesis test to the null hypothesis that the target is not maneuvering. Second, an arbitrary size window of residual errors is used to form a least squares estimate of the bias (i.e. acceleration), and the significance of that estimate is tested against the corresponding covariance. Both methods are shown to be an improvement over a standard χ2 test.

ABSTRACT. A star-convex shape based on Cartesian B-splines provides a good model for detailed extended target tracking, suited for, e.g., high resolution automotive sensors. Motivated by real-world sensor data from traffic scenarios, we present an extended object tracking filter that (i) solves the problem of bad object initialization for contour tracking of mixed-size vehicles in a range of common traffic scenarios; (ii) enables accurate tracking of objects such as motorcycles, that generates detections distributed on the surface, rather than on the contour. Our approach is based on star-convex Cartesian B-spline polynomials, iterative closest point (ICP) and the convex hull. In particular, we implement the ICP algorithm to find the translation and rotation of the contour that best fit the sensor point cloud. We show that, while the original B-spline filter with a ”second-time-step-initialization-procedure” fails to robustly track the object, our approach performs on par to the original B-spline filter with ground truth initialization. Furthermore, for targets generating detections on the surface, we utilize the convex hull algorithm on the point cloud. We show that our algorithm successfully tracks the object, while the original B-spline filter fails to robustly track the contour of a motorcycle.

ABSTRACT. This paper examines the use of Poisson multi-Bernoulli mixture (PMBM) filters with realistic signal propagation models for tracking of target 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 develop practical approaches to the problem of accurately representing sonar propagation within an advanced tracking filter.

ABSTRACT. Precise indoor localization remains a challenging problem for several essential applications. Radio frequency simultaneous localization and mapping (RF-SLAM) is a promising solution relying on radio signals exchanged between mobile agents and static physical anchors (PAs) that are reflected at flat surfaces in an indoor environment. RF-SLAM jointly estimates the time-varying location of mobile agents as well as the static locations of these surfaces. Recent work on RF-SLAM methods has shown that each surface can be efficiently represented by a single master virtual anchor (MVA). The measurement model related to this MVA-based RF-SLAM method is highly nonlinear. Thus, Bayesian estimation relies on sampling-based techniques. The original MVA-based RF-SLAM method employs conventional “bootstrap” sampling. In challenging scenarios it was observed that the original method might converge to incorrect MVA positions corresponding to local maxima. In this paper, we introduce MVA-based RF-SLAM with an improved sampling technique that succeeds in the aforementioned challenging scenarios. Our simulation results demonstrate significant performance advantages of the proposed method.

ABSTRACT. 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.

ABSTRACT. Recent advances in the Optimal Transport theory allow to rewrite several known problems in a neat way, while providing a more general perspective. When dealing with mixture densities, or in general with intensities, such a framework naturally induces composite dissimilarities, together with corresponding Greedy Reduction and Refinement algorithms. In applications like target tracking in clutter, it is common to deal with the Mixture Reduction problem, since the optimal Bayesian recursion leads to a combinatorial explosion of hypotheses for the posterior distribution. Moreover, in the extended target case, more complex distributions are being considered to describe the features of an object, for instance the Gamma Gaussian Inverse-Wishart density, which makes the reduction problem intrinsically more difficult. For the reasons above, having theoretically sound reduction algorithms results to be important for many practical problems. In this work, we will provide an optimal transport perspective to the Gamma Gaussian Inverse-Wishart mixture reduction problem, together with algorithms which are suitable for real-time applications.

ABSTRACT. This paper presents a Gaussian implementation of a multi-Bernoulli track-before-detect filter for multi-target tracking with superpositional sensors. The proposed filter runs independent Bernoulli filters for each potential target. At each update step, each Bernoulli filter shares its predicted measurement information with the rest of the Bernoulli filters so that they can account for the influence of this target in the likelihood. The Bernoulli filters are implemented using unscented Kalman filters. Simulation results show the benefits of the proposed algorithm.

ABSTRACT. The swarm is used to describe a set of individual targets which are very close together in the measurement space (relative to the resolution of the sensor). In this paper, we consider to estimate the number, shape and density of target swarms in addition to their motion states. In order to deal with the uncertain number of measurement origins, we use amplitude information (AI) to construct hypotheses about the number of individual target source of the merged measurement in the probability hypothesis density (PHD) update step. On this basis, we propose the PHD filter for target swarms (S-PHD filter) and develop Gaussian mixture (GM) implementation to the resulting filter. The performance of this algorithm is demonstrated by a multi swarms scenario with merged measurements, and the results highlight the significant improvement in the estimates of the number of individuals and the density of swarms.

ABSTRACT. This paper presents a Gaussian implementation of the Poisson multi-Bernoulli mixture (PMBM) filter for sets of trajectories with non-linear/non-Gaussian measurements. In this filter, the single-trajectory densities are Gaussian and their updates are performed using the iterated posterior linearisation technique, applied on the current target state. With this approach, we first compute the posterior distribution of the current target state by iteratively refining the linear approximation of the measurement, and the resulting mean square error of the linearisation, based on our current guess of the posterior distribution. After obtaining a Gaussian approximation of the current target state, the distribution of the past states of the trajectory can be obtained in closed form. Via numerical simulations, we compare different algorithms to approximate the single-trajectory posteriors and normalising constants for trajectory PMBM and trajectory Poisson multi-Bernoulli filters.

ABSTRACT. This paper introduces Poisson Multi-Bernoulli filters for reducing the complexity. This technique is derived based on Poisson Multi-Bernoulli Mixture (PMBM) filters and Poisson Multi-Bernoulli (PMB) filters for point targets. In this paper, we call this technique Fast Multi-Bernoulli (FMB) filters. The complexity of PMB is increased exponentially with the number of propagated Bernoulli components. There are many cases in which this expansion of complexity is an obstacle blocking incorporation into consumer products. FMB dramatically lower the complexity by using approximation for the data association, which are a bottleneck in PMB processing. Also, under conditions in which tracking has a high degree of difficulty and much clutter is generated, FMB showed performance equivalent to PMB.

ABSTRACT. Multi-object tracking filters require a birth density to detect new objects from measurement data. If the initial positions of new objects are unknown, it may be useful to choose an adaptive birth density. In this paper, a circular birth density is proposed, which is placed like a band around the surveillance area. This allows for 360° coverage. The birth density is described in polar coordinates and considers all point-symmetric quantities such as radius, radial velocity and tangential velocity of objects entering the surveillance area. Since it is assumed that these quantities are unknown and may vary between different targets, detected trajectories, and in particular their initial states, are used to estimate the distribution of initial states. The adapted birth density is approximated as a Gaussian Mixture so that it can be used for filters operating on Cartesian coordinates.

ABSTRACT. The goal in tracking is to combine sensor information about an object over time to estimate its position and other parameters. One way to improve this estimation is to incorporate information from multiple sensors observing the same target competitively. If each sensor tracks the target locally and sends its estimate and uncertainty to neighboring sensors or a central fusion unit, the fusion of these estimates is called track-to-track fusion. If an object is larger than a single sensor resolution cell, its extent needs to be part of the target state as well. Such an extended object brings unique challenges for track-to-track fusion, such as ambiguity in the parameterization. We handled this challenge in previous work by introducing a so called Random Ellipse Density (RED), as well as a Minimum Mean Gaussian Wasserstein (MMGW) estimator, which finds an estimate minimizing a distance measure on ellipses, the Gaussian Wasserstein (GW) distance, on the RED. In reality, estimates from different tracks are often correlated. Ignoring these correlations can lead to an underestimation of the state's covariance, worsening the fusion results. Therefore, we will present an extension of the REDs to handle known correlation in a distributed fusion architecture with a central fusion unit. We also provide a simulation in which measurements from different sensors are tracked by elliptic extended object trackers, fusing the trackers' estimates to improve the estimation.

ABSTRACT. This paper presents an extended object tracking algorithm. We model visibility constraints and other intricacies of the measurement process. A sequential importance sampling and resampling particle filter is used, which permits a flexible modeling of the target shape. We compare our method to the standard approach of just rotating and translating the target extent model. Our approach is applicable for both radar and LiDAR sensors. Results are presented in a a simulated scenario with LiDAR data. A proof of concept is conducted in a real world scenario with radar data.

ABSTRACT. This paper mainly addresses the scalable detection and tracking of extended target in the low signal-to-noise(SNR) environment. As the appearance and shape of extended target is constantly varied, it is challenging to achieve the robust detection and tracking. For this, a novel adaptive scale (AS) kernelize correction filter (KCF) based on multi-frame track-before-detect (MF-TBD) framework is proposed. By embedding scaling pools into the response map to handle the scale variation and accumulating target energy over all feasible trajectories, AS-MF-TBD estimates the kinematic state and geometric shapes simultaneously. Both simulation data and real radar data are used to demonstrate the superiority of the proposed method in terms of detection performance and estimation accuracy.

ABSTRACT. Augmented reality (AR) in mobile devices (such as smartphones and tablets) is becoming more popular each day, and because of this many newer devices are starting to ship with embedded depth sensors. This presents a great opportunity for the field of extended object tracking, whose algorithms are well-suited for dealing with varying measurement quality while requiring little CPU usage. In this paper, we present an application in the field of robotics, based on the idea of reconstructing the dynamic state of a robot (joint positions and velocities) simply by observing it with an AR device, and using only the robot specification (its URDF file) as prior knowledge, without requiring a connection to the robot’s control system. This can allow the mobile device to identify where a robot is, or viceversa, without requiring markers such as QR codes. Additionally, this can serve as a stepping stone for more sophisticated assistance systems that can interact with the robot without requiring any access to its internals, which could otherwise make it difficult to deploy the AR app in sensitive systems. Using the iPad Pro 2020 as an example device, we will examine the challenges involved in processing mobile depth images, how to develop a robust shape model and the corresponding estimator, and how the app can ask the user to help in its initialization using AR. We will also provide an evaluation with real data that shows how the proposed system can track a moving robot robustly even if measurement quality is reduced significantly

ABSTRACT. Simultaneously estimating the kinematic properties and the extent of an object is a ubiquitous problem in a variety of applications. We propose a novel approach to online shape estimation of extended objects by employing a neural network architecture to infer the axes length of an ellipse. Based on kinematic state estimation, the input image to the network is continuously updated as new measurements arrive, incorporating uncertainties. The proposed method is evaluated based on noisy simulated data, and found to perform competitively with state-of-the-art methods. In the considered challenging scenarios with low measurement rate, it is even capable of outperforming these methods.

ABSTRACT. State estimation can significantly benefit from prior knowledge about a system’s dynamics and state. In this paper, we investigate a special class of prior knowledge: Events that correspond to a subset of the state space. This class of knowledge was introduced in pedestrian activity classification to improve the position estimation. We argue that the methodology can be generalized and applied to other applications in human motion tracking, in which the same class of knowledge is available. We apply this methodology to estimate the pose of climbers using inertial sensors and previously measured route maps. For our evaluation, we collected an open source dataset with 27 participants, including IMU data and ground truth positions of the hands. We detect gripping holds (as events), estimate the transition between holds in a least squares optimizer and use a particle filter to deploy the route map constraints (as state subset). In this scenario, our approach achieves a position median of 0.133m and thus demonstrates its possible effectiveness for this application class.

ABSTRACT. Inertial measurement units are widely used for motion tracking of kinematic chains in numerous applications. While magnetometer-free sensor fusion enables reliably high accuracy in indoor environments and near magnetic disturbances, the use of sparse sensor setups would yield additional advantages in cost, effort, and usability. However, it is unclear which sparse sensor setups can be used to track which motions of which kinematic chains, since observability of the underlying nonlinear dynamics is barely understood to date. We propose a method that utilises recurrent neural networks (RNNs) and automatically generated training data to assess the observability of the relative pose of kinematic chains in sparse inertial motion tracking (IMT) systems. We apply this method to a range of double hinge-joint systems that perform fully-exciting random motion. Results show how the degree of observability depends on the kinematic structure and that RNN-based observers can achieve small tracking errors in a large range of sparse and magnetometer-free setups. The proposed methods enables systematic assessment of observability properties in complex nonlinear dynamics and represents a key step toward enabling reliably accurate and non-restrictive IMT solutions.

ABSTRACT. The fusion of camera sensor and inertial data is a leading method for ego-motion tracking in autonomous and smart devices. State estimation techniques that rely on non-linear filtering are a strong paradigm for solving the associated information fusion task. The de facto inference method in this space is the celebrated extended Kalman filter (EKF), which relies on first-order linearizations of both the dynamical and measurement model. This paper takes a critical look at the practical implications and limitations posed by the EKF, especially under faulty visual feature associations and the presence of strong confounding noise. As an alternative, we revisit the assumed density formulation of Bayesian filtering and employ a moment matching (unscented Kalman filtering) approach to both visual-inertial odometry and visual SLAM. Our results highlight important aspects in robustness both in dynamics propagation and visual measurement updates, and we show state-of-the-art results on EuRoC MAV drone data benchmark.

ABSTRACT. Saddle point approximation methods are proposed for particle filters whose likelihood functions have high computational complexity due to combinatorial enumerations of the kind that arises in assignment problems, e.g., in multitarget, multisensor, and smoothing filters. Using techniques drawn from random matrix theory, it is shown that the approximation is, remarkably, independent of the number of measurements for the class of probabilistic data association filters. The saddle point approximation method is also applicable to the class of stochastic flow filters.

ABSTRACT. Accurate localization is one of the key requirements for the automation of mobile machines. While GNSS-based systems are widely used due to their high accuracy and accessibility, redundant systems have to be developed to decrease the dependency on GNSS signals for autonomous machines. Although altitude measurements have been used for many decades by human explorers, they are not yet exploited for localization purposes on mobile machines. Based on single barometric measurements, no localization is possible as the vehicle could be at various positions with the same absolute altitude. In this paper, we propose an algorithm based on sequential importance sampling to fuse altitude measurements with surface profiles, which allows real-time tracking and localization of mobile machines. When moving through hilly terrain, a machine constantly changes its altitude, and the altitude profile can be used to track the vehicle's position. The proposed algorithm offers a supplementary localization and verification method for mountainous and potentially GNSS-obstructed areas.

ABSTRACT. This paper deals with motion modeling for 2-dimensional tracking of a maneuvering object. Specifically, a new class of nonlinear dynamic motion models, called Lambda:Omicron, is introduced with the purpose of accurately modeling maneuvers (regarded as variations of speed and turning rate) of the moving object. These models rely on the unicycle navigation model suitably augmented with two chains of integrators to account for the unknown speed and turning rate command inputs. Quasi-exact time-discretization of the continuous-time Lambda:Omicron models is also carried out to allow their exploitation in nonlinear recursive filters. Simulation experiments are presented to show how the proposed models can outperform state-of-the-art linear and nonlinear motion models for tracking of strongly maneuvering objects.

ABSTRACT. In order to be properly addressed, many practical problems require an accurate stochastic characterization of the involved uncertainties. In this regard, a common approach is the use of mixtures of parametric densities which allow, in general, to arbitrarily approximate complex distributions by a sum of simpler elements. Nonetheless, in contexts like target tracking in clutter, where mixture of densities are commonly used to approximate the posterior distribution, the optimal Bayesian recursion leads to a combinatorial explosion in the number of mixture components. For this reason, many mixture reduction algorithms have been proposed in the literature to keep limited the number of hypotheses, but very few of them have addressed the problem of finding a suitable model order for the resulting approximation. The commonly followed approach in those algorithms is to reduce the mixture to a fixed number of components, disregarding its features which may vary over time. In general, finding an optimal number of components is a very difficult task: once a meaningful optimality criterion is identified, potentially burdensome computational procedures must be devised to reach the optimum. In this work, by exploiting the optimal transport theory, an efficient and intuitive model selection criterion for the mixture reduction problem is proposed.

ABSTRACT. In this paper, a method for ensuring the maintenance of multiple hypotheses in the presence of context data is proposed. In many practical context-based tracking problems where particle filtering is used, the filtering distribution is distinctly multimodal. Several of the state hypotheses may be lost owing to resampling of a finite number of particles, when the target leaves sensor coverage for several timesteps. This is especially the case where there is no sensor coverage in areas of the state space where particle density is low, and tracking is confined to narrow pathways, such as narrow roads and alleyways. The approach followed in this paper is to cluster particles into hypotheses using expectation maximisation of a multivariate Gaussian mixture, and to ensure that the number of particles per cluster is maintained using modified resampling. When no measurements are received for extended periods, two criteria are used to modify resampling to ensure hypothesis maintenance. This first adjusts resampling probabilities such that each hypothesis or cluster has roughly the same number of particles. The second adjusts resampling probabilities such that each hypothesis or cluster has a number of particles proportional to the narrowest dimension of the cluster (minimum eigenvalue of the cluster). This ensures that the particle density of each hypothesis remains roughly the same over all the hypotheses. The particular application will dictate which criterion is the most suitable.

ABSTRACT. This paper provides a comparative analysis between the adaptive birth model used in the labelled random finite set literature and the track initialisation in the Poisson multi-Bernoulli mixture (PMBM) filter. The PMBM track initialisation is obtained via Bayes' rule applied on the predicted PMBM density, and creates one Bernoulli for each received measurement in point-target models. Adaptive birth mimics this procedure by creating a Bernoulli birth for each measurement. However, it uses 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 Bernoulli initialisation 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.

ABSTRACT. This paper proposes two probability correction functions to make adaptively the transition probability matrix(TPM). In a traditional interacting multiple model(IMM) estimator, TPM is usually considered a constant as initial values, so it is conveniently calculated by fixing prior information. However, inaccurate TPM can result in a large target state estimation error. To solve the problem, The IMM algorithm needs to have a time-varying transition probability so that the system model changes promptly according to the target movement. Therefore, a two-stage correction function is designed according to the period. The first phase is the accumulating transition probability correction function which increases the probability of the model matching the target movement and decreases others when the model jump does not occur. The second phase is the activating transition probability correction function which quickly updates the probability when the model jump occurs. By the performance comparison between the proposed adaptive IMM and the traditional IMM, the effect of probability correction functions is confirmed and the performance is improved.

ABSTRACT. In this paper, aiming at the scenario of the multi-target formation penetrates the multi-station radar (MSR) system, a robust jamming beam selection and power scheduling (RJBSPS) strategy is proposed for cooperatively suppressing the MSR system. The purpose of the RJBSPS strategy is to maximize the cooperative jamming performance of the multi-jammer system by optimizing the limited jamming resources. In the jamming environment, the information reduction factor-based posterior Cram\'{e}r-Rao lower bound (PCRLB) provides a lower bound on the accuracy of target state estimation, the sum of the PCRLBs for multiple targets is adopted to evaluate the cooperative jamming performance of the multi-jammer system to the MSR system. In addition, the generalization error caused by the uncertainty of the MSR system parameter estimation is considered and combined with the resource optimization model. The formulated RJBSPS strategy, while subject to the limited jamming resource, is non-convex, due to the coupled parameters. Thus, based on the particle swarm optimization (PSO), a two-step decomposition method is proposed. The simulation results show that the effectiveness and robustness of the proposed robust resource scheduling strategy in terms of degrading the multi-target tracking performance of the MSR system.

ABSTRACT. This paper addresses the problem of the low probability of intercept (LPI) performance optimization for target tracking in the distributed MIMO radar systems through the transmitting resource scheduling (TRS) strategy. The mechanism of the proposed LPI-based TRS strategy is to adopt the optimization technique to collaboratively schedule the transmit radar node and signal power with the target tracking accuracy requirement, which aims to enhance LPI performance of the overall system. Based on the existing papers, here we develop an intercept model to describe the two stages of the signal intercept process with the specific interceptor equipped on the target (intercept and detection). The probability of report (PR) is proposed to evaluate the LPI performance for the transmitting radar node. Then, we use the maximum PR to represent the performance metric for the overall MIMO radar systems. Hence it is used as the objective function to establish the optimization problem with the constraint of target tracking requirement. By introducing the two-step partition-based solution, the proposed non-convex optimization problem is solved efficiently. Finally, several numerical simulations are given to demonstrate the theoretical calculations and to validate the effectiveness of the proposed LPI-based TRS strategy. It is also shown that the LPI performance of the proposed strategy is better than that in the traditional scheduling methods.

ABSTRACT. In this paper, for targets tracking in cluttered environment with colocated MIMO radar network (CMRN), a joint detection threshold optimization and transmit resource allocation (JDTO-TRA) algorithm is proposed to simultaneously maximize tracking performance and minimize resource consumption, whose key mechanism is to adaptively control the working parameters at both the transmitters and the detectors via optimization technique. To be more specific, we formulate the JDTO-TRA as a mixed-integer and non-convex bi-objective optimization problem that is generally intractable. The analytical expression for the posterior Cram\'{e}r-Rao lower bound (PCRLB) incorporated with information reduction factor (IRF), which is caused by the measurement origin uncertainty, under covariance intersection (CI) fusion rule is calculated and adopted as the tracking performance metric. To tackle the formulated problem effectively, we propose an iterative and efficient two-step solution technique incorporating the simulated annealing (SA)-based hybrid particle swarm optimization (HPSO) and the cyclic minimization algorithm (CMA), where the radar-target assignment, the sub-array number and transmit energy of each activated colocated MIMO radar, and the false alarm rate (FAR) of target with respect to radar can be controlled jointly and adaptively. Numerical simulation results are provided to demonstrate the effectiveness as well as the advantages of our proposed JDTO-TRA algorithm compared with other four existing benchmark algorithms.

ABSTRACT. Data fusion in a communication constrained sensor network is considered. The problem is to reduce the dimensionality of the joint state estimate without significantly decreasing the estimation performance. A method based on scalar subspace projections is derived for this purpose. We consider the cases where the estimates to be fused are: (i) uncorrelated, and (ii) correlated. It is shown how the subspaces can be derived using eigenvalue optimization. In the uncorrelated case guarantees on mean square error optimality are provided. In the correlated case an iterative algorithm based on alternating minimization is proposed. The methods are analyzed using parametrized examples. A simulation evaluation shows that the proposed method performs well both for uncorrelated and correlated estimates.

ABSTRACT. This paper presents a private-partial distributed least mean square~(PP-DLMS) algorithm that offers energy efficiency while preserving privacy and is suitable for applications with limited resources and strict security requirements. The proposed PP-DLMS allows every agent to exchange only a fraction of their perturbed data with neighbors during the collaboration process to minimize communication costs and guarantee privacy simultaneously. In order to understand how partial-sharing of perturbed data affects the learning performance, we conduct mean convergence analysis.  Moreover, to investigate the privacy-preserving properties of the proposed algorithm, we characterize agent privacy in the presence of an honest-but-curious (HBC) adversary. Analytical results show that the proposed PP-DLMS is resilient against an HBC adversary by providing a fair energy-privacy trade-off compared to the conventional LMS algorithm. Numerical simulations corroborate the analytical findings. 

ABSTRACT. In complex sound scenes, where multiple sounds are present around a listener, selective attention to one auditory stream is hypothesized to synchronize low-frequency brain activity with the envelope of the attended streams. Recent research has employed stimulus reconstruction from neural data to decode to which auditory stream a listener is paying attention. This could be used to create an auditory attention decoder (AAD), that could be embedded in smart headphones or hearing aids, that would adapt the sound processing based on the attention of the user.

However, most of these studies use full scalp electroencephalogram, with 32 or 64 electrodes, which is bulky for the user, and not suitable for implementations in audio devices. To that aim, a smaller EEG device, with fewer electrodes could be used.

In the present study, we explore the performance of an AAD based on a smaller number of electrodes during speech and music listening. 33 participants were presented with two sounds simultaneously, and spatially separated in the horizontal plane: a target that they were told to pay attention to and a distracter that they were asked to ignore. During the listening, their cortical response was continuously recorded with a 64-channels EEG system. Using a greedy approach based on reconstruction accuracy, a subset of EEG electrodes that are optimized for linear stimulus reconstruction were selected. The goal of this study is to explore the performance of an AAD composed of a limited number of selected electrodes. A second aim is to compare the placement of electrodes optimized for speech or optimized for music, which can help to get a better understanding of cortical processing for speech and music.

Results suggest that four well-selected electrodes can be sufficient for a miniaturized AAD as it performs as well as a 64-channels setup. Channel selection varies depending on the type of sound attended, suggesting that different electrodes placement should be used to decode attention during music listening and speech listening.

ABSTRACT. Linearized Direction of Arrival (LinDoA) is a method for sound source localization that is designed for use with wearable microphone arrays. The method uses a Taylor series expansion of the sound source signal in the time domain to beamform and estimate the direction of arrival. The original method is limited to spatial sampling, but is here generalized to also consider temporal sampling for improved performance and usability. The proposed generalization allows for time-domain formulations of the Delay-and-Sum and minimum-variance distortionless response beamformers in addition to the original formulation by implementing interpolation and estimating the noise covariance. A number of variants of the method are described and the design choices are discussed. The methods are evaluated on data gathered by a head-worn array in real and simulated experiments and are compared to conventional methods. They are shown to perform on par with conventional methods at a reduced computational cost.

ABSTRACT. A tightly integrated magnetic-field aided inertial navigation system is presented.  The system uses a magnetometer sensor array to measure spatial variations in the local magnetic-field.  The variations in the field are --- via a recursively updated polynomial magnetic-field model --- mapped into displacement and orientation changes of the array, which in turn are used to aid the inertial navigation system. Simulation results show that the resulting navigation system has three orders of magnitude lower position error at the end of a 40 seconds trajectory as compared to a standalone inertial navigation system. Thus, the proposed navigation solution has the potential to solve one of the key challenges faced with current magnetic-field simultaneous localization and mapping (SLAM) systems --- the very limited allowable length of the exploration phase during which unvisited areas are mapped.

ABSTRACT. We propose a multistage approach for enhancing speech captured by a drone-mounted microphone array. The key challenge is suppressing the drone ego-noise, which is the major source of interference in such captures. Since the location of the target is not known a priori, we first apply a UNet-based deep-denoising autoencoder (AE) individually to each microphone signal. The AE generates a time-frequency mask in [0,1] per signal, where high values correspond to time-frequency points with relatively good SNRs. The masks are pooled across all microphones and the aggregated mask is used to steer an adaptive, frequency domain beamformer, yielding a signal with an improved SNR. This beamformer output, when fed back to the AE, now yields an improved mask -- which is used for re-focussing the beamformer. This combination of AE and beamformer, which can be applied to the signals in multiple ‘passes’ is termed multistage beamforming. The approach is developed and evaluated on a self-collected database. For the AE - when used to steer a beamformer - a training target that preserves more speech at the cost of less noise suppression outperforms an aggressive training target that suppresses more noise at the cost of more speech distortion. This, in combination with max-pooling of the multi-channel mask -- which also lets through more speech (and noise) compared with median pooling -- performs best. The experiments further demonstrate that the multistage approach brings extra benefit to the speech quality and intelligibility when the input SNR is greater or equal to -10 dB, and yields comprehensible outputs when the input has a SNR above -5 dB.

ABSTRACT. The inverse of the Fisher information, known as the Cramer Rao bound, provides a bound on the estimator of a parameter and is fundamental for statistical analysis. It provides a minimum achievable variance or covariance for a parameter for a univariate or vector-valued parameter. However, multi-target systems often have parameters that are described by functions and the variance and covariance for point processes are themselves functions with spatial variates. Consequently, the usual formulation of the Cram er Rao bound in these contexts is not applicable for providing a bound for the covariance of a point process. In this article we consider commonly used multitarget tracking models and determine Cram er Rao lower bounds on the variance for different parameters, including the detection probabilities, the false alarm intensity, and the intensity of the process. This provides the first application of the Cramer Rao bound for point processes for the analysis of practical algorithms

ABSTRACT. For quantum classification methods, the quantum kernel has a role in encoding the data set from its original low-dimensional real space into a high-dimensional quantum state space utilizing quantum circuits. Finding quantum kernels that provide an advantage in real-world data classification is a major challenge, especially when dealing with heterogeneous data or a large data set, requiring more qubits than are available on current devices.

Here, we propose two new methods: first, we implement a multiple kernel method for data coming from multiple sources, and second, we propose to combine quantum chips to process larger data sets. The latter can be realized by splitting larger quantum circuits into smaller sub-circuits. We experimentally implement a multiple quantum kernel approach for different data sets on IBM quantum computers and benchmark their results.

ABSTRACT. Given is a set of images, where all images show views of the same area at different points in time and from different viewpoints. The task is the alignment of all images such that relevant information, e.g., poses, changes, and terrain, can be extracted from the fused image. In this work, we focus on quantum methods for keypoint extraction and feature matching, due to the demanding computational complexity of these sub-tasks. To this end, k-medoids clustering, kernel density clustering, nearest neighbor search, and kernel methods are investigated and it is explained how these methods can be re-formulated for quantum annealers and gate-based quantum computers. Experimental results obtained on digital quantum emulation hardware, quantum annealers, and quantum gate computers show that classical systems still deliver superior results. However, the proposed methods are ready for the current and upcoming generations of quantum computing devices which have the potential to outperform classical systems in the near future.

ABSTRACT. We consider the problem of assigning n_1 targets to be illuminated by n_2 radars over n_3 time slots with n_1<=n_2<=n_3, whereby no two radars illuminate the same target in the same time slot, as many targets are illuminated each time as possible, and all radars illuminate all targets over the span of all time slots. The problem is formulated as a planar three-index assignment problem. A branch-and-bound algorithm as well as an approximate Lagrangian relaxation algorithm are presented. The Lagrangian relaxation algorithm can efficiently approximate solutions to very large optimization problems.

ABSTRACT. We present a novel Double Deep Q Network (DDQN) application to a sensor management problem in space situational awareness (SSA). Frequent launches of satellites into Earth orbit pose a significant sensor management challenge, whereby a limited number of sensors are required to detect and track an increasing number of objects. In this paper, we demonstrate the use of reinforcement learning to develop a sensor management policy for SSA. We simulate a controllable Earth-based telescope, which is trained to maximise the number of satellites tracked using an extended Kalman filter. The estimated state covariance matrices for satellites observed under the DDQN policy are greatly reduced compared to the those generated by an alternate (random) policy. This work provides the basis for further advancements and motivates the use of reinforcement learning for SSA.

ABSTRACT. This paper presents the motion-based technique to do fusing and matching of multiple ground targets, particularly human, from multiple cameras and other electrooptical devices. The main advantage of this motion-based method over traditional image-based method for matching and re-identification is that there is no prior image-based training required; instead, relatively simpler graph matching algorithms are used. Based on the recently proposed twodimensional kinematics relies solely on the kinematic and geometric projections of the detected targets onto the images captured by the cameras. Matching and re-identification across frames are done using a series of correlation-based methods. This method is suitable for all targets with distinct motion observed by the cameras. This work extends the applications to match and re-identify multiple human targets on the ground and ships targets in the sea (2D plane).

ABSTRACT. This paper aims at adressing specific issues of extended target tracking. Firstly, we propose a method to accurately model the origin of the measurements on the surface of the target. This is achieved by removing the usual hypothesis of the independence of the association of the measurements to possible measurement sources to allow us to assume that a certain number of measurements shall be originating from some specific sources. Secondly, a Gaussian distribution is a poor representation for the length of a target. We developed a method discretizing the length to estimate its distribution without the Gaussian assumption but avoiding the computational burden of a multi-hypothesis tracking for each target. The implementation effectiveness is shown on simulated as well as real data from RADAR.

ABSTRACT. In this paper, approximating the shape of a sailing boat using elliptical cones is investigated. Measurements are assumed to be gathered from the targets surface recorded by 3D scanning devices such as multilayer LiDAR sensors. Therefore, different models for estimating the sailing boats extent are presented and evaluated in simulated and real-world scenarios. In particular, the measurement source association problem is addressed in the models. Simulated investigations are conducted with a static and a moving elliptic cone. The real world scenario was recorded with a Velodyne Alpha Prime (VLP-128) mounted on a ferry of Lake Constance. Final results of this paper constitute the extent estimation of a single sailing boat using LiDAR data applying various measurement models.

ABSTRACT. In some defence applications, it is required to identify targets separated by a certain distance as group-targets. This allows the system to use a suitable tracking and mitigation strategy for a group different from what is used for a point-target. A natural choice to identify a group of this type is the density-based spatial clustering of applications with noise (DBSCAN) algorithm. The DBSCAN algorithm uses the available track information to identify the groups/clusters. Information on these tracks are, in the vast majority of tracking systems, based on the Kalman filter estimate. In this work, we present a scenario where the out-group target is inseparable from the group-target using a Kalman filter. Thereafter, we show that the separability could be significantly improved using the estimates of the joint probability density of the kinematic target states accumulated over a certain time window, up to the present time, given the time series of all sensor data. These densities are known as Accumulated State Densities (ASDs).

ABSTRACT. Distributed acoustic sensing (DAS) has been shown to be a reliable tool for monitoring highways traffic in an efficient and cost-effective fashion. Nevertheless, multiple-lane highways and noise sources reduce the vehicle detection capabilities of DAS sensors, especially in high-traffic scenarios. In this paper, we propose a novel approach derived from harmonic analysis techniques to estimate vehicle trajectories from DAS data. Our method aims to detect closely-spaced lines by iteratively notching the contribution of the lines already estimated. The results show the remarkable performance of the proposed method compared to the Hough transform, proving the potential of the notched power vehicle detector in a wide range of noise levels.

ABSTRACT. We present a novel nonparametric scheme for modeling circular random variables. For that, the circular Cramér-von Mises distance (CCvMD) is proposed to measure the statistical divergence between two circular discrete models based on a smooth characterization of the localized cumulative distribution. Given a set of weighted samples from empirical data, the underlying unknown distribution is then reapproximated by another sample set of configurable size and dispersion-adaptive layout in the sense of least CCvMD. Built upon the proposed circular discrete reapproximation (CDR), a new method is introduced for density estimation with von Mises mixtures. Moreover, the CDR scheme is extended to topological spaces composing the unit circle and Euclidean space of arbitrary dimension, and a new regression model for random circular vector fields is proposed based thereon. We provide case studies using synthetic and real-world data from wind climatology. Numerical results validate the efficacy of proposed approaches with promising potential of outperforming competitive methods.

ABSTRACT. Estimating the position and orientation of 3-D objects is a ubiquitous challenge. In our novel filter, the position and orientation of objects are modeled using the Cartesian product of R^3 for the position and a 3-D hyperhemisphere. The latter is used to describe orientations in the form of unit quaternions. The hyperhemisphere is subdivided into equally sized areas. The joint density for the position and orientation is split up into a marginal density for the orientation and a density for the position that is conditioned on the orientation. In our filter, we assume that the function values of the marginal density and the conditional density is the same for all points within that area. By assuming all conditional densities to be Gaussians, efficient formulae can be implemented for the update and prediction steps. The filter is evaluated based on a simulation scenario, for which it showed very high accuracy at low run times.

ABSTRACT. Satellite navigation has become a widely used resource in many fields. However, satellite signals are vulnerable to different interference sources, both intentional and unintentional. In safety critical situations such as rescue and tactical operations a robust alternative for Global Navigation Satellite Systems (GNSS) is needed. In this work we use magnetometers and Ultra Wideband ranging together with inertial sensors in cooperative manner for heading estimation in infrastructure independent pedestrian navigation. We utilize von Mises-Fisher distribution in order to appropriately model directions, and use a particle filter for state estimation. We demonstrate our distributed and scalable approach in two real-life tests, partially GNSS-denied outdoor navigation scenario and indoor navigation scenario. The results show that with appropriate modeling it is possible to estimate heading in a robust manner and correct for heading drift typical in footmounted pedestrian dead reckoning.

ABSTRACT. We define morphological operators and filters for directional images whose pixel values are vectors on the unit sphere. This requires an ordering relation for unit vectors which is obtained by using depth functions. They provide a centreoutward ordering with respect to a specified centre vector. We apply our operators on synthetic directional images and compare them with classical morphological operators for greyscale images. As application example, we enhance the fault region in a compressed glass foam.

ABSTRACT. In this paper, novel association and fusion methods for range-azimuth tracks are proposed. The association method requires calculating the distance between two tracks which lack the elevation information. An iterative algorithm is proposed to find the closest distance between the two arcs defined by the range azimuth tracks. This procedure provides an auxiliary elevation information for the associated tracks which is also used for track fusion process. The performance of the algorithms is illustrated in experiments with simulated data.