Bayesian Filtering Research Articles

Real-time localization with probabilistic maps and unscented kalman filtering: a dynamic sensor fusion approach

This paper presents a robust position estimation technique for autonomous vehicles navigating urban and highway environments. It employs a probabilistic framework, integrating Monte Carlo simulation and Bayesian filtering via particle filters to represent position estimates beyond Gaussian distributions. To improve accuracy, Unscented Kalman Filtering (UKF) is used to fuse radar and lidar data, facilitating the detection of static, pole-like objects. These objects are matched with landmarks from a detailed reference map generated through 3D lidar scans. The proposed method addresses both lateral and longitudinal localisation challenges, ensuring precise vehicle positioning. Comprehensive simulation tests validate the system's effectiveness, demonstrating reliable performance across various driving conditions.

Pedestrian Path Choice in Crowded Indoor Environments

Abstract. Indoor crowds can be regarded as dynamic obstacles and they could impede the movement of pedestrians. For instance, the scope of crowds could significantly impact accurate path choices. There are few discussions from an individual’s perspective to reveal the decision-making process of reasonable path choices. In this paper, we aim to address how an indoor pedestrian would walk in a crowded indoor environment. We propose a method to simulate a pedestrian’s path choices during wayfinding process. It is wrapped in a workflow that can capture near-real-time crowd uncertainty. First, the measurement errors of crowds are alleviated with a Bayesian filter. According to crowd locations at each moment, the method of Kernel Density Estimation (KDE) is applied to a grid model of the building to obtain the uncertainty map of the crowds. Based on a two-level spatial model, the logical path represented by a room sequence can be derived from a ’room-door’ network, while detailed path choices on the ’operational’ level are refined in each room. By considering both crowd uncertainty and time cost, path choices for a user are determined by using the A* algorithm at each time slot. By iterating the optimal path to the next door/the target in the current room, the user location of the next moment can be inferred. Our test initially validated the feasibility of the method on the path choices of a pedestrian. In the future, we plan to further conduct field tests with different users in crowded indoor environments.

A Wind Power Forecasting Model Incorporating Recursive Bayesian Filtering State Estimation and Time-Series Data Mining

A Wind Power Forecasting Model Incorporating Recursive Bayesian Filtering State Estimation and Time-Series Data Mining

Mathematical Techniques for Autonomous Vehicle Navigation Systems

Advanced mathematical methods are used a lot in autonomous car guidance systems to make sure they work correctly, reliably, and efficiently. This abstract talks about some of the most important mathematics methods used to create and improve these systems. One important method is probabilistic robots, which uses Bayesian filters, such as the Kalman filter and its nonlinear versions (Extended Kalman Filter and Unscented Kalman Filter), to estimate a vehicle's state and make sense of sensor data that isn't always clear or loud. Path planning algorithms, like A and Dijkstra's algorithm, are needed to find the best routes. Sampling-based methods, like Rapidly-exploring Random Trees (RRT), can help with problems in high-dimensional space. Control theory is a very important part of keeping a car stable and following the direction you want it to take. Model Predictive Control (MPC), for example, is used a lot because it can handle control jobs with multiple variables while considering the system's behavior. To model how a vehicle moves, differential equations and dynamical systems theory are used to show how control inputs affect how the vehicle acts over time. Also, methods that combine data from different sources like LiDAR, cameras, and GPS are very important for making an accurate and complete picture of the world. Optimization methods improve tracking even more by adjusting the path of the car, cutting down on energy use, and shortening trip times. Besides these methods, machine learning and deep learning are being added to guidance systems more and more to help them make better decisions and be more flexible in settings that are changing quickly and are very complicated. These models can learn from very large datasets by finding trends and making predictions that are important for tasks like finding objects, understanding scenes, and making decisions on their own. Autonomous car tracking systems are getting smarter, more capable, and more reliable by using both old-fashioned math methods and new, cutting-edge machine learning methods together. This makes it possible for them to be widely used in real life.

A review of Bayes filters with machine learning techniques and their applications

A Bayes filter is a widely used estimation algorithm, but it has inherent limitations. Performance can degrade when the dynamics are highly nonlinear or when the probability distribution of the state is unknown. To mitigate these issues, machine learning (ML) techniques have been incorporated into many Bayes filters, due to their advantage of being able to map between the input and the output without explicit instructions. In this review, we reviewed 90 papers that proposed the use of ML techniques with Bayes filters to improve estimation performance. This review provides an overview of Bayes filters with ML techniques, categorised according to the role of ML, remaining challenges and research gaps. In the concluding section of this review, we point out directions for future research.

Locally Adaptive Shrinkage Priors for Trends and Breaks in Count Time Series

Non-stationary count time series characterized by features such as abrupt changes and fluctuations about the trend arise in many scientific domains including biophysics, ecology, energy, epidemiology, and social science domains. Current approaches for integer-valued time series lack the flexibility to capture local transient features while more flexible models for continuous data types are inadequate for universal applications to integer-valued responses such as settings with small counts. We present a modeling framework, the negative binomial Bayesian trend filter (NB-BTF), that offers an adaptive model-based solution to capturing multiscale features with valid integer-valued inference for trend filtering. The framework is a hierarchical Bayesian model with a dynamic global-local shrinkage process. The flexibility of the global-local process allows for the necessary local regularization while the temporal dependence induces a locally smooth trend. In simulation, the NB-BTF outperforms a number of alternative trend filtering methods. Then, we demonstrate the method on weekly power outage frequency in Massachusetts townships. Power outage frequency is characterized by a persistent low level trend with occasional spikes. These illustrations show the estimation of a smooth, non-stationary trend with adequate uncertainty quantification.

Autonomous Vehicles Traversability Mapping Fusing Semantic–Geometric in Off-Road Navigation

This paper proposes an evaluating and mapping methodology of terrain traversability for off-road navigation of autonomous vehicles in unstructured environments. Terrain features are extracted from RGB images and 3D point clouds to create a traversal cost map. The cost map is then employed to plan safe trajectories. Bayesian generalized kernel inference is employed to assess unknown grid attributes due to the sparse raw point cloud data. A Kalman filter also creates density local elevation maps in real time by fusing multiframe information. Consequently, the terrain semantic mapping procedure considers the uncertainty of semantic segmentation and the impact of sensor noise. A Bayesian filter is used to update the surface semantic information in a probabilistic manner. Ultimately, the elevation map is utilized to extract geometric characteristics, which are then integrated with the probabilistic semantic map. This combined map is then used in conjunction with the extended motion primitive planner to plan the most effective trajectory. The experimental results demonstrate that the autonomous vehicles obtain a success rate enhancement ranging from 4.4% to 13.6% and a decrease in trajectory roughness ranging from 5.1% to 35.8% when compared with the most developed outdoor navigation algorithms. Additionally, the autonomous vehicles maintain a terrain surface selection accuracy of over 85% during the navigation process.

MonoVisual3DFilter: 3D tomatoes’ localisation with monocular cameras using histogram filters

Abstract Performing tasks in agriculture, such as fruit monitoring or harvesting, requires perceiving the objects’ spatial position. RGB-D cameras are limited under open-field environments due to lightning interferences. So, in this study, we state to answer the research question: “How can we use and control monocular sensors to perceive objects’ position in the 3D task space?” Towards this aim, we approached histogram filters (Bayesian discrete filters) to estimate the position of tomatoes in the tomato plant through the algorithm MonoVisual3DFilter. Two kernel filters were studied: the square kernel and the Gaussian kernel. The implemented algorithm was essayed in simulation, with and without Gaussian noise and random noise, and in a testbed at laboratory conditions. The algorithm reported a mean absolute error lower than 10 mm in simulation and 20 mm in the testbed at laboratory conditions with an assessing distance of about 0.5 m. So, the results are viable for real environments and should be improved at closer distances.

Gaussian-inverse gamma mixture distribution–based extended Kalman observer for dynamic positioning control system of offshore platform

Under different working conditions and control objectives, fuzzy model predictive control is used to optimize the control effect by adjusting the weight to achieve stable and accurate control for the dynamic positioning control of offshore platforms. Also, aiming at the situation where the measurement noise of dynamic positioning control may be time-varying and non-Gaussian and the statistics of the noise are not exact, this paper proposes a variational Bayesian extended Kalman filter observer. In order to model non-Gaussian noise more reasonably, the joint posterior distribution of non-Gaussian noise with state and time-varying covariance is described as the product of Gaussian and independent inverse gamma distributions. Then, the variational Bayesian (VB) method was used to simultaneously estimate the system state, the intermediate variable values of the new distribution, and the noise parameters through fixed-point iteration. The fuzzy algorithm is applied to the model predictive control, and the weight parameters of the model predictive control are adaptively changed to better adapt to the changing working conditions in the control process. The simulation results show that the variational Bayesian extended Kalman filter observer has better performance than the existing algorithms when dealing with the time-varying non-Gaussian observation noise, whose statistics are not exact. The variational Bayesian extended Kalman filter observer can significantly improve the accuracy of the control when it is used in fuzzy model predictive control.

Adaptive and self-learning Bayesian filtering algorithm to statistically characterize and improve signal-to-noise ratio of heart-rate data in wearable devices.

The use of wearable sensors to monitor vital signs is increasingly important in assessing individual health. However, their accuracy often falls short of that of dedicated medical devices, limiting their usefulness in a clinical setting. This study introduces a new Bayesian filtering (BF) algorithm that is designed to learn the statistical characteristics of signal and noise, allowing for optimal smoothing. The algorithm is able to adapt to changes in the signal-to-noise ratio (SNR) over time, improving performance through windowed analysis and Bayesian criterion-based smoothing. By evaluating the algorithm on heart-rate (HR) data collected from Garmin Vivoactive 4 smartwatches worn by individuals with amyotrophic lateral sclerosis and multiple sclerosis, it is demonstrated that BF provides superior SNR tracking and smoothing compared with non-adaptive methods. The results show that BF accurately captures SNR variability, reducing the root mean square error from 2.84 bpm to 1.21 bpm and the mean absolute relative error from 3.46% to 1.36%. These findings highlight the potential of BF as a preprocessing tool to enhance signal quality from wearable sensors, particularly in HR data, thereby expanding their applications in clinical and research settings.

Comparison of the Applicability of Bayesian Filters for System Identification of Sudden Structural Damage

Comparison of the Applicability of Bayesian Filters for System Identification of Sudden Structural Damage

Novel autoantibodies help diagnose anti-SSA antibody negative Sjögren disease and predict abnormal labial salivary gland pathology

ObjectivesSjögren disease (SjD) diagnosis often requires either positive anti-SSA antibodies or a labial salivary gland biopsy with a positive focus score (FS). One-third of patients with SjD lack anti-SSA antibodies...

Maneuvering extended target tracking method based on transformer network

This research introduces a new approach to address the challenges related to inaccuracies in shape estimation and motion state tracking during the tracking of maneuvering extended targets. The method combines a novel neural network model with a cubature Kalman filter. Initially, the target’s shape variation is represented using a second-order autoregressive model, and Bayesian filtering is employed for target contour estimation in static environments. Subsequently, the kinematic state tracking of maneuvering targets is enhanced by modifying a neural network model based on Transformer architecture. Through the effective integration of these techniques, precise tracking of maneuvering extended targets is achieved, facilitating accurate estimation of irregular contour information while tracking the targets’ motion state in real-time. The efficacy of the proposed approach is further confirmed through various simulation scenarios, underscoring its suitability for tracking maneuvering extended targets.

Optimal Inference of Hidden Markov Models Through Expert-Acquired Data.

This paper focuses on inferring a general class of hidden Markov models (HMMs) using data acquired from experts. Expert-acquired data contain decisions/actions made by humans/users for various objectives, such as navigation data reflecting drivers' behavior, cybersecurity data carrying defender decisions, and biological data containing the biologist's actions (e.g., interventions and experiments). Conventional inference methods rely on temporal changes in data without accounting for expert knowledge. This paper incorporates expert knowledge into the inference of HMMs by modeling expert behavior as an imperfect reinforcement learning agent. The proposed method optimally quantifies experts' perceptions about the system model, which, alongside the temporal changes in data, contributes to the inference process. The proposed inference method is derived through a combination of dynamic programming and optimal recursive Bayesian estimation. The applicability of this method is demonstrated to a wide range of inference criteria, such as maximum likelihood and maximum a posteriori. The performance of the proposed method is investigated through a comprehensive numerical experiment using a benchmark problem and biological networks.

Recursive and batch Bayesian estimation of exponential non-viscous damping systems

Non-viscous damping systems include a convolutional integral and a kernel function in their equation of motion to incorporate time-hysteresis damping effects, which are present in dynamical behavior of most engineering materials yet are absent in commonly used viscous damping models. When an exponential kernel function is adopted by the non-viscous model, the unique damping characteristic is realized by an additional model parameter known as the relaxation parameter. The objective of this paper is to investigate various aspects of estimation problems on exponential non-viscous damping systems through recursive and batch Bayesian time-domain frameworks, with a focus on how the relaxation parameter introduces additional complexity in estimation problems compared to viscous damping systems. Two well-established algorithms are employed: the unscented Kalman filter (UKF) for recursive Bayesian estimation and the transitional Markov Chain Monte Carlo (TMCMC) for batch Bayesian estimation. We first analyze the complexity of estimation problems in SDOF viscous and non-viscous damping systems. The TMCMC algorithm offers a quantitative analysis that reveals greater uncertainty and stronger parameter correlation in non-viscous damping systems compared to viscous damping systems. Subsequently, the same SDOF systems are utilized to study recursive Bayesian estimation via UKF such as the effects of measurement data type, discretization, and initial conditions. Based on the results of the TMCMC algorithm, we study the dependence of UKF performance on the initial condition for various SDOF non-viscous damping systems with different levels of non-viscosity. In the end, a laboratory experiment compares the estimation results between viscous and non-viscous damping systems using both TMCMC and UKF.

A comparative study on state-of-charge estimation for lithium-rich manganese-based battery based on Bayesian filtering and machine learning methods

In this paper, a comparative study on the state of charge (SOC) estimation of the lithium-rich manganese-based battery (LRMB) has been conducted by systematically considering the equivalent circuit model (ECM), aging state and algorithms. The results show that the first-order RC model combined with the Extended Kalman filter (EKF) is more suitable for the SOC estimation of the LRMB when the battery decays less severely. The maximum value of root mean square error of SOC estimation error no exceeds 1.6 % under various dynamic operating conditions, which can well meet the practical application. Besides, the first-order model based EKF algorithm occupies least computing resource and simultaneously possesses the best convergence velocity against the initial SOC value deviation. When the LRMB suffers a severe aging, the SOC estimation performance decreases significantly with the max error exceeding 6 %, to overcome this, a new algorithm combined deep learning and Extend Kalman filter (EKF) is proposed, which exhibit high SOC estimation accuracy with the RMSE less than 0.16 %. In summary, a systematic study about the SOC estimation of LRMB has been carried out, which can provide great guidance for the future engineering application of LRMB.

Cost-benefit analysis for SHM systems based on minimum detectable parameter change

Value of information (VoI) analysis can be used to assess the benefit of monitoring the health of infrastructure such as bridges and waterway locks. Such information supports decision-making processes, guiding operators towards the best actions for the infrastructure. In recent studies, VoI analysis is integrated with the modeling of the temporal evolution of structural conditions, so that the value of Structural Health Monitoring (VoSHM) can be assessed over the life cycle of the infrastructure. However, none of these studies considers the ability of the measurement system to detect small changes and its impact on the assessment of the VoI. This paper presents an approach to VoI assessment based on the concept of minimum change detectability and Bayesian linear filters. By exploiting a feature of the Kalman filter whereby posterior covariance is independent of observations, it is possible to predict the minimum shift in the mean value of a structural parameter for which its posterior density function would exceed a user-defined safety threshold. By constructing the decision tree and considering the cost of monitoring and maintenance, the value of detecting smaller changes can be estimated, which is the value of early change detection and performing preventive maintenance. As a proof of concept, this approach is applied to assess the VoSHM for a navigation lock built with precast reinforced concrete elements, where the steel bars in the chamber are damaged by fatigue and corrosion. The VoSHM is compared with the VoI associated to other Non Destructive Tests. The paper then discusses the implications of applying Bayesian linear filters in SHM for parameter change detection, the main one being the development of refined scales for structural condition assessment before any data from the changed state is available. Ultimately, the VoSHM is the benefit brought by adopting these refined scales in maintenance management.

Research and comparison of algorithms based on multi-modal fusion

Abstract A multi-modal fusion algorithm is an important method for information fusion on multi-modal data provided by different sensors. It can make full use of the advantages of multiple sensors and improve the accuracy and robustness of data processing and decision-making. This paper aims to study the performance difference between the extended Kalman filter (EKF) algorithm and other algorithms in multi-modal fusion and explore a method to fuse multiple algorithms further to improve the accuracy of fusion results. The author uses the classic test set data set for experiments to evaluate the performance of different algorithms. By comparing and analyzing the performance of each algorithm in data fusion tasks, we can get their advantages and disadvantages in different scenarios. Among them, the extended Kalman filter algorithm is a classical algorithm based on Bayesian filtering, which can estimate the system state through recursive state estimation and covariance update. In addition, the author also uses linear regression, random forest, and other algorithms to compare. Then, the author uses several test sets to evaluate the performance of each algorithm. Through a comprehensive analysis of the MSE and MAE errors output by the algorithm, the applicability, advantages, and disadvantages of each algorithm in different scenarios are obtained.

A score-based filter for nonlinear data assimilation

We propose a score-based generative sampling method for solving the nonlinear filtering problem with superior accuracy. A major drawback of existing nonlinear filtering methods, e.g., particle filters, is the low accuracy in handling high-dimensional nonlinear problems. To overcome this issue, we incorporate the score-based diffusion model into the recursive Bayesian filter framework to develop a novel score-based filter (SF). The key idea of SF is to store the information of the recursively updated filtering density function in the score function, instead of storing the information in a set of finite Monte Carlo samples (used in particle filters and ensemble Kalman filters). By leveraging the reverse-time diffusion process, SF can generate unlimited samples to characterize the filtering density. An essential aspect of SF is its analytical update step, gradually incorporating data information into the score function. This step is crucial in mitigating the degeneracy issue faced when dealing with very high-dimensional nonlinear filtering problems. Three benchmark problems are used to demonstrate the performance of our method. In particular, SF provides surprisingly impressive performance in reliably capturing/tracking the 100-dimensional stochastic Lorenz system that is a well-known challenging problem for existing filtering methods.

Adaptive Multi-Hypothesis Marginal Bayes Filter for Tracking Multiple Targets

Tracking multiple targets in the presence of unknown number of targets, missed detection, clutter, and noise is a challenging problem. To cope with this problem, a novel approach for generating the potential birth targets was developed, a mathematical model for multiple hypotheses was established, and an adaptive multi-hypothesis marginal Bayes filter is herein proposed in terms of the established mathematical model for multiple hypotheses and the novel birth approach. This filter delivers the existence probabilities of targets and their probability density functions. It uses multiple hypotheses to solve the data association problem to form the existence probabilities of targets and their probability density functions. To obviate the requirement for prior birth models, this filter uses the observations from two consecutive time steps to establish the birth models adaptively. Its tracking performance was tested by comparing it with other adaptive filters, showing that the proposed filter is robust, and it can obtain higher tracking accuracy than other filters.