Bayesian Particle Filter Research Articles

Sequential Monte Carlo with Adaptive Lookahead Support for Improved Importance Sampling

The sequential Monte Carlo, also called the Bayesian particle filter, approximates a posterior probability density function of a latent target state from noisy sensor measurements using a set of Monte Carlo samples. These samples are predicted using an importance density function and then updated using the Bayes’s rule. The updated samples and their corresponding weights provide an estimate of the latent state. The said filtering process is iterated over time for tracking dynamic target states. It is critical to have enough particles in regions of the target state space that contribute to the posterior. The auxiliary and the improved auxiliary particle filters accomplish this by a process that mimics drawing from an importance density that leverages the incoming observation into the sampling step. However these filters are known to fail when the sensor measurements are highly informative and the diffusion over the state transition is large. This paper presents an improvement to the auxiliary particle filter by taking two support points that act as limits in a univariate state space within which particles are samples. The choice of the limits is adaptive. The proposed method is successfully tested using a nonlinear model using simulations.

Estimation of the cell membrane permeability for gas transport from surface pH measurements

Bayesian particle filters (PFs) are a viable alternative to sampling methods such as Markov chain Monte Carlo methods to estimate model parameters and related uncertainties when the forward model is a dynamical system, and the data are time series that depend on the state vector. PF techniques are particularly attractive when the dimensionality of the state space is large and the numerical solution of the dynamical system over the time interval corresponding to the data is time consuming. Moreover, information contained in the PF solution can be used to infer on the sensitivity of the unknown parameters to different temporal segments of the data. This, in turn, can guide the design of more efficient and effective data collection procedures. In this article the PF method is applied to the problem of estimating cell membrane permeability to gases from pH measurements on or near the cell membrane. The forward model in this case comprises a spatially distributed system of coupled reaction–diffusion differential equations. The high dimensionality of the state space and the need to account for the micro-environment created by the pH electrode measurement device are additional challenges that are addressed by the solution method.

Robust Bayesian Particle Filter for Space Object Tracking Under Severe Uncertainty

This paper introduces a robust Bayesian particle filter that can handle epistemic uncertainty in the measurements, dynamics, and initial conditions. The robust filter returns robust bounds on the output quantity of interest, rather than a crisp value. Particles are generated with an importance sampling technique and propagated only one time during the estimation process. The proposal distribution is constructed by running a parallel unscented Kalman filter to drive particles in regions of high expected likelihood and achieve a high effective sample size. The bounds are then computed by an inexpensive tuning of the importance weights via numerical optimization. A Branch & Bound algorithm over simplexes with a Lipschitz bounding function is employed to achieve guaranteed convergence to the lower and upper bounds in a finite number of steps. The filter is applied to the robust computation of the collision probability of SENTINEL 2B with a FENGYUN 1C debris in different operational instances, all characterized by a mix of aleatory and epistemic uncertainty on initial conditions and observation likelihoods.

Bayesian particle filter algorithm for learning epidemic dynamics

In this article, we consider a dynamic model for the spread of epidemics, in particular of COVID-19, and the inverse problem of estimating sequentially the time evolution of the unknown state and the model parameters based on noisy observations of the new daily infections. A characteristic of COVID-19 is the significant proportion of secondary infections though contacts with asymptomatic or oligosymptomatic infectious individuals. Since most of these individuals are not accounted for in the number of new daily infections, the size of this cohort can be inferred only indirectly through the underlying model. The evolution model used to propagate the current state from one data instance to the next is a suitably modified SEIR compartment model, providing the expected value for the new daily infection count that is modeled as a Poisson distributed random variable. The estimation of the state and the model parameters is based on a Bayesian particle filtering algorithm. The sequential Bayesian framework naturally provides a quantification of the uncertainty in the estimates of the model parameters, basic reproduction number, and size of the cohorts. Of particular interest is the fact that the algorithm makes it possible to estimate the size of the asymptomatic cohort, a key component for understanding the COVID-19 dynamics, and for planning mitigation measures. Alternative versions of the classical basic reproduction number for estimating the speed of the propagation of the disease are also proposed. The viability of the algorithm is demonstrated through a set of computed examples with both simulated realistic data and actual real data from selected US counties. The numerical tests show that the algorithm reproduces a ratio of asymptomatic vs symptomatic cohort sizes remarkably close to what is currently suggested by the Center for Disease Control.

A triangulation estimation and forecasting framework for agricultural time series

This study proposes a framework implementing triangular estimation for better modeling and forecasting time series. In order to improve the performance of estimation, we employ two sources of triangulation to generate a time series, which is statistically indistinguishable with the latent time series hidden in a system. Thanks to Bayesian hierarchical estimation, which is akin to deep learning but more sophisticate and longer history, the framework has been validated by a large amount of records in vegetable auctions. The hierarchical Bayesian estimation and Monte Carlo Markov Chain particle filters used in hidden Markov model are appreciated during the massive bootstrapping of data. Our results demonstrate excellent estimation performance in discovering hidden states.

Bayesian Fill Volume Estimation Based on Point Level Sensor Signals

In dry bulk and fluid processing, the composites are usually stored in hoppers, tanks, or other containers. Due to the economic advantages, binary point level sensors, which detect fill level exceeding, are widely used for process monitoring and control. In this paper, we propose different filters for estimating the probability distribution of the fill volume based on a time-variant measurement distribution and a stochastic physical model with white process noise. A filter based on the model prediction with separated measurement update and two Bayesian particle filters are proposed and compared with a simulated ground truth. The performance measures are the root-mean-square error, the precision of the 95 % and 75 % credible intervals, and the average value of the estimated probability density function at the simulated fill volumes.

Sequential Optimal Inference for Experiments With Bayesian Particle Filters

In behavioral experiments, carefully choosing the stimuli is critical for success. Recently, several adaptive Bayesian methods gained popularity by proposing to optimally select the stimulus in each trial based on the results of the preceding trials. However, current methods are computationally expensive and might require a long waiting period between each question. Moreover, they are often tailored to a particular model and a particular objective, such as parameter estimation, prediction or model selection. It is left to the researcher to extend these approaches to other models by providing a suitable Bayesian inference method. We propose to apply the Sequential Monte Carlo (SMC) framework to solve both the inference problem and the optimal experimental design problem. This new method, called Sequential Optimal Inference (SOI) provides gains in computational efficiency and allows for the use of a broad class of complex models and objectives. We demonstrate its validity with simulation studies. An implementation of the method in MATLAB and Python is provided.

Hamiltonian Servo: Control and Estimation of a Large Team of Autonomous Robotic Vehicles

This paper proposes a novel Hamiltonian servo system, a combined modeling framework for control and estimation of a large team/fleet of autonomous robotic vehicles. The Hamiltonian servo framework represents high-dimensional, nonlinear and non-Gaussian generalization of the classical Kalman servo system. After defining the Kalman servo as a motivation, we define the affine Hamiltonian neural network for adaptive nonlinear control of a team of UGVs in continuous time. We then define a high-dimensional Bayesian particle filter for estimation of a team of UGVs in discrete time. Finally, we formulate a hybrid Hamiltonian servo system by combining the continuous-time control and the discrete-time estimation into a coherent framework that works like a predictor-corrector system.

A real-time probabilistic channel flood-forecasting model based on the Bayesian particle filter approach

Reliable real-time probabilistic flood forecasting is critical for effective water management and flood protection all over the world. In this study, we develop a real-time probabilistic channel flood-forecasting model by combining a channel hydraulic model with the Bayesian particle filter approach. The new model is tested in the upstream river reach of Three Gorges Dam (TGD) on the Yangtze River, China. Stage observations at seven hydrological stations are used simultaneously to adjust the Manning's roughness coefficients and to update discharges and stages along the river reach to attain reliable probabilistic flood forecasting. The synthetic experiments are applied to demonstrate the new model's correction and forecasting performances. The real-world experiments show that the new model can make accurate flood forecasting as well as derive reliable intervals for different confidence levels. The new probabilistic flood forecasting model not only outperforms the existing deterministic channel flood-forecasting models in accuracy, but also provides a more robust tool with which to incorporate uncertainty into flood-control efforts.

Bayesian Particle Tracking of Traffic Flows

We develop a Bayesian particle filter for tracking traffic flows that is capable of capturing non-linearities and discontinuities present in flow dynamics. Our model includes a hidden state variable that captures sudden regime shifts between traffic free flow, breakdown and recovery. We develop an efficient particle learning algorithm for real time on-line inference of states and parameters. This requires a two step approach, first, resampling the current particles, with a mixture predictive distribution and second, propagation of states using the conditional posterior distribution. Particle learning of parameters follows from updating recursions for conditional sufficient statistics. To illustrate our methodology, we analyze measurements of daily traffic flow from the Illinois interstate I-55 highway system. We demonstrate how our filter can be used to inference the change of traffic flow regime on a highway road segment based on a measurement from freeway single-loop detectors. Finally, we conclude with directions for future research.

Localization and Tracking of Objects Using Cross-Correlation of Shadow Fading Noise

Multipath and shadow fading are the primary cause for positioning errors in a Received Signal Strength Indicator (RSSI) based localization scheme. While fading, in general, is detrimental to localization accuracy, cross-correlation and divergence properties of shadow fading residuals may be utilized to improve localization and tracking accuracy of mobile IEEE 802.15.4 transmitters. Therefore, this paper begins by presenting a stochastic filter that models the fast changing multipath fading as a mean reverting Ornstein-Uhlenbeck (OU) process followed by a Generalized Auto Regressive Conditional Heteroskedasticity (GARCH) filtering to isolate the slow changing shadow fading residuals from measured RSSI values. Subsequently, a novel wireless transmitter localization scheme that combines the measured cross-correlation in shadow fading residuals between adjacent receivers using a Student-t Copula likelihood function is proposed. However, the long convergence time for this highly non-convex copula function might render our method unsuitable for tracking applications. Therefore, we present a faster tracking method where the velocity and heading of a mobile transmitter are estimated from α-Divergence between shadow fading signals and an onboard gyroscope respectively. To bind the localization error in this tracking method, the transmitter location estimates are smoothed by a Bayesian particle filter. The performance of our proposed localization and tracking method is validated over simulations and hardware experiments.

Bayesian Estimation of Multiple Static Dipoles from a Time Series of MEG Data

Estimating current dipoles from MEG data is difficult because of the ill–posedness of the inverse problem, and the need of heuristically choices concerning, e.g., the number of sources. Bayesian Particle Filters, [1], are recent methods which produce automatic estimation for the dipole number and their parameters, casting the MEG inverse problem as a dynamic inverse problem. In [2] a new method has been proposed that allow to estimate the dipole configuration given a single topography: the space to be explored is reduced, thus more accurate approximations are obtained. Here we extend this work and present a novel approach that exploits the linear dependence of the data over the dipole moments. Assuming source number and positions being fixed in time it is able to analyze even whole time–series without increasing the computational cost and with an obvious advantage in term of SNR. SMC samplers for Bayesian Inverse Problem

Real-Time Identification of Incipient Surface Morphology Variations in Ultraprecision Machining Process

Real-time monitoring and control of surface morphology variations in their incipient stages are vital for assuring nanometric range finish in the ultraprecision machining (UPM) process. A real-time monitoring approach, based on predicting and updating the process states from sensor signals (using advanced neural networks (NNs) and Bayesian analysis) is reported for detecting the incipient surface variations in UPM. An ultraprecision diamond turning machine is instrumented with three miniature accelerometers, a three-axis piezoelectric dynamometer, and an acoustic emission (AE) sensor for process monitoring. The machine tool is used for face-turning aluminum 6061 discs to a surface finish (Ra) in the range of 15–25 nm. While the sensor signals (especially the vibration signal in the feed direction) are sensitive to surface variations, the extraneous noise from the environment, machine elements, and sensing system prevents direct use of raw signal patterns for early detection of surface variations. Also, nonlinear and time-varying nature of the process dynamics does not lend conventional statistical process monitoring techniques suitable for characterizing UPM-machined surfaces. Consequently, instead of just monitoring the raw sensor signal patterns, the nonlinear process dynamics wherefrom the signal evolves are more effectively captured using a recurrent predictor neural network (RPNN). The parameters of the RPNN (weights and biases) serve as the surrogates of the process states, which are updated in real-time, based on measured sensor signals using a Bayesian particle filter (PF) technique. We show that the PF-updated RPNN can effectively capture the complex signal evolution patterns. We use a mean-shift statistic, estimated from the PF-estimated surrogate states, to detect surface variation-induced changes in the process dynamics. Experimental investigations show that variations in surface characteristics can be detected within 15 ms of their inception using the present approach, as opposed to 30 ms or higher with the conventional statistical change detection methods tested.

Nonlinear estimation for 60GHz millimeter-wave radar system based on Bayesian particle filtering

In the 60GHz millimeter-wave radar communication systems, the nonlinear power amplifier is inevitable. In order to combat this problem, a promising estimation algorithm based on the particle filtering (PF) is presented here. By employing the conception of Bayesian approximation and sequential importance sampling, this appealing Monte Carlo random sampling method can address this complicated statistic estimation problem. In sharp contrast to the classical linear equalization problem, nevertheless, in the considered situation the PF-based method may become invalid due to the hardware nonlinearity and the resulting non-analytical importance function. To remedy this difficulty, based on the linearization technique a novel PF framework is suggested, and we show in particular how to linearize the involved nonlinearity transform in the formulated discrete dynamic state-space modeling (DSM). The merit of this method is that it can efficiently deal with discrete DSMs that are practically nonlinear and non-Gaussian. Experimental simulations verify the superior performance of our presented PF-based detection scheme, which may properly be applied to 60GHz millimeter-wave radar communication systems.

Low-Cost MEMS Sensors and Vision System for Motion and Position Estimation of a Scooter

The possibility to identify with significant accuracy the position of a vehicle in a mapping reference frame for driving directions and best-route analysis is a topic which is attracting a lot of interest from the research and development sector. To reach the objective of accurate vehicle positioning and integrate response events, it is necessary to estimate position, orientation and velocity of the system with high measurement rates. In this work we test a system which uses low-cost sensors, based on Micro Electro-Mechanical Systems (MEMS) technology, coupled with information derived from a video camera placed on a two-wheel motor vehicle (scooter). In comparison to a four-wheel vehicle; the dynamics of a two-wheel vehicle feature a higher level of complexity given that more degrees of freedom must be taken into account. For example a motorcycle can twist sideways; thus generating a roll angle. A slight pitch angle has to be considered as well; since wheel suspensions have a higher degree of motion compared to four-wheel motor vehicles. In this paper we present a method for the accurate reconstruction of the trajectory of a “Vespa” scooter; which can be used as alternative to the “classical” approach based on GPS/INS sensor integration. Position and orientation of the scooter are obtained by integrating MEMS-based orientation sensor data with digital images through a cascade of a Kalman filter and a Bayesian particle filter.

Finite Element based Bayesian Particle Filtering for the estimation of crack damage evolution on metallic panels

A lot of studies are nowadays devoted to structural health monitoring, especially inside the aeronautical environment. In particular, focusing the attention on metallic structures, fatigue cracks represent both a design and maintenance issue. The disposal of real time diagnostic technique for the assessment of structural health has led the attention also toward the prognostic assessment of the residual useful life, trying to develop robust prognostic health management systems to assist the operators in scheduling maintenance actions. The work reported inside this paper is about the development of a Bayesian particle filter to be used to refine the posterior probability density functions of both the damage condition and the residual useful life, given a prior knowledge on damage evolution is available from NASGRO material characterization. The prognostic algorithm has been applied to two cases. The former consists in an off-line application, receiving diagnostic inputs retrieved with manual structure scanning for fault identification. The latter is used on-line to filter the input coming from a real-time automatic diagnostic system. A massive usage of FEM simulations is used in order to enhance the algorithm performances.

Estimation Algorithm of Machine Operational Intention by Bayes Filtering with Self-Organizing Map

We present an intention estimator algorithm that can deal with dynamic change of the environment in a man-machine system and will be able to be utilized for an autarkical human-assisting system. In the algorithm, state transition relation of intentions is formed using a self-organizing map (SOM) from the measured data of the operation and environmental variables with the reference intention sequence. The operational intention modes are identified by stochastic computation using a Bayesian particle filter with the trainedSOM. This method enables to omit the troublesome process to specify types of information which should be used to build the estimator. Applying the proposed method to the remote operation task, the estimator's behavior was analyzed, the pros and cons of the method were investigated, and ways for the improvement were discussed. As a result, it was confirmed that the estimator can identify the intention modes at 44–94 percent concordance ratios against normal intention modes whose periods can be found by about 70 percent of members of human analysts. On the other hand, it was found that human analysts' discrimination which was used as canonical data for validation differed depending on difference of intention modes. Specifically, an investigation of intentions pattern discriminated by eight analysts showed that the estimator could not identify the same modes that human analysts could not discriminate. And, in the analysis of the multiple different intentions, it was found that the estimator could identify the same type of intention modes to human-discriminated ones as well as 62–73 percent when the first and second dominant intention modes were considered.

Map‐aided localization in sparse global positioning system environments using vision and particle filtering

AbstractA map‐aided localization approach using vision, inertial sensors when available, and a particle filter is proposed and empirically evaluated. The approach, termed PosteriorPose, uses a Bayesian particle filter to augment global positioning system (GPS) and inertial navigation solutions with vision‐based measurements of nearby lanes and stop lines referenced against a known map of environmental features. These map‐relative measurements are shown to improve the quality of the navigation solution when GPS is available, and they are shown to keep the navigation solution converged in extended GPS blackouts. Measurements are incorporated with careful hypothesis testing and error modeling to account for non‐Gaussian and multimodal errors committed by GPS and vision‐based detection algorithms. Using a set of data collected with Cornell's autonomous car, including a measure of truth via a high‐precision differential corrections service, an experimental investigation of important design elements of the PosteriorPose estimator is conducted. The algorithm is shown to statistically outperform a tightly coupled GPS/inertial navigation solution both in full GPS coverage and in extended GPS blackouts. Statistical performance is also studied as a function of road type, filter likelihood models, bias models, and filter integrity tests. © 2011 Wiley Periodicals, Inc.

A window to the amygdala: concurrent encoding of choice preference in multi-unit activity in the amygdala and in eye movements

was fitted to a subset of data which excluded that trial. Choice outcome was then predicted at each time point in the trial using a sequential Bayesian particle filter from likelihoods generated by the fitted model. The filter was considered to favor the right option over the left when the proportion of particles favoring right exceeded some threshold. The quality of the prediction was quantified at each time point using mutual information between predicted and observed outcomes across multiple thresholds. Averaging over thresholds reduces noise variance in the estimate of MI, allowing for a clearer representation of the time course of the prediction

Incremental object matching and detection with Bayesian methods and particle filters

This study is about object matching, that is, a problem of locating the corresponding points of an object in an image. Conventional approaches to object matching are batch methods, meaning that the methods first learn the object model from a training set of example images that contain instances of the object, and then use the learned object model to match instances of the same object (or object class) in unseen test images. Such batch learning often leads to computationally heavy learning, at least when the images are incorporated sequentially into the system and large memory requirements. In computer vision, little work has been done in developing incremental object learners. Especially, an incremental object-matching method has – to the best knowledge of the authors – never been introduced. In this paper, the authors present such a method. Our technique finds the corresponding points of similar object instances, appearing in natural greyscale images with arbitrary location, scale and orientation, by processing the images sequentially. The approach is Bayesian and combines the shape and appearance of the corresponding points into the posterior distribution for the location of them. The posterior distribution is recursively sampled with particle filters to locate the most probable corresponding point sets in the image being processed. The results indicate that the matched corresponding points can be used in forming a representation of the object with which instances of the object in novel test images are successfully detected.