Sequential Bayesian Estimation Research Articles

Localization and Tracking of Discrete Mobile Scatterers in Vehicular Environments Using Delay Estimates.

This paper describes an approach to detect, localize, and track moving, non-cooperative objects by exploiting multipath propagation. In a network of spatially distributed transmitting and receiving nodes, moving objects appear as discrete mobile scatterers. Therefore, the localization of mobile scatterers is formulated as a nonlinear optimization problem. An iterative nonlinear least squares algorithm following Levenberg and Marquardt is used for solving the optimization problem initially, and an extended Kalman filter is used for estimating the scatterer location recursively over time. The corresponding performance bounds are derived for both the snapshot based position estimation and the nonlinear sequential Bayesian estimation with the classic and the posterior Cramér–Rao lower bound. Thereby, a comparison of simulation results to the posterior Cramér–Rao lower bound confirms the applicability of the extended Kalman filter. The proposed approach is applied to estimate the position of a walking pedestrian sequentially based on wideband measurement data in an outdoor scenario. The evaluation shows that the pedestrian can be localized throughout the scenario with an accuracy of m at 90% confidence.

A state-space model for dynamic functional connectivity.

Dynamic functional connectivity (DFC) analysis involves measuring correlated neural activity over time across multiple brain regions. Significant regional correlations among neural signals, such as those obtained from resting-state functional magnetic resonance imaging (fMRI), may represent neural circuits associated with rest. The conventional approach of estimating the correlation dynamics as a sequence of static correlations from sliding time-windows has statistical limitations. To address this issue, we propose a multivariate stochastic volatility model for estimating DFC inspired by recent work in econometrics research. This model assumes a state-space framework where the correlation dynamics of a multivariate normal observation sequence is governed by a positive-definite matrix-variate latent process. Using this statistical model within a sequential Bayesian estimation framework, we use blood oxygenation level dependent activity from multiple brain regions to estimate posterior distributions on the correlation trajectory. We demonstrate the utility of this DFC estimation framework by analyzing its performance on simulated data, and by estimating correlation dynamics in resting state fMRI data from a patient with a disorder of consciousness (DoC). Our work advances the state-of-the-art in DFC analysis and its principled use in DoC biomarker exploration.

Bayesian sequential least-squares estimation for the drift of a Wiener process

Given a Wiener process with unknown and unobservable drift, we try to estimate this drift as effectively but also as quickly as possible, in the presence of a quadratic penalty for the estimation error and of a fixed, positive cost per unit of observation time. In a Bayesian framework, where the unobservable drift is assumed to have a known “prior” distribution, this question reduces to choosing judiciously a stopping time for an appropriate diffusion process in natural scale. We establish structural properties of the solution for the corresponding problem of optimal stopping. In particular, we show that, regardless of the prior distribution, the continuation region is monotonically shrinking in time. Moreover, we provide conditions on the prior distribution that guarantee a one-sided stopping region. Lastly, some concrete prior distributions are studied to illustrate the theoretical results.

Sequential Bayesian estimation of state and input in dynamical systems using output-only measurements

• A sequential Bayesian method is proposed for estimating the state and input forces. • Covariance matrices of the process and measurement noise are updated sequentially. • Estimations of the state and input have decent accuracy and stability. • Low-frequency drift appearing in estimations of the input and state is eliminated. The problem of joint estimation of the state and input in linear time-invariant dynamical systems is revisited proposing novel sequential Bayesian formulations. An appealing feature of the proposed method is the promise it delivers for updating the covariance matrices of the process and measurement noise in a real-time fashion using asymptotic approximations. The proposed method avoids the direct transmission of the input into predictions of the state using a zero-mean Gaussian distribution for the input. This prior distribution aims to eliminate low-frequency drifts from estimations of the state and input. Moreover, the method is outlined in a computational algorithm offering real-time estimations of the state and input forces. Numerical and experimental examples are used to examine and demonstrate the efficacy of the method. It is observed that the proposed method achieves decent accuracy for estimating the state, input forces, and noise covariance matrices when compared to the actual values. Contrary to the present methods that produce significant low-frequency drifts while using noisy acceleration response-only measurements, the proposed method offers drift-free perfect predictions. This Bayesian filtering-technique proposed for the reconstruction of the state and input forces can next be employed in the emerging fatigue prognosis frameworks.

Bayesian sequential procedure to estimate the viability of seeds Coffea arabica L. in tetrazolium test

Tetrazolium tests use conventional sampling techniques in which a sample has a fixed size. These tests may be improved by sequential sampling, which does not work with fixedsize samples. When data obtained from an experiment are analyzed sequentially the analysis can be terminated when a particular decision has been made, and thus, there is no need to pre-establish the number of seeds to assess. Bayesian statistics can also help, if we have sufficient knowledge about coffee production in the area to construct a prior distribution. Therefore, we used the Bayesian sequential approach to estimate the percentage of viable coffee seeds submitted to tetrazolium testing, and we incorporated priors with information from other analyses of crops from previous years. We used the Beta prior distribution and, using data obtained from sample lots of Coffea arabica, determined its hyperparameters with a histogram and O’Hagan’s methods. To estimate the lowest risk, we computed the Bayes risks, which provided us with a basis for deciding whether or not we should continue the sampling process. The results confirm that the Bayesian sequential estimation can indeed be used for the tetrazolium test: the average percentage of viability obtained with the conventional frequentist method was 88 %, whereas that obtained with the Bayesian method with both priors was 89 %. However, the Bayesian method required, on average, only 89 samples to reach this value while the traditional estimation method needed as many as 200 samples.

Proprioceptive Localization Assisted by Magnetoreception: A Minimalist Intermittent Heading Based Approach

We report a localization method that does not rely on the perception and recognition of landmarks for a robot/vehicle traveling in urban area. This is intended to be a fall back solution when everything else fails due to bad weather or other environmental challenges. The method is also very low cost and does not require intensive computation. Named as proprioceptive localization assisted by magnetoreception (PLAM), it employs a gyroscope and a compass to sense heading changes and matches the heading sequence with a preprocessed heading graph to localize the robot. We track the sensory and map uncertainties and model them in the process to formulate a sequential Bayesian estimation problem framework. Not all cases can be successful because degenerated maps may consist of rectangular grid-like streets and the robot may travel in a loop. To analyze these, we use information entropy to model map characteristics and perform both simulation and experiments to find out typical heading and information entropy requirements for localization. We have implemented our algorithm and tested it with both simulated and physical experiments. The results have confirmed that PLAM can localize vehicles on the map for nondegenerated cases.

A Scalable Algorithm for Network Localization and Synchronization

The Internet of Things (IoT) will seamlessly integrate a large number of densely deployed heterogeneous devices and will enable new location-aware services. However, fine-grained localization of IoT devices is challenging as their computation and communication resources are typically limited and different devices may have different qualities of internal clocks and different mobility patterns. To address these challenges, we propose a cooperative, scalable, and time-recursive algorithm for network localization and synchronization (NLS). Our algorithm is based on time measurements and supports heterogeneous devices with limited computation and communication resources, time-varying clock and location parameters, arbitrary state-evolution models, and time-varying network connectivity. These attributes make the proposed algorithm attractive for IoT-related applications. The algorithm is furthermore able to incorporate measurements from additional sensors for positioning, navigation, and timing such as receivers for global navigation satellite systems. Based on a factor graph representation of the underlying spatiotemporal Bayesian sequential estimation problem, the algorithm uses belief propagation (BP) for an efficient marginalization of the joint posterior distribution. To account for the nonlinear measurement model and nonlinear state-evolution models while keeping the communication and computation requirements low, we develop an efficient second-order implementation of the BP rules by means of the recently introduced sigma point belief propagation technique. Simulation results demonstrate the high synchronization and localization accuracy as well as the low computational complexity of the proposed algorithm. In particular, in sufficiently dense networks, the proposed algorithm outperforms the state-of-the-art BP-based algorithm for NLS in terms of both estimation accuracy and computational complexity.

Bayesian sequential joint detection and estimation

Joint detection and estimation refers to deciding between two or more hypotheses and, depending on the test outcome, simultaneously estimating the unknown parameters of the underlying distribution. This problem is investigated in a sequential framework under mild assumptions on the underlying random process. We formulate an unconstrained sequential decision problem, whose cost function is the weighted sum of the expected run-length and the detection/estimation errors. Then, a strong connection between the derivatives of the cost function with respect to the weights, which can be interpreted as Lagrange multipliers, and the detection/estimation errors of the underlying scheme is shown. This property is used to characterize the solution of a closely related sequential decision problem, whose objective function is the expected run-length under constraints on the average detection/estimation errors. We show that the solution of the constrained problem coincides with the solution of the unconstrained problem with suitably chosen weights. These weights are characterized as the solution of a linear program, which can be solved using efficient off-the-shelf solvers. The theoretical results are illustrated with two example problems, for which optimal sequential schemes are designed numerically and whose performance is validated via Monte Carlo simulations.

Covariance Modeling in Applications of Data Assimilation to High-dimensional Earth and Geospace Systems

Data assimilation and inverse methods play a key role in integrating remote-sensing and in-situ Earth and Geospace observations into models of the Earth and Geospace system and subsystems, enabling weather prediction and climate projection of high societal relevance. The problem presents considerable methodological and computational challenges because of the high-dimensionality and non-linearity of the underling dynamics of the Earth and Geospace system and the large volumes of heterogeneous observations from various observing platforms, including Low-Earth-Orbit and geosynchronous-Earth-orbit satellites as well as ground-based and airborne platforms. To make the problem tractable, most data assimilation methods resort to scalable methods derived from well-established Gaussian process-based formulation of the sequential Bayesian estimation problem. One such approach is to use approximate Kalman filters that rely on low-rank approximations of the covariance matrices. In ensemble data assimilation, the covariance is expressed in the subspace spanned by the model ensemble that evolves dynamically. Though the low-rank ensemble-based approximation allows the covariance to track non-linear dynamics with a moderate computational cost, the impact of the observations that lie outside of the subspace represented by the ensemble cannot be effectively incorporated into the assimilation analysis. One heuristic remedy widely used in numerical weather prediction is to adopt a hybrid method that uses the full-rank stationary covariance and the ensemble-based covariance. As a scalable approach to modeling the full-rank nonstationary covariance, the use of a multiresolution-based covariance is discussed.

Parametric estimation of dispersive viscoelastic layered media with application to structural health monitoring

We present a sequential Bayesian estimation method to estimate the material parameters that govern the one-dimensional propagation of shear waves through continuous, layered, viscoelastic solids. While the proposed estimation method is generic, namely, can be applied to waveform inversion problems that satisfy the above conditions, we here employ it for system identification of building structures. We approximate the linear-elastic response of building structures subjected to low-amplitude earthquake base excitations by a multilayer dispersive shear beam model with Kelvin-Voigt material subjected to vertically propagating shear waves. Utilizing the proposed sequential Bayesian estimation method, we sequentially update the probability distribution function of the unknown parameters to reduce the discrepancies between the estimated and measured frequency response functions. We next verify and validate the performance of the proposed estimation method and investigate the limitations of the presented structural system identification approach using two case studies. In the first case study, we use the simulated structural response of a three-dimensional 52-story building model subjected to bi-directional low-amplitude ground shakings. We estimate the frequency-dependent phase velocity and damping ratio, as well as the mass distribution along the building height. Then, we verify the structural damage detection and localization capabilities of the presented system identification approach by comparing the wave model parameters estimated from simulated response of undamaged and damaged structural models. In the second case study, we use data measured from a shake table experiment on a full-scale five-story reinforced concrete building specimen, where the estimated wave model parameters capture the progressive structural damage in the test specimen. The validation studies suggest that the sequential Bayesian estimation method based on viscoelastic dispersive wave propagation can be used for system and damage identification of building structures.

Asymptotically optimal procedures in multivariate Bayesian sequential estimation

ABSTRACTIn this article, we consider the problem of multivariate Bayesian sequential estimation of the unknown mean vector. We propose a robust sequential procedure without using the prior information or any auxiliary data, which is similar to multivariate non-Bayesian sequential estimation by M. Ghosh et al. (1976). The proposed procedure, depending only on the present data but not on its distribution, is shown to be asymptotically as well as or better than the optimal fixed-sample-size procedures for the arbitrary distributions and asymptotically pointwise optimal and asymptotically optimal for multivariate exponential family with a large class of prior distributions.

Sequential Bayesian learning for stochastic volatility with variance‐gamma jumps in returns

In this work, we investigate sequential Bayesian estimation for inference of stochastic volatility with variance‐gamma (SVVG) jumps in returns. We develop an estimation algorithm that combines the sequential learning auxiliary particle filter with the particle learning filter. Simulation evidence and empirical estimation results indicate that this approach is able to filter latent variances, identify latent jumps in returns, and provide sequential learning about the static parameters of SVVG. We demonstrate comparative performance of the sequential algorithm and off‐line Markov Chain Monte Carlo in synthetic and real data applications.

Optimizing player’s formations for corner-kick situations in RoboCup soccer 2D simulation

In the domain of the Soccer simulation 2D league of the RoboCup, appropriate player positioning against the opponent team formation is an important factor of soccer team performance. In this work, we propose to use a meta-heuristic algorithm called the firefly algorithm to optimize player positioning. We used sequential Bayesian estimation as well as parallelization to reduce the necessary number of time-consuming simulated soccer matches. As a first trial of our system, we optimized the corner-kick formation. Preliminary results in optimizing the corner-kick formation are not advantageous over the previous handmade formation due to the difficulty in tuning the meta-heuristic algorithm parameters. However, it is also shown that the proposed system is effective in handling a high load of simulations over the span of weeks and therefore is promising to be usable to optimize player positioning.

Neuromusculoskeletal model self-calibration for on-line sequential bayesian moment estimation

Objective. Neuromusculoskeletal models involve many subject-specific physiological parameters that need to be adjusted to adequately represent muscle properties. Traditionally, neuromusculoskeletal models have been calibrated with a forward-inverse dynamic optimization which is time-consuming and unfeasible for rehabilitation therapy. Non self-calibration algorithms have been applied to these models. To the best of our knowledge, the algorithm proposed in this work is the first on-line calibration algorithm for muscle models that allows a generic model to be adjusted to different subjects in a few steps. Approach. In this paper we propose a reformulation of the traditional muscle models that is able to sequentially estimate the kinetics (net joint moments), and also its full self-calibration (subject-specific internal parameters of the muscle from a set of arbitrary uncalibrated data), based on the unscented Kalman filter. The nonlinearity of the model as well as its calibration problem have obliged us to adopt the sum of Gaussians filter suitable for nonlinear systems. Main results. This sequential Bayesian self-calibration algorithm achieves a complete muscle model calibration using as input only a dataset of uncalibrated sEMG and kinematics data. The approach is validated experimentally using data from the upper limbs of 21 subjects. Significance. The results show the feasibility of neuromusculoskeletal model self-calibration. This study will contribute to a better understanding of the generalization of muscle models for subject-specific rehabilitation therapies. Moreover, this work is very promising for rehabilitation devices such as electromyography-driven exoskeletons or prostheses.

Approximate Inference for Time-Varying Interactions and Macroscopic Dynamics of Neural Populations

The models in statistical physics such as an Ising model offer a convenient way to characterize stationary activity of neural populations. Such stationary activity of neurons may be expected for recordings from in vitro slices or anesthetized animals. However, modeling activity of cortical circuitries of awake animals has been more challenging because both spike-rates and interactions can change according to sensory stimulation, behavior, or an internal state of the brain. Previous approaches modeling the dynamics of neural interactions suffer from computational cost; therefore, its application was limited to only a dozen neurons. Here by introducing multiple analytic approximation methods to a state-space model of neural population activity, we make it possible to estimate dynamic pairwise interactions of up to 60 neurons. More specifically, we applied the pseudolikelihood approximation to the state-space model, and combined it with the Bethe or TAP mean-field approximation to make the sequential Bayesian estimation of the model parameters possible. The large-scale analysis allows us to investigate dynamics of macroscopic properties of neural circuitries underlying stimulus processing and behavior. We show that the model accurately estimates dynamics of network properties such as sparseness, entropy, and heat capacity by simulated data, and demonstrate utilities of these measures by analyzing activity of monkey V4 neurons as well as a simulated balanced network of spiking neurons.

Feasibility study on real-time γ-ray spectrum / dose measurement system

Recently, medical applications of radiation have been widely spread. However, exposure of medical staffs is sometimes not focused on because treatment of patients is the first priority. It is thus important to decrease exposure for them as much as possible. The purpose of this study is to develop a system which can measure energy spectrum and dose of gamma-rays at the same time in real time in medical application spots. As a result, the medical staff could be guided to aware the risk of radiation and finally the exposure dose to them could be suppressed substantially. We first decided to use a CsI(Tl) scintillator as the gamma-ray detection device. A Multi-Pixel Photon Counter (MPPC) was attached to the scintillator to detect gamma-ray signals. Pulse height spectra were measured with several standard gamma-ray sources. The detection efficiency and energy resolution were deduced from the measured results and the detection efficiency was compared with the calculation result by MCNP5. After evaluating the response function, the energy spectrum was derived with the spectrum type Bayesian estimation and the sequential Bayesian estimation procedure. From the result, it was confirmed that the sequential Bayesian estimation could be applied to real time measurement of gamma-ray energy spectrum and dose.

Real-time 3D reconstruction of non-rigid shapes with a single moving camera

This paper describes a real-time sequential method to simultaneously recover the camera motion and the 3D shape of deformable objects from a calibrated monocular video. For this purpose, we consider the Navier-Cauchy equations used in 3D linear elasticity and solved by finite elements, to model the time-varying shape per frame. These equations are embedded in an extended Kalman filter, resulting in sequential Bayesian estimation approach. We represent the shape, with unknown material properties, as a combination of elastic elements whose nodal points correspond to salient points in the image. The global rigidity of the shape is encoded by a stiffness matrix, computed after assembling each of these elements. With this piecewise model, we can linearly relate the 3D displacements with the 3D acting forces that cause the object deformation, assumed to be normally distributed. While standard finite-element-method techniques require imposing boundary conditions to solve the resulting linear system, in this work we eliminate this requirement by modeling the compliance matrix with a generalized pseudoinverse that enforces a pre-fixed rank. Our framework also ensures surface continuity without the need for a post-processing step to stitch all the piecewise reconstructions into a global smooth shape. We present experimental results using both synthetic and real videos for different scenarios ranging from isometric to elastic deformations. We also show the consistency of the estimation with respect to 3D ground truth data, include several experiments assessing robustness against artifacts and finally, provide an experimental validation of our performance in real time at frame rate for small maps.

Asymptotic optimality of myopic information-based strategies for Bayesian adaptive estimation

This paper presents a general asymptotic theory of sequential Bayesian estimation giving results for the strongest, almost sure convergence. We show that under certain smoothness conditions on the probability model, the greedy information gain maximization algorithm for adaptive Bayesian estimation is asymptotically optimal in the sense that the determinant of the posterior covariance in a certain neighborhood of the true parameter value is asymptotically minimal. Using this result, we also obtain an asymptotic expression for the posterior entropy based on a novel definition of almost sure convergence on “most trials” (meaning that the convergence holds on a fraction of trials that converges to one). Then, we extend the results to a recently published framework, which generalizes the usual adaptive estimation setting by allowing different trial placements to be associated with different, random costs of observation. For this setting, the author has proposed the heuristic of maximizing the expected information gain divided by the expected cost of that placement. In this paper, we show that this myopic strategy satisfies an analogous asymptotic optimality result when the convergence of the posterior distribution is considered as a function of the total cost (as opposed to the number of observations).

Inversion of ship-noise scalar and vector fields to characterize sediments: A critical review of experimental results (2007–2014)

During geophysical and ecosystem surveys in Mediterranean and Atlantic shallow waters, research vessels, fishing boats, and passenger ferries were used as acoustic sources of opportunity to characterize bottom sediments of different types including mud, fluid mud, and sand. The ships sailed a straight course at constant engine speed while a compact vertical array of pressure or pressure-gradient sensors, deployed from a small boat, sampled the generated noise field over a broad frequency range. Different acoustic observables were investigated that do not depend on the knowledge of ship noise characteristics to mitigate the impact of such uncertainty. For sole pressure measurement, extraction and parameterization of striation structures in range-frequency spectrograms at different receiver depths allow to determine effectively compression wave speed and thickness of a sediment layer as compared to a reference. For additional pressure gradient measurement, vertical impedances are estimated at different depths whose range and frequency dependence are highly sensitive to bottom properties and, in particular, density. Global optimization via genetic algorithm and sequential Bayesian estimation via particle filtering maximize the degree of similarity between predicted and measured impedance data. The paper will critically review the experimental results and compare them with ground truth data. [Work supported by ONR, FNRS-CNPq, WBI-CAPES, PREFACE project EC DG Env FP7.]

Structure-Induced Complex Kalman Filter for Decentralized Sequential Bayesian Estimation

The letter considers a multi-sensor state estimation problem configured in a decentralized architecture where local complex statistics are communicated to the central processing unit for fusion instead of the raw observations. Naive adaptation of the augmented complex statistics to develop a decentralized state estimation algorithm results in increased local computations, and introduces extensive communication overhead, making it practically unattractive. The letter proposes a structure-induced complex Kalman filter framework with reduced communication overhead. In order to further reduce the local computations, the letter proposes a non-circularity criterion which allows each node to examine the non-circularity of its local observations. A local sensor node disregards its extra second-order statistical information when the non-circularity coefficient is small. In cases where the local observations are highly non-circular, an intuitively pleasing circularization approach is proposed to avoid computation and communication of the pseudo-covariance matrices. Simulation results indicate that the proposed structured-induced complex Kalman filter (SCKF) provides significant performance improvements over its traditional counterparts.