Correntropy: Answer to non-Gaussian noise in modern SLAM applications?

The problem of non-Gaussian noise/outliers has been intrinsic in modern Simultaneous Localization and Mapping (SLAM) applications. Despite numerous algorithms in SLAM, it has become crucial to address this problem in the realm of modern robotics applications. This work focuses on addressing the above-mentioned problem by incorporating the usage of correntropy in SLAM. Before correntropy, multiple attempts of dealing with non-Gaussian noise have been proposed with significant progress over time but the underlying assumption of Gaussianity might not be enough in real-life applications in robotics.Most of the modern SLAM algorithms propose the `best' estimates given a set of sensor measurements. Apart from addressing the non-Gaussian problems in a SLAM system, our work attempts to address the more complex part concerning SLAM: (a) If one of the sensors gives faulty measurements over time (`Faulty' measurements can be non-Gaussian in nature), how should a SLAM framework adapt to such scenarios? (b) In situations where there is a manual intervention or a 3rd party attacker tries to change the measurements and affect the overall estimate of the SLAM system, how can a SLAM system handle such situations?(addressing the Self Security aspect of SLAM). Given these serious situations how should a modern SLAM system handle the issue of the previously mentioned problems in (a) and (b)? We explore the idea of correntropy in addressing the above-mentioned problems in popular filtering-based approaches like Kalman Filters(KF) and Extended Kalman Filters(EKF), which highlights the `Localization' part in SLAM. Later on, we propose a framework of fusing the odometeries computed individually from a stereo sensor and Lidar sensor (Iterative Closest point Algorithm (ICP) based odometry). We describe the effectiveness of using correntropy in this framework, especially in situations where a 3rd party attacker attempts to corrupt the Lidar computed odometry. We extend the usage of correntropy in the `Mapping' part of the SLAM (Registration), which is the highlight of our work. Although registration is a well-established problem, earlier approaches to registration are very inefficient with large rotations and translation. In addition, when the 3D datasets used for alignment are corrupted with non-Gaussian noise (shot/impulse noise), prior state-of-the-art approaches fail. Our work has given birth to another variant of ICP, which we name as Correntropy Similarity Matrix ICP (CoSM-ICP), which is robust to large translation and rotations as well as to shot/impulse noise. We verify through results how well our variant of ICP outperforms the other variants under large rotations and translations as well as under large outliers/non-Gaussian noise. In addition, we deploy our CoSM algorithm in applications where we compute the extrinsic calibration of the Lidar-Stereo sensor as well as Lidar-Camera calibration using a planar checkerboard in a single frame. In general, through results, we verify how efficiently our approach of using correntropy can be used in tackling non-Gaussian noise/shot noise/impulse noise in robotics applications

Approximate Gaussian conjugacy: parametric recursive filtering under nonlinearity, multimodality, uncertainty, and constraint, and beyond

Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

Sensory fusion applied to power system state estimation considering information theory concepts

With the increasing integration of synchronized phasor measurement units (PMU) in power grids appears the necessity to create methods capable to merge the information obtained from different classes of sensors, namely PMU and the conventional sensors already integrated in the SCADA system. Thus, this dissertation proposes a sensory fusion that guarantees the previous requirement. Beyond that, this thesis proposes an application of concepts related with Information theory to the state estimation problem. This application aims to propose a robust state estimator without the necessity of previous treatment of the acquired data

Novel Computational Methods for State Space Filtering

The state-space formulation for time-dependent models has been long used invarious applications in science and engineering. While the classical Kalman filter(KF) provides optimal posterior estimation under linear Gaussian models, filteringin nonlinear and non-Gaussian environments remains challenging.Based on the Monte Carlo approximation, the classical particle filter (PF) can providemore precise estimation under nonlinear non-Gaussian models. However, it suffers fromparticle degeneracy. Drawing from optimal transport theory, the stochastic map filter(SMF) accommodates a solution to this problem, but its performance is influenced bythe limited flexibility of nonlinear map parameterisation. To account for these issues,a hybrid particle-stochastic map filter (PSMF) is first proposed in this thesis, wherethe two parts of the split likelihood are assimilated by the PF and SMF, respectively.Systematic resampling and smoothing are employed to alleviate the particle degeneracycaused by the PF. Furthermore, two PSMF variants based on the linear and nonlinearmaps (PSMF-L and PSMF-NL) are proposed, and their filtering performance is comparedwith various benchmark filters under different nonlinear non-Gaussian models.Although achieving accurate filtering results, the particle-based filters require expensive computations because of the large number of samples involved. Instead, robustKalman filters (RKFs) provide efficient solutions for the linear models with heavy-tailednoise, by adopting the recursive estimation framework of the KF. To exploit the stochasticcharacteristics of the noise, the use of heavy-tailed distributions which can fit variouspractical noises constitutes a viable solution. Hence, this thesis also introduces a novelRKF framework, RKF-SGαS, where the signal noise is assumed to be Gaussian and theheavy-tailed measurement noise is modelled by the sub-Gaussian α-stable (SGαS) distribution. The corresponding joint posterior distribution of the state vector and auxiliaryrandom variables is estimated by the variational Bayesian (VB) approach. Four differentminimum mean square error (MMSE) estimators of the scale function are presented.Besides, the RKF-SGαS is compared with the state-of-the-art RKFs under three kinds ofheavy-tailed measurement noises, and the simulation results demonstrate its estimationaccuracy and efficiency.One notable limitation of the proposed RKF-SGαS is its reliance on precise modelparameters, and substantial model errors can potentially impede its filtering performance. Therefore, this thesis also introduces a data-driven RKF method, referred to asRKFnet, which combines the conventional RKF framework with a deep learning technique. An unsupervised scheduled sampling technique (USS) is proposed to improve theistability of the training process. Furthermore, the advantages of the proposed RKFnetare quantified with respect to various traditional RKFs

Development of nonlinear techniques based on time-frequency representation and information theory for the analysis of EEG signals to assess different states of consciousness

Electroencephalogram (EEG) recordings provide insight into the changes in brain activity associated with various states of anesthesia, epilepsy, brain attentiveness, sleep disorders, brain disorders, etc. EEG's are complex signals whose statistical properties depend on both space and time. Their randomness and non-stationary characteristics make them impossible to be described in an accurate way with a simple technique, requiring analysis and characterization involves techniques that take into account their non-stationarity. For that, new advanced techniques in order to improve the efficiency of the EEG based methods used in the clinical practice have to be developed. The main objective of this thesis was to investigate and implement different methods based on nonlinear techniques in order to develop indexes able to characterize the frequency spectrum, the nonlinear dynamics and the complexity of the EEG signals recorded in different state of consciousness. Firstly, a new method for removing peak and spike in biological signal based on the signal envelope was successfully designed and applied to simulated and real EEG signals, obtaining performances significantly better than the traditional adaptive filters. Then, several studies were carried out in order to extract and evaluate EEG measures based on nonlinear techniques in different contexts such as the automatic detection of sleepiness and the characterization and prediction of the nociceptive stimuli and the assessment of the sedation level. Four novel indexes were defined by calculating entropy of the Choi-Williams distribution (CWD) with respect to time or frequency, by using the probability mass function at each time instant taken independently or by using the probability mass function of the entire CWD. The values of these indexes tend to decrease, with different proportion, when the behavior of the signals evolved from chaos or randomness to periodicity and present differences when comparing EEG recorded in eyes-open and eyes-closed states and in ictal and non-ictal states. Measures obtained with time-frequency representation, mutual information function and correntropy, were applied to EEG signals for the automatic sleepiness detection in patients suffering sleep disorders. The group of patients with excessive daytime sleepiness presented more power in ¿ band than the group without sleepiness, which presented higher spectral and cross-spectral entropy in the frontal zone in d band. More complexity in the occipital zone was found in the group of patients without sleepiness in ß band, while a stronger nonlinear coupling between the occipital and frontal regions was detected in patients with excessive daytime sleepiness, in ß band. Time-frequency representation and non-linear measures were also used in order to study how adaptation and fatigue affect the event-related brain potentials to stimuli of different modalities. Differences between the responses to infrequent and frequent stimulation in different recording periods were found in series of averaged EEG epochs recorded after thermal, electrical and auditory stimulation. Nonlinear measures calculated on EEG filtered in the traditional frequency bands and in higher frequency bands improved the assessment of the sedation level. These measures were obtained by applying all the developed techniques on signals recorded from patients sedated, in order to predict the responses to pain stimulation such as nail bad compression and endoscopy tube insertion. The proposed measures exhibit better performances than the bispectral index (BIS), a traditional indexes used for hypnosis assessment. In conclusion, nonlinear measures based on time-frequency representation, mutual information functions and correntropy provided additional information that helped to improve the automatic sleepiness detection, the characterization and prediction of the nociceptive responses and thus the assessment of the sedation level.El registro de la señal Electroencefalografíca (EEG) proporciona información sobre los cambios en la actividad cerebral asociados con varios estados de la anestesia, la epilepsia, la atención cerebral, los trastornos del sueño, los trastornos cerebrales, etc. Los EEG son señales complejas cuyas propiedades estadísticas dependen del espacio y del tiempo. Sus características aleatorias y no estacionarias hacen imposible que el EEG se describa de forma precisa con una técnica sencilla requiriendo un análisis y una caracterización que implica técnicas que tengan en cuenta su no estacionariedad. Todo esto aumenta la necesidad de desarrollar nuevas técnicas avanzadas con el fin de mejorar la eficiencia de los métodos utilizados en la práctica clínica que son basados en el análisis de EEG. En esta tesis se han investigado y aplicado diferentes métodos utilizando técnicas no lineales con el fin de desarrollar índices capaces de caracterizar el espectro de frecuencias, la dinámica no lineal y la complejidad de las señales EEG registradas en diferentes estados de conciencia. En primer lugar, se ha desarrollado un nuevo algoritmo basado en la envolvente de la señal para la eliminación de ruido de picos en las señales biológicas. Este algoritmo ha sido aplicado a señales simuladas y reales obteniendo resultados significativamente mejores comparados con los filtros adaptativos tradicionales. Seguidamente, se han llevado a cabo varios estudios con el fin de extraer y evaluar las medidas de EEG basadas en técnicas no lineales en diferentes contextos. Se han definido nuevos índices mediante el cálculo de la entropía de la distribución de Choi-Williams (DCW) con respecto al tiempo o la frecuencia. Se ha observado que los valores de estos índices tienden a disminuir, en diferentes proporciones, cuando el comportamiento de las señales evoluciona de caótico o aleatorio a periódico. Además, se han encontrado valores diferentes de estos índices aplicados a la señal EEG registrada en diferentes estados. Diferentes medidas basadas en la representación tiempo-frecuencia, la función de información mutua y la correntropia se han aplicado al EEG para la detección automática de la somnolencia en pacientes que sufren trastornos del sueño. Se ha observado en la zona frontal que la potencia en la banda θ es mayor en los pacientes con somnolencia diurna excesiva, mientras que la entropía espectral y la entropía espectral cruzada en la banda δ es mayor en los pacientes sin somnolencia. En el grupo sin somnolencia se ha encontrado más complejidad en la zona occipital, mientras que el acoplamiento no lineal entre las regiones occipital y frontal ha resultado más fuerte en pacientes con somnolencia diurna excesiva, en la banda β. La representación tiempo-frecuencia y las medidas no lineales se han utilizado para estudiar cómo la adaptación y la fatiga afectan a los potenciales cerebrales relacionados con estímulos térmicos, eléctricos y auditivos. Analizando el promedio de varias épocas de EEG grabadas después de la estimulación, se han encontrado diferencias entre las respuestas a la estimulación frecuente e infrecuente en diferentes períodos de registro. Todas las técnicas que se han desarrollado, se han aplicado a señales EEG registradas en pacientes sedados, con el fin de predecir las respuestas a la estimulación del dolor. Un conjunto de medidas calculadas en señales EEG filtradas en diferentes bandas de frecuencia ha permitido mejorar la evaluación del nivel de sedación. Las medidas propuestas han presentado un mejor rendimiento comparado con el índice bispectral, un indicador de hipnosis tradicional. En conclusión, las medidas no lineales basadas en la representación tiempofrecuencia, funciones de información mutua y correntropia han proporcionado informaciones adicionales que contribuyeron a mejorar la detección automática de la somnolencia, la caracterización y predicción de las respuestas nociceptivas y por lo tanto la evaluación del nivel de sedación

Robust state estimation methods for robotics applications

State estimation is an integral component of any autonomous robotic system. Finding the correct position, velocity, and orientation of an agent in its environment enables it to do other tasks like mapping and interacting with the environment, and collaborating with other agents. State estimation is achieved by using data obtained from multiple sensors and fusing them in a probabilistic framework. These include inertial data from Inertial Measurement Unit (IMU), images from camera, range data from lidars, and positioning data from Global Navigation Satellite Systems (GNSS) receivers. The main challenge faced in sensor-based state estimation is the presence of noisy, erroneous, and even lack of informative data. Some common examples of such situations include wrong feature matching between images or point clouds, false loop-closures due to perceptual aliasing (different places that look similar can confuse the robot), presence of dynamic objects in the environment (odometry algorithms assume a static environment), multipath errors for GNSS (signals for satellites jumping off tall structures like buildings before reaching receivers) and more. This work studies existing and new ways of how standard estimation algorithms like the Kalman filter and factor graphs can be made robust to such adverse conditions without losing performance in ideal outlier-free conditions. The first part of this work demonstrates the importance of robust Kalman filters on wheel-inertial odometry for high-slip terrain. Next, inertial data is integrated into GNSS factor graphs to improve the accuracy and robustness of GNSS factor graphs. Lastly, a combined framework for improving the robustness of non-linear least squares and estimating the inlier noise threshold is proposed and tested with point cloud registration and lidar-inertial odometry algorithms followed by an algorithmic analysis of optimizing generalized robust cost functions with factor graphs for GNSS positioning problem

Approximate Gaussian Conjugacy: Parametric Recursive Filtering Under Nonlinearity, Multimodal, Uncertainty, and Constraint, and Beyond

This is a post-peer-review, pre-copyedit version of an article published in Frontiers of Information Technology & Electronic Engineering. The final authenticated version is available online at: https://doi.org/10.1631/FITEE.1700379Since the landmark work of R. E. Kalman in the 1960s, considerable efforts have been devoted to time series state space models for a large variety of dynamic estimation problems. In particular, parametric filters that seek analytical estimates based on a closed-form Markov–Bayes recursion, e.g., recursion from a Gaussian or Gaussian mixture (GM) prior to a Gaussian/GM posterior (termed ‘Gaussian conjugacy’ in this paper), form the backbone for a general time series filter design. Due to challenges arising from nonlinearity, multimodality (including target maneuver), intractable uncertainties (such as unknown inputs and/or non-Gaussian noises) and constraints (including circular quantities), etc., new theories, algorithms, and technologies have been developed continuously to maintain such a conjugacy, or to approximate it as close as possible. They had contributed in large part to the prospective developments of time series parametric filters in the last six decades. In this paper, we review the state of the art in distinctive categories and highlight some insights that may otherwise be easily overlooked. In particular, specific attention is paid to nonlinear systems with an informative observation, multimodal systems including Gaussian mixture posterior and maneuvers, and intractable unknown inputs and constraints, to fill some gaps in existing reviews and surveys. In addition, we provide some new thoughts on alternatives to the first-order Markov transition model and on filter evaluation with regard to computing complexity

COVLIAS 1.0Lesion vs. MedSeg : An Artificial Intelligence Framework for Automated Lesion Segmentation in COVID-19 Lung Computed Tomography Scans

COVID-19 is a disease with multiple variants, and is quickly spreading throughout the world. It is crucial to identify patients who are suspected of having COVID-19 early, because the vaccine is not readily available in certain parts of the world.Lung computed tomography (CT) imaging can be used to diagnose COVID-19 as an alternative to the RT-PCR test in some cases. The occurrence of ground-glass opacities in the lung region is a characteristic of COVID-19 in chest CT scans, and these are daunting to locate and segment manually. The proposed study consists of a combination of solo deep learning (DL) and hybrid DL (HDL) models to tackle the lesion location and segmentation more quickly. One DL and four HDL models-namely, PSPNet, VGG-SegNet, ResNet-SegNet, VGG-UNet, and ResNet-UNet-were trained by an expert radiologist. The training scheme adopted a fivefold cross-validation strategy on a cohort of 3000 images selected from a set of 40 COVID-19-positive individuals.The proposed variability study uses tracings from two trained radiologists as part of the validation. Five artificial intelligence (AI) models were benchmarked against MedSeg. The best AI model, ResNet-UNet, was superior to MedSeg by 9% and 15% for Dice and Jaccard, respectively, when compared against MD 1, and by 4% and 8%, respectively, when compared against MD 2. Statistical tests-namely, the Mann-Whitney test, paired t-test, and Wilcoxon test-demonstrated its stability and reliability, with p < 0.0001. The online system for each slice was <1 s.The AI models reliably located and segmented COVID-19 lesions in CT scans. The COVLIAS 1.0Lesion lesion locator passed the intervariability test