Recursive Bayesian State Estimation Research Articles

Evaluation of recursive Bayesian filters for modal contribution estimation in high-tech compliant mechanisms

This study evaluates three recursive Bayesian input and state estimation algorithms, as introduced in the field of Structural Health Monitoring, for estimating modal contributions for high-tech compliant mechanisms. The aim of estimating modal contributions is the use for active vibration control. High-tech compliant motion stages allow for different sensor configurations, making new and interesting performance evaluations of these filters possible. The algorithms used, namely, the Augmented Kalman Filter (AKF), Dual Kalman Filter (DKF) and Gilijns de Moor Filter (GDF) are implemented on a compliant motion stage for guidance flexure deformation estimation. Our results show the GDF performs overall best, with good estimation performance and real-world tuning capability.

Cubature Kalman Filter Based Training of Hybrid Differential Equation Recurrent Neural Network Physiological Dynamic Models.

Modeling biological dynamical systems is challenging due to the interdependence of different system components, some of which are not fully understood. To fill existing gaps in our ability to mechanistically model physiological systems, we propose to combine neural networks with physics-based models. Specifically, we demonstrate how we can approximate missing ordinary differential equations (ODEs) coupled with known ODEs using Bayesian filtering techniques to train the model parameters and simultaneously estimate dynamic state variables. As a study case we leverage a well-understood model for blood circulation in the human retina and replace one of its core ODEs with a neural network approximation, representing the case where we have incomplete knowledge of the physiological state dynamics. Results demonstrate that state dynamics corresponding to the missing ODEs can be approximated well using a neural network trained using a recursive Bayesian filtering approach in a fashion coupled with the known state dynamic differential equations. This demonstrates that dynamics and impact of missing state variables can be captured through joint state estimation and model parameter estimation within a recursive Bayesian state estimation (RBSE) framework. Results also indicate that this RBSE approach to training the NN parameters yields better outcomes (measurement/state estimation accuracy) than training the neural network with backpropagation through time in the same setting.

Recursive Bayesian state estimation method for run‐to‐run control in high‐mixed semiconductor manufacturing process

AbstractOne of the challenges in semiconductor manufacturing processes is the state estimation of a high‐mix production system. The traditional algorithm consists of constructing a context matrix based on the product fabricating thread. The state of the context matrix is estimated using the Moore‐Penrose pseudo‐inverse method. Although the method works well, the context matrix is often singular. Taking an integrated moving average disturbance into consideration, a novel state estimation method is proposed in a high‐mix manufacturing scenario. Furthermore, the recursive Bayesian estimation is presented to obtain the estimations of states combined with a moving window and an analysis of variance model. As a result, the calculation of the inverse of the context matrix is avoided and the unobservability problem is addressed. Both simulated and industrial cases are presented to demonstrate the effectiveness of the proposed algorithm.

Target tracking via recursive Bayesian state estimation in cognitive radar networks

To cope with complicated environments and stealthier targets, incorporating intelligence and cognition cycles into target tracking is of great importance in modern sensor network management. With remarkable advances in sensor techniques and deployable platforms, a sensing system has freedom to select a subset of available radars, plan their trajectories, and transmit designed waveforms. In this paper, we propose a general framework for single target tracking in cognitive networks of radars, including consideration of waveform design, path planning, and radar selection, which are separately but not jointly taken into account in existing work. The tracking procedure, built on the theories of dynamic graphical models (DGM) and recursive Bayesian state estimation (RBSE), is formulated as two iterative steps: (i) solving a combinatorial optimization problem to select the optimal subset of radars, waveforms, and locations for the next tracking instant, and (ii) acquiring the recursive Bayesian state estimation to accurately track the target. Further, an illustrative example introduces a specific scenario in 2-D space. Simulation results based on the scenario demonstrate that the proposed framework can accurately track the target under the management of the network of radars.

An Active RBSE Framework to Generate Optimal Stimulus Sequences in a BCI for Spelling.

A class of brain computer interfaces (BCIs) employs noninvasive recordings of electroencephalography (EEG) signals to enable users with severe speech and motor impairments to interact with their environment and social network. For example, EEG based BCIs for typing popularly utilize event related potentials (ERPs) for inference. Presentation paradigm design in current ERP-based letter by letter typing BCIs typically query the user with an arbitrary subset characters. However, the typing accuracy and also typing speed can potentially be enhanced with more informed subset selection and flash assignment. In this manuscript, we introduce the active recursive Bayesian state estimation (active-RBSE) framework for inference and sequence optimization. Prior to presentation in each iteration, rather than showing a subset of randomly selected characters, the developed framework optimally selects a subset based on a query function. Selected queries are made adaptively specialized for users during each intent detection. Through a simulation-based study, we assess the effect of active-RBSE on the performance of a language-model assisted typing BCI in terms of typing speed and accuracy. To provide a baseline for comparison, we also utilize standard presentation paradigms namely, row and column matrix presentation paradigm and also random rapid serial visual presentation paradigms. The results show that utilization of active-RBSE can enhance the online performance of the system, both in terms of typing accuracy and speed. Moreover, we conduct real time experiments with human participants to study the human-in-the-loop effect on the performance of the proposed active-RBSE framework and consistent with the simulation results, the results of these experiments show improvement both in typing speed and accuracy.

A Moving Window Formulation for Recursive Bayesian State Estimation of Systems with Irregularly Sampled and Variable Delays in Measurements

The time delay involved between sampling and obtaining measurements of certain quality variables is a common scenario in various process applications. Further, this delay is not fixed and can vary for various reasons. Moreover, certain measurements may be sampled at irregular time intervals. The state estimation algorithms available in the literature have been developed for the scenario where the measurements are sampled regularly or are available after a fixed time delay. In this work, a recursive moving window Bayesian state estimator formulation is proposed to utilize such measurements with variable time delays to compute the state estimates. The length of the moving window ensures that the algorithm utilizes all the available measurements (delayed or otherwise) for computing the state estimates. In practice, it may also become necessary to account for the physical bounds on the states. A constrained version of the moving window recursive state estimator is also developed to yield state estimates that are consistent with their respective bounds and constraints. The efficacy of the unconstrained moving window state estimator is demonstrated by application on the benchmark Tennessee Eastman simulation case study and an experimental two-tank heater−mixer setup, while the efficacy of the constrained moving window state estimator is demonstrated by simulation of a benchmark gas-phase batch reactor system.

Using particle filter to track horizontal variations of atmospheric duct structure from radar sea clutter

Abstract. This paper addresses the problem of estimating range-varying parameters of the height-dependent refractivity over the sea surface from radar sea clutter. In the forward simulation, the split-step Fourier parabolic equation (PE) is used to compute the radar clutter power in the complex refractive environments. Making use of the inherent Markovian structure of the split-step Fourier PE solution, the refractivity from clutter (RFC) problem is formulated within a nonlinear recursive Bayesian state estimation framework. Particle filter (PF), which is a technique for implementing a recursive Bayesian filter by Monte Carlo simulations, is used to track range-varying characteristics of the refractivity profiles. Basic ideas of employing PF to solve RFC problem are introduced. Both simulation and real data results are presented to confirm the feasibility of PF-RFC performances.

Bayesian histogram filter localizer performance in a multiple contact, continental shelf environment.

Model-based recursive Bayesian state estimation provides a straight forward way of including a priori environmental knowledge in a localization framework. Previous work by Jemmott et al. demonstrates successful range and depth localization of an acoustic source using this method and data from a single hydrophone. However, that work utilized a relatively benign environment from the SWellEx 96 experiment in which only two source signals were present. This talk will extend the work of Jemmott et al. and discuss the performance of the localization scheme in a multiple contact, continental shelf environment. [Work supported by ONR Undersea Signal Processing.]

Recursive Bayesian state estimation for passive sonar localization.

A model‐based recursive Bayesian signal processing framework is shown to localize a moving source emitting a low‐frequency tonal signal in a shallow water environment. Source motion maps spatial variation in transmission loss into amplitude modulation of the signal received on a passive horizontal array. Acoustic propagation modeling predicts this variability, which is used to estimate source range, depth, range rate, and acoustic level. Uncertainty in transmission loss resulting from uncertainty in environmental parameters is predicted using Monte Carlo modal propagation modeling. Monte Carlo marginalization over environmental uncertainty provides robustness against data‐model mismatch. The maximum entropy method is used to construct a probability density function (pdf) of transmission loss at each range depth location based on the Monte Carlo results. The resulting pdfs belong to the exponential family and result in an implementable recursive Bayesian processor. The physics of acoustic modeling determine the form of the processor through the transmission loss pdfs and are an intimate part of the localization technique. This processor is distinct from Bayesian matched field processing in that it neither relies on a vertical array nor computes modal amplitudes from received data. Results using SWellEx‐96 will be shown. [Work supported by ONR Undersea Signal Processing.]

Recursive Bayesian electromagnetic refractivity estimation from radar sea clutter

Estimation of the range‐ and height‐dependent index of refraction over the sea surface facilitates prediction of ducted microwave propagation loss. In this paper, refractivity estimation from radar clutter returns is performed using a Markov state space model for microwave propagation. Specifically, the parabolic approximation for numerical solution of the wave equation is used to formulate the refractivity from clutter (RFC) problem within a nonlinear recursive Bayesian state estimation framework. RFC under this nonlinear state space formulation is more efficient than global fitting of refractivity parameters when the total number of range‐varying parameters exceeds the number of basis functions required to represent the height‐dependent field at a given range. Moreover, the range‐recursive nature of the estimator can be easily adapted to situations where the refractivity modeling changes at discrete ranges, such as at a shoreline. A fast range‐recursive solution for obtaining range‐varying refractivity is achieved by using sequential importance sampling extensions to state estimation techniques, namely, the forward and Viterbi algorithms. Simulation and real data results from radar clutter collected off Wallops Island, Virginia, are presented which demonstrate the ability of this method to produce propagation loss estimates that compare favorably with ground truth refractivity measurements.