Bayesian Filtering Method Research Articles

Bayesian filter for failure times identification of moving heat sources in 2D geometry

This study investigates the application of the Bayesian filter method for identifying failure times in a 2D parabolic partial differential equation system. The identification of failure times in thermal systems, which are subject to partial differential equations, presents significant difficulties, especially due to their ill-posed nature, which makes them highly sensitive to measurement errors. A Bayesian inference framework was previously developed in a related study, aiming to solve inverse heat conduction problems by utilising temperature measurements from sensors to estimate failure times or potential restarts of fixed heat sources. This paper focuses on the case of mobile sources, where a set of fixed sensors is considered and the trajectories of the heating sources are known and follow a constant velocity. The main objective is to accurately identify the failing heat sources and determine the exact failure time, as well as the possibility of resuming normal operation. A Monte Carlo simulation is performed to assess the impact of sensor measurements.

A Probabilistic Approach for Stereo 3D Point Cloud Reconstruction from Airborne Single-Channel Multi-Aspect SAR Image Sequences

We investigate the problem of obtaining dense 3D reconstruction from airborne multi-aspect synthetic aperture radar (SAR) image sequences. Dense 3D reconstructions of multi-view SAR images are vulnerable to anisotropic scatters. To address this issue, we propose a probabilistic 3D reconstruction method based on jointly estimating the pixel’s height and degree of anisotropy. Specifically, we propose a mixture distribution model for the stereo-matching results, where the degree of anisotropy is modeled as an underlying error source. Then, a Bayesian filtering method is proposed for dense 3D point cloud generation. For real-time applications, redundancy in multi-aspect observations is further exploited in a probabilistic manner to accelerate the stereo-reconstruction process. To verify the effectiveness and reliability of the proposed method, 3D point cloud generation is tested on Ku-band drone SAR data for a domestic airport area.

Variational Bayesian implicit unscented Kalman filter for celestial navigation using time delay measurement

Sunlight arrival time delay is an innovative measurement for celestial navigation, which provides the distance information between the spacecraft and the nearby celestial body. For deep space detectors, the time delay measurement noise is time-varying, and its statistics cannot be accurately determined. The too-large deviation between the measured noise covariance matrix (R) and the noise statistics seriously reduces navigation accuracy. A variational Bayesian implicit unscented Kalman filter (VBIUKF) method is proposed and applied to celestial navigation using time delay measurement in this paper. VBIUKF adaptively estimates R using the innovation sequence and the predicted measurement covariance matrix to make R closest to the measurement noise statistics. Simulation results indicate that VBIUKF can obtain high accuracy navigation results under time-varying measurement noise.

Fast Bayesian graph update for SLAM

Robust, accurate localization is crucial to many of the current challenges in robotics. In recent years, visual simultaneous localization and mapping (SLAM) approaches have been studied intensively. The majority of approaches realize an excellent performance through precise visual odometry (VO) and loop closing based on a graph optimization technique. However, as the graph size increases, the computation time required for the graph optimization increases significantly. This makes it difficult to implement on mobile devices and causes a decrease in online performance. We propose a novel Bayesian graph update (BGU) to accelerate the loop closing of graph-based SLAM. The proposed method comprises sequentially updating the graph each time a new edge is obtained instead of optimizing the entire graph. Consequently, the update latency of one loop closing is reduced. The fundamental idea is to update whole edges on the graph using a Bayesian filtering method. We propose a fast algorithm based on a decoupled extended Kalman filter; its calculation time is proportionate to the number of edges at most. We confirm the speed and accuracies of our BGU using a simulated dataset. We also demonstrate that our BGU works well with actual visual SLAM methods by equipping it on ORB-SLAM2.

Observer-Based Control of LPV Systems with Input Delay and Saturation and Matched Disturbances via a Generalized Sector Condition

This paper examines the control design for parameter-dependent input-delay linear parameter-varying (LPV) systems with saturation constraints and matched input disturbances. A gain-scheduled dynamic output feedback controller, coupled with a disturbance observer to cancel out input disturbance effects, was augmented with an anti-windup compensator to locally stabilize the input-delay LPV system under saturation, model uncertainty, and exogenous disturbances. Sufficient delay-dependent conditions to asymptotically stabilize the closed-loop system were derived using Lyapunov-Krasovskii functionals and a modified generalized sector condition to address the input saturation nonlinearity. The level of disturbance rejection was characterized via the closed-loop inducedL2-norm of the closed-loop system in the form of linear matrix inequality (LMI) constraints. The results are examined in the context of the mean arterial pressure (MAP) control in the clinical resuscitation of critical hypotensive patients. The MAP variation response to the injection of vasopressor drugs was modeled as an LPV system with a varying input delay and was susceptible to model uncertainty and input/output disturbances. A Bayesian filtering method known as the cubature Kalman filter (CKF) was used to estimate the instantaneous values of the parameters. The varying delay was estimated via a multiple-model approach. The proposed input-delay LPV control was validated in closed-loop simulations to demonstrate its merits and capabilities in the presence of drug administration constraints.

Estimation of the Path-Loss Exponent by Bayesian Filtering Method.

Regarding wireless sensor network parameter estimation of the propagation model is a most important issue. Variations of the received signal strength indicator (RSSI) parameter are a fundamental problem of a system based on signal strength. In the present paper, we propose an algorithm based on Bayesian filtering techniques for estimating the path-loss exponent of the log-normal shadowing propagation model for outdoor RSSI measurements. Furthermore, in a series of experiments, we will demonstrate the usefulness of the particle filter for estimating the RSSI data. The stability of this algorithm and the differences in determined path-loss exponent for both method were also analysed. The proposed method of dynamic estimation results in significant improvements of the accuracy of RSSI values when compared with the experimental measurements. It should be emphasised that the path-loss exponent mainly depends on the RSSI data. Our results also indicate that increasing the number of inserted particles does not significantly raise the quality of the estimated parameters.

UWB Localization in a Smart Factory: Augmentation Methods and Experimental Assessment

The advent of the fourth industrial revolution (Industry 4.0) aims at increasing automation and efficiency in manufacturing processes by the adoption of information and communication technologies. Several of the proposed solutions rely on precise localization of material, equipment, or operators. This article investigates the employment of ultrawideband (UWB) real-time location systems (RTLS) in a factory environment and proposes an augmentation technique to mitigate the impairments that arise in such a complex scenario. A Bayesian filtering method is developed to jointly track the motion dynamics and the time-varying visibility conditions of the UWB antennas, with particle-based implementation to deal with the nonlinearity of the UWB measurements. Laboratory tests and industrial experiments are carried out to evaluate the performance of three commercial off-the-shelf UWB technologies: Decawave, Sewio, and Ubisense. The experimental data are then used to calibrate and test the developed filtering technique, showing that it is possible to significantly reduce the positioning error originating from dense multipath and NLOS effects by jointly tracking the target dynamics and visibility conditions.

Bayesian Filtering Multi-Baseline Phase Unwrapping Method Based on a Two-Stage Programming Approach

Phase unwrapping (PU) has been a key step in the processing of interferometric synthetic aperture radar (InSAR) data, and its processing accuracy will directly affect the reconstruction results of digital elevation models (DEMs). The traditional single-baseline (SB) PU must be calculated under continuity assumptions. However, multi-baseline (MB) PU can get rid of the limitation of continuity assumption, so reasonable results can be obtained in regions with large gradient changes. However, the poor noise robustness of MBPU has always been a key problem. To address this issue, we transplant three Bayesian filtering methods with a two-stage programming approach (TSPA), and propose corresponding MBPU models. First, we propose a gradient-estimation method based on the first step of TSPA, and then the corresponding PU model is determined according to different Bayesian filtering. Finally, the wrapped phase can be obtained by unwrapping, one by one, using an effective quality map based on heapsort. These methods can improve the robustness of the MBPU methods. More significantly, this paper establishes a novel TSPA-based Bayesian filtering MBPU framework for the first time. This is of great significance for broadening the research of MBPU. The proposed methods experiments on simulated and real MB InSAR datasets. From the results, we can see that the TSPA-based Bayesian filtering MBPU framework can significantly improve the robustness of the MBPU method.

Time-Varying Massive MIMO Channel Estimation: Capturing, Reconstruction, and Restoration

To estimate time-varying MIMO channel at base station, traditional downlink (DL) channel restoration schemes usually require the reconstruction for the covariance of downlink process noise vector, which is dependent on DL channel covariance matrix (CCM). However, the acquisition of the CCM leads to extremely high overhead in massive MIMO systems. To tackle this problem, we propose a novel scheme for DL channel tracking in this paper. First, by utilizing virtual channel representation (VCR), we develop a dynamic uplink (UL) massive MIMO channel model with the consideration of off-grid refinement. Then, a coordinate-wise expectation maximization (EM) algorithm is adopted for capturing model parameters, including the spatial signatures, time-correlation factors, off-grid bias, channel power, and noise power. By exploiting the UL/DL angle reciprocity, the spatial signatures, time-correlation factors and off-grid bias of the DL channel model can be reconstructed with the knowledge of UL. However, channel power and noise power are closely related with the carrier frequency, which cannot be perfectly inferred from the UL. Instead of discovering these two parameters with dedicated training, we resort to the optimal Bayesian Kalman filter (OBKF) method to accurately track the DL channel with partial prior knowledge. At the same time, the model parameters will be gradually restored. Specially, the factor-graph and the Metropolis Hastings MCMC are utilized within the OBKF framework. Finally, numerical results are provided to demonstrate the efficiency of our proposed scheme.

A calibration method of ultra-short baseline installation error with large misalignment based on variational Bayesian unscented Kalman filter.

The ultrashort baseline system is widely used in ships and underwater navigation and positioning. The misalignment and level arm with the inertial measurement unit are the two sources of positioning inaccuracy. The accuracy of calibration is usually affected by measurement noise and linearization of the observation equation. In order to improve the calibration accuracy, the variational Bayesian unscented Kalman filter (VBUKF) method is proposed for the calibration of the ultrashort baseline installation error in the paper. The detailed derivation of VBUKF for the calibration is presented in the paper. Simulation experiments and field experiments were carried out, respectively, to verify the algorithm. The simulation results show that the proposed method can calibrate the installation error of the sensors in real time on line. The field experiment verified that the algorithm improves the calibration accuracy of the installation error under the large misalignment. The positioning accuracy is also improved compared with the traditional method.

Indoor Pedestrian Localization Using iBeacon and Improved Kalman Filter.

The reliable and accurate indoor pedestrian positioning is one of the biggest challenges for location-based systems and applications. Most pedestrian positioning systems have drift error and large bias due to low-cost inertial sensors and random motions of human being, as well as unpredictable and time-varying radio-frequency (RF) signals used for position determination. To solve this problem, many indoor positioning approaches that integrate the user’s motion estimated by dead reckoning (DR) method and the location data obtained by RSS fingerprinting through Bayesian filter, such as the Kalman filter (KF), unscented Kalman filter (UKF), and particle filter (PF), have recently been proposed to achieve higher positioning accuracy in indoor environments. Among Bayesian filtering methods, PF is the most popular integrating approach and can provide the best localization performance. However, since PF uses a large number of particles for the high performance, it can lead to considerable computational cost. This paper presents an indoor positioning system implemented on a smartphone, which uses simple dead reckoning (DR), RSS fingerprinting using iBeacon and machine learning scheme, and improved KF. The core of the system is the enhanced KF called a sigma-point Kalman particle filter (SKPF), which localize the user leveraging both the unscented transform of UKF and the weighting method of PF. The SKPF algorithm proposed in this study is used to provide the enhanced positioning accuracy by fusing positional data obtained from both DR and fingerprinting with uncertainty. The SKPF algorithm can achieve better positioning accuracy than KF and UKF and comparable performance compared to PF, and it can provide higher computational efficiency compared with PF. iBeacon in our positioning system is used for energy-efficient localization and RSS fingerprinting. We aim to design the localization scheme that can realize the high positioning accuracy, computational efficiency, and energy efficiency through the SKPF and iBeacon indoors. Empirical experiments in real environments show that the use of the SKPF algorithm and iBeacon in our indoor localization scheme can achieve very satisfactory performance in terms of localization accuracy, computational cost, and energy efficiency.

Combined state and parameter identification of nonlinear structural dynamical systems based on Rao-Blackwellization and Markov chain Monte Carlo simulations

The problem of combined state and parameter estimation in nonlinear state space models, based on Bayesian filtering methods, is considered. A novel approach, which combines Rao-Blacicwellized particle filters for state estimation with Markov chain Monte Carlo (MCMC) simulations for parameter identification, is proposed. In order to ensure successful performance of the MCMC samplers, in situations involving large amount of dynamic measurement data and (or) low measurement noise, the study employs a modified measurement model combined with an importance sampling based correction. The parameters of the process noise covariance matrix are also included as quantities to be identified. The study employs the Rao-Blackwellization step at two stages: one, associated with the state estimation problem in the particle filtering step, and, secondly, in the evaluation of the ratio of likelihoods in the MCMC run. The satisfactory performance of the proposed method is illustrated on three dynamical systems: (a) a computational model of a nonlinear beam moving oscillator system, (b) a laboratory scale beam traversed by a loaded trolley, and (c) an earthquake shake table study on a bending-torsion coupled nonlinear frame subjected to uniaxial support motion. (C) 2017 Elsevier Ltd. All rights reserved.

A Review of the Bayesian Occupancy Filter.

Autonomous vehicle systems are currently the object of intense research within scientific and industrial communities; however, many problems remain to be solved. One of the most critical aspects addressed in both autonomous driving and robotics is environment perception, since it consists of the ability to understand the surroundings of the vehicle to estimate risks and make decisions on future movements. In recent years, the Bayesian Occupancy Filter (BOF) method has been developed to evaluate occupancy by tessellation of the environment. A review of the BOF and its variants is presented in this paper. Moreover, we propose a detailed taxonomy where the BOF is decomposed into five progressive layers, from the level closest to the sensor to the highest abstract level of risk assessment. In addition, we present a study of implemented use cases to provide a practical understanding on the main uses of the BOF and its taxonomy.

Serial and Parallel Bayesian Spam Filtering using Aho-Corasick and PFAC

With the rapid growth of Internet, E-mail, with its convenient and efficient characteristics, has become an important means of communication in people‟s life. It reduces the cost of communication. It comes with Spam. Spam emails, also known as „junk e-mails‟, are unsolicited one‟s sent in bulk with hidden or forged identity of the sender, address, and header information. It is vital to pursue more effective spam filtering approaches to maintain normal operations of e-mail systems and to protect the interests of email users. In this paper we developed a Spam filter based on Bayesian filtering method using Aho-corasick and PFAC string matching algorithm. This filter developed an improved version of spam filter based on traditional Bayesian spam filtering to improve spam filtering efficiency, and to reduce chances of misjudgement of malignant spam. For further improvement of Spam filtering process we are transform the filter in to parallel spam filter on GPGPU's by using PFAC Algorithm.

Time-frequency analysis with Bayesian filtering methods for dispersion tracking and geoacoustic inversion in the ocean

Iterative and sequential Bayesian filtering methods have been previously used in dispersion tracking for long range sound propagation in oceanic environments. The methods rely on accurate modeling of (i) the acoustic field in the frequency domain as a function of time and (ii) the statistical model governing the behavior of errors in the measured data. Normal distributions are typically used for the latter but may not necessarily be the most accurate models for the description of the data. We investigate alternative methods for describing the statistical errors in power spectra, which we then use for linking the extracted time-frequency information to geoacoustic inversion. Probability density functions computed for frequencies and arrival times via filtering are propagated “backwards” through sound propagation models for quantification of the uncertainty in the estimation process. [Work supported by ONR].

A Model for Prediction of Spontaneous Preterm Birth in Asymptomatic Women

Preterm birth is a complex health problem with social, environmental, behavioral, and genetic determinants of an individual's risk and remains a major challenge in obstetrics. Recent research has caused improvements in predicting preterm birth; however, there is still controversy about the prediction of preterm birth in asymptomatic women. The purpose of this study was to determine if Bayesian filtering can be used in a clinical setting to predict spontaneous preterm birth in asymptomatic women. A model of predicting spontaneous preterm birth using PopBayes based on a Bayesian filtering algorithm was developed using a previously collected dataset, then applied to a prospectively collected cohort of asymptomatic women who delivered singleton live newborns at or after 24 weeks of gestation. Cases complicated with major congenital malformations were excluded. The proportion of patients with spontaneous preterm birth was 18.4% (96 of 522) at <37 weeks gestation, 5.4% (28 of 522) at <34 weeks gestation, and 2.7% (14 of 522) at <32 weeks gestation. The match rates with the combination of demographic, clinical, and genetic factors using a Bayesian filtering method (PopBayes) were higher than the match rates using demographic and clinical factors only, including maternal age, maternal body mass index (BMI), prior preterm birth, education, occupation, income, and active and passive smoking. The match rates in preterm delivery before 32 weeks of gestation were higher than the match rates in preterm delivery before 37 and 34 weeks of gestation (94.3% vs. 84.7% and 82.0%, respectively). The negative predictive values for demographic, clinical, and genetic factors in predicting preterm delivery using PopBayes were consistently >90%. We suggest that Bayesian filtering (PopBayes) is a customizable and useful tool in establishing a model for the prediction of preterm birth.

A Geometric Modelling Approach to Determining the Best Sensing Coverage for 3-Dimensional Acoustic Target Tracking in Wireless Sensor Networks

Existing 3-dimensional acoustic target tracking methods that use wired/wireless networked sensor nodes to track targets based on four sensing coverage do not always compute the feasible spatio-temporal information of target objects. To investigate this discrepancy in a formal setting, we propose a geometric model of the target tracking problem alongside its equivalent geometric dual model that is easier to solve. We then study and prove some properties of dual model by exploiting its relationship with algebra. Based on these properties, we propose a four coverage axis line method based on four sensing coverage and prove that four sensing coverage always yields two dual correct answers; usually one of them is infeasible. By showing that the feasible answer can be only sometimes identified by using a simple time test method such as the one proposed by ourselves, we prove that four sensing coverage fails to always yield the feasible spatio-temporal information of a target object. We further prove that five sensing coverage always gives the feasible position of a target object under certain conditions that are discussed in this paper. We propose three extensions to four coverage axis line method, namely, five coverage extent point method, five coverage extended axis lines method, and five coverage redundant axis lines method. Computation and time complexities of all four proposed methods are equal in the worst cases as well as on average being equal to Θ(1) each. Proposed methods and proved facts about capabilities of sensing coverage degree in this paper can be used in all other methods of acoustic target tracking like Bayesian filtering methods.

Extended Monte Carlo localization algorithm for mobile sensor networks

A real-world localization system for wireless sensor networks that adapts for mobility and irregular radio propagation model is considered. The traditional range-based techniques and recent range-free localization schemes are not well competent for localization in mobile sensor networks, while the probabilistic approach of Bayesian filtering with particle-based density representations provides a comprehensive solution to such localization problem. Monte Carlo localization is a Bayesian filtering method that approximates the mobile node’s location by a set of weighted particles. In this paper, an enhanced Monte Carlo localization algorithm—Extended Monte Carlo Localization (Ext-MCL) is proposed, i.e., the traditional Monte Carlo localization algorithm is improved and extended to make it suitable for the practical wireless network environment where the radio propagation model is irregular. Simulation results show the proposal gets better localization accuracy and higher localizable node number than previously proposed Monte Carlo localization schemes not only for ideal radio model, but also for irregular one.

Optimal filtering for Bayesian detection and attribution of climate change

In the conventional approach to the detection of an anthropogenic or other externally forced climate change signal, optimal filters (fingerprints) are used to maximize the ratio of the observed climate change signal to the natural variability noise. If detection is successful, attribution of the observed climate change to the hypothesized forcing mechanism is carried out in a second step by comparing the observed and predicted climate change signals. In contrast, the Bayesian approach to detection and attribution makes no distinction between detection and attribution. The purpose of filtering in this case is to maximize the impact of the evidence, the observed climate change, on the prior probability that the hypothesis of an anthropogenic origin of the observed signal is true. Whereas in the conventional approach model uncertainties have no direct impact on the definition of the optimal detection fingerprint, in optimal Bayesian filtering they play a central role. The number of patterns retained is governed by the magnitude of the predicted signal relative to the model uncertainties, defined in a pattern space normalized by the natural climate variability. Although this results in some reduction of the original phase space, this is not the primary objective of Bayesian filtering, in contrast to the conventional approach, in which dimensional reduction is a necessary prerequisite for enhancing the signal-to-noise ratio. The Bayesian filtering method is illustrated for two anthropogenic forcing hypotheses: greenhouse gases alone, and a combination of greenhouse gases plus sulfate aerosols. The hypotheses are tested against 31-year trends for near-surface temperature, summer and winter diurnal temperature range, and precipitation. Between six and thirteen response patterns can be retained, as compared with the one or two response patterns normally used in the conventional approach. Strong evidence is found for the detection of an anthropogenic climate change in temperature, with some preference given to the combined forcing hypothesis. Detection of recent anthropogenic trends in diurnal temperature range and precipitation is not successful, but there remains strong net evidence for anthropogenic climate change if all data are considered jointly.

Sequential control of a monetary policy model for India

Abstract This paper attempts to incorporate expectation generating mechanisms in a formal economic planning model. We have tried to introduce a simple bayesian filter method into an econometric model to see how the system parameters would change subject to a ‘policy-optimization-process’. The method was applied to a monetary policy model for India to see how the political authorities would react to private sector reactions to the policy-optimization-process. Through continuous updating of the response parameters, we can derive a very different type of monetary-fiscal policy structure than that which can be obtained through the usual optimal control process.