Variational Gaussian filter (VGF) approximates the intractable posterior of the state of a non-linear non-Gaussian system using a single Gaussian density normally found through Kullback-Leibler divergence minimization. This paper focuses on the VGFs whose measurement update is realized by employing the natural gradient descent (NGD). Under the assumption that the state predictive distribution is also Gaussian, we re-examine the iterative NGD-based measurement update under two different parameterizations of the Gaussian posterior. The first one consists of the mean and covariance, while the other comprises the mean and precision matrix (i.e., the inverse of the covariance). Their NGD-based update rules are derived in an alternative but unified way using matrix calculus. They are compared against each other and with the one developed using the natural parameterization of the Gaussian density. Important new insights are obtained. Modifications to the established update rules, which guarantee the positive definiteness of the covariance/precision matrix of the Gaussian posterior, are re-visited as well. Simulations are used to corroborate the theoretical results and evaluate the performance of the developed algorithms in range-bearing tracking.

This paper introduces a new variational Gaussian filtering approach for estimating the state of a nonlinear dynamic system. We first assume that the predictive distribution of the state is Gaussian and derive an iterative method for updating the state posterior in the natural parameter space through KullbackLeibler divergence minimization. The obtained update rule is the same as that of the conjugate-computation variational inference technique in Bayesian learning. The derivation here is simpler and more insightful. We then impose a Wishart prior on the inverse of the state prediction covariance to take into account the impact of approximating the state predictive distribution using a Gaussian density on the state posterior estimation. The prediction covariance is identified jointly with the state using variational inference and the established state posterior update rule to achieve the desired Gaussian filtering. Simulation study examines the performance of the proposed filtering framework in target tracking based on bearing and range measurements.

Active sensing plays an essential role in searching and tracking a target without initial target state information. This paper studies the active sensing approach for sensor management problems using multiple unmanned aerial vehicles based on the received signal strength measurements of the target. A Bayesian optimisation-based approach is proposed which adopts the Gaussian process method to model the received signal strength in an area over time and then the expected improvement acquisition function is leveraged to decide where to take new measurements considering the uncertainty of the Gaussian process. A unique contribution of this paper consists of the designed spatial-temporal composite kernel function that accounts for the time-varying nature of the signal strength. Numerical results obtained from different measurement noise levels and varying initial Bayesian optimisation settings demonstrate that the proposed approach can efficiently schedule multiple unmanned aerial vehicles to locate the target within a minimum number of initial data. Particularly, it achieves at most $57 \%$ lower tracking error and $46 \%$ lower lost-track probability as compared to the benchmark approach.

This paper explores the application of centralised and distributed Gaussian process algorithms to real-time target tracking and compares their performance. By embedding the algorithms into the Stone Soup, the focus is on the innovative implementation of Gaussian process methods with learning hyperparameters and implementation with a factorised variance of the Gaussian kernel. The performance of the methods with different kernels was evaluated, not only with the Gaussian kernel. Extensive experiments with various kernel configurations demonstrate their importance in enhancing prediction accuracy and efficiency, especially in real-time tracking. The case studies with manoeuvring targets show significant advancements in tracking capabilities, particularly in wireless sensor networks, using optimised Gaussian process methods. This work advances Stone Soup’s capabilities and lays the groundwork for future investigations into adaptive Gaussian Process applications in tracking and sensor data analysis.

The quotient of two multivariate Gaussian densities can be written as an unnormalized Gaussian density, which has been applied in some recently developed multiple-model fixed-interval smoothing algorithms. However, this expression is invalid if instead of being positive definite, the covariance of the unnormalized Gaussian density is indefinite (i.e., it has both positive and negative eigenvalues) or undefined (i.e., computing it requires inverting a singular matrix). This paper considers approximating the quotient of two Gaussian densities in this case using two different approaches to mitigate the caused numerical problems. The first approach directly replaces the indefinite covariance of the unnormalized Gaussian density with a positive definite matrix nearest to it. The second approach computes the approximation through solving, using the natural gradient, an optimization problem with a Kullback-Leibler divergence-based cost function. This paper illustrates the application of the theoretical results by incorporating them into an existing smoothing method for jump Markov systems and utilizing the obtained smoothers to track a maneuvering target.

Fine-grained plant pathology classification is an important task for precision agriculture, but at the same time, it is challenging due to the subtle difference in plant categories. Variances in the lighting conditions, position, and stages of disease symptoms usually lead to degradation of classification accuracy. Knowledge distillation is a popular method to improve the model performance to deal with the indistinguishable image classification problem. It aims to have a well-optimised small student network guided by a large teacher network. Existing knowledge distillation methods mainly consider training a teacher network that needs a high storage space and considerable computing resources. Self-knowledge distillation methods have been proposed to distil knowledge from the same network. Although self-knowledge distillation saves time and space compared with knowledge distillation, it only learns label knowledge. In this paper, we propose a novel self-distillation method to recognize the fine-grained plant category, which considers holistic knowledge based on the Squeeze and Excitation Network. We label this new method as holistic self-distillation because it captures knowledge through spatial features and labels. The performance validation of the proposed approach is performed on two public fine-grained plant datasets: Plant Pathology 2021 and Plant Pathology 2020 with the accuracy of 98.22% and 90.72% respectively. We also present experiments on the state-of-the-art algorithm (ResNet-50). The classification results demonstrate the effectiveness of the proposed approach with respect to accuracy.

The superior performance of object detectors is often established under the condition that the test samples are in the same distribution as the training data. However, in many practical applications, out-of-distribution (OOD) instances are inevitable and usually lead to uncertainty in the results. In this paper, we propose a novel, intuitive, and scalable probabilistic object detection method for OOD detection. Unlike other uncertainty-modeling methods that either require huge computational costs to infer the weight distributions or rely on model training through synthetic outlier data, our method is able to distinguish between in-distribution (ID) data and OOD data via weight parameter sampling from proposed Gaussian distributions based on pre-trained networks. We demonstrate that our Bayesian object detector can achieve satisfactory OOD identification performance by reducing the FPR95 score by up to 8.19% and increasing the AUROC score by up to 13.94% when trained on BDD100k and VOC datasets as the ID datasets and evaluated on COCO2017 dataset as the OOD dataset.

The application of multiple target tracking algorithms has exponentially increased during the last two decades. Recently, model-free approaches, such as Gaussian process regression and convolutional neural networks, have been developed for target tracking. This paper presents a simulation-based study on the practical aspects of a very promising and recently proposed Gaussian process method, namely the Gaussian process motion tracker [1]. The paper also provides design guidelines on the various aspects of the above-mentioned tracking method.

Sleep apnea is a sleep disorder which is common in many children and adults. It is characterised by abnormal breath pauses or shallow breathing during sleep. Traditional diagnosis of apnea requires special equipment for data collection in clinical conditions and manual analysis by clinicians which is expensive and time-consuming. This paper presents a framework for autonomous detection of sleep apnea, using peripheral blood haemoglobin oxygen saturation (SpO2) data based on the fusion of multiple features and Dirichlet process mixture model. The SpO2signals are segmented into overlapping sub-sequences and several features are extracted from each segment. The distributions of features extracted from disorder and normal segments are modelled by two Gaussian mixture models, respectively, with the Dirichlet process as the prior. The advantage of the framework is that the number of clusters within mixture models can be learned from training data without strong assumptions, which contributes to accurate estimation of the distributions. The proposed framework is subject-independent and it is trained and tested on two publicly available databases with 10-fold cross-validation. It obtains accuracy of 84.89% on the St. Vincent's University Hospital Sleep Apnea Database and accuracy of 97.01% on the Apnea-ECG Database, outperforming state-of-the-art approaches. The results show that the proposed model is capable of representing the distributions of features independently of subjects and can accurately classify segmented signals from patients with symptoms of different severity. The results show the potential of the developed classification framework to support clinicians in their decision making.

The Schmidt-Kalman filter (SKF) achieves filtering consistency in the presence of biases in system dynamic and measurement models through accounting for their impacts when updating the state estimate and covariance. However, the performance of the SKF may break down when the measurements are subject to non-Gaussian and heavy-tail noise. To address this, we impose the Wishart prior distribution on the precision matrix of measurement noise, such that the measurement likelihood now has heavier tails than the Gaussian distribution to deal with the potential occurrence of outliers. Variational inference is invoked to establish analytically tractable methods for computing the posterior of the system state, system biases, and the measurement noise precision matrix. The principle of the SKF considers the effect of system biases but does not actively estimate them when two variants of outlier-robust SKFs are incorporated. We evaluate their performance in terms of estimation accuracy and filtering consistency using simulations and real-world data. Promising results are obtained.

This paper proposes a computer vision framework aimed to segment hot steel sections and contribute to rolling precision. The steel section dimensions are calculated for the purposes of automating a high temperature rolling process. A structured forest algorithm along with the developed steel bar edge detection and regression algorithms extract the edges of the high temperature bars in optical videos captured by a GoPro® camera. To quantify the impact of noises that affect the segmentation process and the final diameter measurements, a weighted variance is calculated, providing a level of trust in the measurements. The results show an accuracy which is in line with the rolling standards, i.e. with a root mean square error less than 2.5 mm.

Many types of cancers such as multiple myeloma cause bone destruction, resulting in pain and fractures in patients and increased fatality. To quantify the degree of bone disease caused by cancer and analyse treatment response for bone repairing, accurate knowledge of the volumetry of all lesions is needed. To this end, this study proposes to apply two main approaches to the segmentation of bone lesions in cancer-induced bone disease from Micro Computed Tomography (μCT) images - structured forest-based edge detection approach and deep learning approach. A fast edge detection approach with structured forest, an extension of [1], is applied to identify the volumetry of all lesions in mice tibia, where the obtained results are evaluated against the manually labelled data, demonstrating the efficiency of the compared approaches. The Gaussian processes (Convnet GP) approach has achieved the best performance among the compared approaches, with 99.6% intersection of union and 99.7% precision. Our results demonstrate that the developed approach provides a reasonable delineation of the samples, showing the great potential towards fully automatic bone tumour segmentation.

Location-based applications attract more and more attention in recent years. Examples of such applications include commercial advertisements, social networking software and patient monitoring. The received signal strength (RSS) based location fingerprinting is one of the most popular solutions for indoor localization. However, there is a big challenge in collecting and maintaining a relatively large RSS fingerprint database. In this work, we propose and compare two algorithms namely, the Gaussian process (GP) and Gaussian process with variogram, to estimate and construct the RSS fingerprints with incomplete data. The fingerprint of unknown reference points is estimated based on measurements at a limited number of surrounding locations. To validate the effectiveness of both algorithms, experiments using Bluetooth-low-energy (BLE) infrastructure have been conducted. The constructed RSS fingerprints are compared to the true measurements, and the result is analyzed. Finally, using the constructed fingerprints, the localization performance of a probabilistic fingerprinting method is evaluated.

Extended object tracking has become an integral part of various autonomous systems in diverse fields. Although it has been extensively studied over the past decade, many complex challenges remain in the context of extended object tracking. In this paper, a new method for tracking multiple irregularly shaped extended objects using surface measurements is proposed. The Gaussian Process Convolution Particle Filter proposed in [1], designed to track a single extended/group object, is enhanced for tracking multiple extended objects. A convolution kernel is proposed to estimate the multi-object likelihood. A target birth/death model based on the proposed method is also introduced for automatic initiation and deletion of the objects. The proposed approach is validated on real-world LiDAR data which shows that the method is efficient in tracking multiple irregularly shaped extended objects in challenging scenarios involving occlusion, dense clutter and low object detection.

Vehicle logo recognition is an important part of vehicle identification in intelligent transportation systems. State-of-the-art vehicle logo recognition approaches use automatically learned features from Convolutional Neural Networks (CNNs). However, CNNs do not perform well when images are rotated and very noisy. This paper proposes an image recognition framework with a capsule network. A capsule is a group of neurons, whose length can represent the existence probability of an entity or part of an entity. The orientation of a capsule contains information about the instantiation parameters such as positions and orientations. Capsules are learned by a routing process, which is more effective than the pooling process in CNNs. This paper, for the first time, develops a capsule learning framework in the field of intelligent transportation systems. By testing with the largest publicly available vehicle logo dataset, the proposed framework gives a quick solution and achieves the highest accuracy (100%) on this dataset. The learning capsules have been tested with different image changes such as rotation and occlusion. Image degradations including blurring and noise effects are also considered, and the proposed framework has proven to be superior to CNNs.

In this paper, a novel robust Rauch-Tung-Striebel smoother is proposed based on the Slash and generalized hyperbolic skew Student's t-distributions. A novel hierarchical Gaussian state-space model is constructed by formulating the Slash distribution as a Gaussian scale mixture form and formulating the generalized hyperbolic skew Student's t-distribution as a Gaussian variance-mean mixture form, based on which the state trajectory, mixing parameters and unknown noise parameters are jointly inferred using the variational Bayesian approach. The posterior probability density functions of mixing parameters of the Slash and generalized hyperbolic skew Student's t-distributions are, respectively, approximated as truncated Gamma and generalized inverse Gaussian. Simulation results illustrate that the proposed robust Rauch-Tung-Striebel smoother has better estimation accuracy than existing state-of-the-art smoothers.

Sign language is a visually oriented, natural, nonverbal communication medium. Having shared similar linguistic properties with its respective spoken language, it consists of a set of gestures, postures and facial expressions. Though, sign language is a mode of communication between deaf people, most other people do not know sign language interpretations. Therefore, it would be constructive if we can translate the sign postures artificially. In this paper, a capsule-based deep neural network sign posture translator for an American Sign Language (ASL) fingerspelling (posture), has been presented. The performance validation shows that the approach can successfully identify sign language, with accuracy like 99%. Unlike previous neural network approaches, which mainly used fine-tuning and transfer learning from pre-trained models, the developed capsule network architecture does not require a pre-trained model. The framework uses a capsule network with adaptive pooling which is the key to its high accuracy. The framework is not limited to sign language understanding, but it has scope for non-verbal communication in Human-Robot Interaction (HRI) also.

Bayesian filters can be made robust to outliers if the solutions are developed under the assumption of heavy-tailed distributed noise. However, in the absence of outliers, these robust solutions perform worse than the standard Gaussian assumption based filters. In this work, we develop a novel robust filter that adopts both Gaussian and multivariate t-distributions to model the outliers contaminated measurement noise. The effects of these distributions are combined within a Bayesian Model Averaging (BMA) framework. Moreover, to reduce the computational complexity of the proposed algorithm, a restricted variational Bayes (RVB) approach handles the multivariate t-distribution instead of its standard iterative VB (IVB) counterpart. The performance of the proposed filter is compared against a standard cubature Kalman filter (CKF) and a robust CKF (employing IVB method) in a representative simulation example concerning target tracking using range and bearing measurements. In the presence of outliers, the proposed algorithm shows a 38 % improvement over CKF in terms of root-mean-square-error (RMSE) and is computationally 2.5 times more efficient than the robust CKF.

Gaussian process regression is a machine learning approach which has been shown its power for estimation of unknown functions. However, Gaussian processes suffer from high computational complexity, as in a basic form they scale cubically with the number of observations. Several approaches based on inducing points were proposed to handle this problem in a static context. These methods though face challenges with real-time tasks and when the data is received sequentially over time. In this paper, a novel online algorithm for training sparse Gaussian process models is presented. It treats the mean and hyperparameters of the Gaussian process as the state and parameters of the ensemble Kalman filter, respectively. The online evaluation of the parameters and the state is performed on new upcoming samples of data. This procedure iteratively improves the accuracy of parameter estimates. The ensemble Kalman filter reduces the computational complexity required to obtain predictions with Gaussian processes preserving the accuracy level of these predictions. The performance of the proposed method is demonstrated on the synthetic dataset and real large dataset of UK house prices.

For several economical, financial and operational reasons, forecasting energy demand becomes a key instrument in energy system management. This paper develops a natural gas forecasting approach, which consists of two major phases: 1) it classifies the natural gas consumption daily pattern sequences into different groups with similar attributes. 2) the design and training of multiple autoregressive Gaussian Process models phase is carried out using the Algerian natural gas market data together with exogenous inputs consisting in weather (temperature) and calendar (day of the week, hour indicator) factors. The main novelty in this work consists of the investigation of multiple different clustering techniques for better analysis and clustering of natural gas consumption data. The impact of the obtained clusters, by each technique, is then summarized and evaluated with respect to the prediction accuracy.

The Gaussian mixture model (GMM) has been extensively investigated in nonlinear/non-Gaussian filtering problems. This paper presents two enhancements for GMM-based nonlinear filtering techniques, namely, the adaptive ordering of the measurement update and normalized innovation square (NIS)-based mixture component management. The first technique selects the order of measurement update by maximizing the marginal measurement likelihood to improve performance. The second approach takes the filtering history of a mixture component into account and prunes those components with NIS larger than a threshold to eliminate their impact on the filtering posterior. The advantage of the proposed enhancements is illustrated via simulations that consider source tracking using the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements received at two unmanned aerial vehicles (UAVs). A GMM-cubature quadrature Kalman filter (CQKF) is implemented and its performances with different measurement update and mixture component management strategies are compared. The superior performance obtained via the use of the two proposed techniques is demonstrated.

Synthetic Aperture Radar (SAR) satellite systems are very efficient in oil spill monitoring due to their capability to operate under all weather conditions. This paper presents a framework using Gaussian process (GP) to fuse SAR images of different modalities and to segment dark areas (assumed oil spill) for oil spill detection. A new covariance function; a product of an intrinsically sparse kernel and a Rational Quadratic Kernel (RQK) is used to model the prior of the estimated image allowing information to be transferred. The accuracy performance evaluation demonstrates that the proposed framework has 37% less RMSE per pixel and a compelling enhancement visually when compared with existing methods.

Traffic prediction approaches face challenges when presented with sparse or missing data. This can be caused by numerous factors such as: i) sensors not being operational; ii) communication issues; iii) cost prohibiting full monitoring of a road network. This present work adds to existing body of knowledge by proposing a particle based framework for dealing with these challenges. An expression of the likelihood function is derived for the case when the missing value is calculated based on Kriging interpolation. With the Kriging interpolation, the missing values of the measurements are predicted, which are subsequently used in the computation of likelihood terms in the particle filter algorithm. The results show 23% to 36.34% improvement in RMSE values for the synthetic data used.

Vehicle logo recognition is an important part of vehicle identification in intelligent transportation systems. State-of-the-art vehicle logo recognition approaches typically consider training models on large datasets. However, there might only be a small training dataset to start with and more images can be obtained during the real-time applications. This paper proposes an online image recognition framework which provides solutions for both small and large datasets. Using this recognition framework, models are built efficiently using a weight updating scheme. Another novelty of this work is that the Cauchy prior logistic regression with conjugate gradient descent is proposed to deal with the multinomial classification tasks. The Cauchy prior results in a quicker convergence speed for the weight updating process which could decrease the computational cost for both online and offline methods. By testing with a publicly available dataset, the Cauchy prior logistic regression deceases the classification time by 59%. An accuracy of up to 98.80% is achieved when the proposed framework is applied.

Advances in sensor systems have resulted in the availability of high resolution sensors, capable of generating massive amounts of data. For complex systems to run online, the primary focus is on computationally efficient filters for the estimation of latent states related to the data. In this paper a novel method for efficient state estimation with the unscented Kalman Filter is proposed. The focus is on applications consisting of a massive amount of data. From a modelling perspective, this amounts to a measurement vector with dimensionality significantly greater than the dimensionality of the state vector. The efficiency of the filter is derived from a parallel filter structure which is enabled by the expectation propagation algorithm. A novel parallel measurement processing expectation propagation unscented Kalman filter is developed. The primary advantage of the novel algorithm is in the ability to achieve computational improvements with negligible loses in filter accuracy. An example of robot localization with a high resolution laser rangefinder sensor is presented. A 47.53% decrease in computational time was exhibited for a scenario with a processing platform consisting of 4 processors, with a negligible loss in accuracy.

Traffic control and vehicle route planning require accurate estimates of the traffic state in order to be successfully implemented. This estimation problem can be solved by using particle filters in conjunction with macroscopic traffic models such as the stochastic compositional model. The accuracy of the estimates can be decreased for road segments where there are no measurements available. However, the inclusion of measurements for all segment boundaries carries a computational cost associated with the evaluation of the likelihood function required by the particle filter. To solve this problem, this paper proposes using the column based matrix decomposition method to select the most significant locations in the road network. This results in the particle filter being applied over a reduced measurement space, allowing a trade-off between computational efficiency and estimation accuracy to be achieved. A performance evaluation based on a simulated stretch of road is provided to validate the proposed method. It shows that by selecting half the original number of measurements, the computational time is reduced by approximately 9% without significantly decreasing the estimation accuracy. A more significant improvement in terms of savings in computational complexity can be expected when considering larger urban road networks.

In this paper we present a method for the tracking of interacting targets disregarding whether or not the targets are close to each other. The method relies on parametric modeling of assumptions about targets interactive motion. Our filtering solution incorporates the parameters of the model in the state vector to perform on-line parameter estimation and exploitation. The proposed method is applied in a simulated Multiple Target Tracking application with radar track-before-detect measurements. Numerical experiments show that this approach results in estimation error reduction, allows detection of interactive target behaviors and reduce labeling uncertainty in closely-spaced targets tracking.

This paper considers locating a static source on Earth using the time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements obtained by a dual-satellite geolocation system. The TDOA and FDOA from the source are subject to unknown time and frequency offsets because the two satellites are imperfectly time-synchronized or frequency-locked. The satellite locations are not known accurately as well. To make the source position identifiable and mitigate the effect of satellite location errors, calibration stations at known positions are used. Achieving the maximum likelihood (ML) geolocation performance usually requires jointly estimating the source position and extra variables (i.e., time and frequency offsets as well as satellite locations), which is computationally intensive. In this paper, a novel closed-form geolocation algorithm is proposed. It first fuses the TDOA and FDOA measurements from the source and calibration stations to produce a single pair of TDOA and FDOA for source geolocation. This measurement fusion step eliminates the time and frequency offsets while taking into account the presence of satellite location errors. The source position is then found via standard TDOA-FDOA geolocation. The developed algorithm has low complexity and performance analysis shows that it attains the Cramér-Rao lower bound (CRLB) under Gaussian noises and mild conditions. Simulations using a challenging scenario with a short-baseline dual-satellite system verify the theoretical developments and demonstrate the good performance of the proposed algorithm.

This paper addresses the problem of object tracking in video sequences. The use of a structural similarity measure for tracking is proposed. The measure reflects the distance between two images by comparing their structural and spatial characteristics and has shown to be robust to illumination and contrast changes. As a result it guarantees robustness of the tracking process under changes in the environment. The previously used Bhattacharyya distance is not robust to such changes. Additionally, when a tracker is run with the Bhattacharyya distance, histograms should be calculated in order to find the likelihood function of the measurements. With the new function there is no need to calculate histograms. A particle filter (PF) is implemented where this measure is used for computing the distance between the reference and current frame. The algorithm performance has been tested and evaluated over real-world video sequences, and has been shown to outperform methods based on colour and edge histograms

This paper addresses the problem of position localisation of mobile nodes in ad hoc wireless networks based on received signal strength indicator measurements. Node mobility is modelled as a linear system driven by a discrete command Markov process. Self-localisation of mobile nodes is performed via an interacting multiple model filter consisting of a bank of unscented Kalman filters (IMM-UKF). Estimation of the mobility state, which comprises the position, speed and acceleration of the mobile nodes is accomplished. The performance of the IMM- UKF filter is investigated and compared to a multiple model particle filter (MM PF) by Monte Carlo simulation