State Space Modeling of Event Count Time Series

This paper proposes a class of algorithms for analyzing event count time series, based on state space modeling and Kalman filtering. While the dynamics of the state space model is kept Gaussian and linear, a nonlinear observation function is chosen. In order to estimate the states, an iterated extended Kalman filter is employed. Positive definiteness of covariance matrices is preserved by a square-root filtering approach, based on singular value decomposition. Non-negativity of the count data is ensured, either by an exponential observation function, or by a newly introduced "affinely distorted hyperbolic" observation function. The resulting algorithm is applied to time series of the daily number of seizures of drug-resistant epilepsy patients. This number may depend on dosages of simultaneously administered anti-epileptic drugs, their superposition effects, delay effects, and unknown factors, making the objective analysis of seizure counts time series arduous. For the purpose of validation, a simulation study is performed. The results of the time series analysis by state space modeling, using the dosages of the anti-epileptic drugs as external control inputs, provide a decision on the effect of the drugs in a particular patient, with respect to reducing or increasing the number of seizures.

Resource-efficient adaptive Bayesian tracking of magnetic fields with a quantum sensor

Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be minimised. Bayesian estimation and adaptive experiment optimisation can speed up the sensing process by reducing the number of measurements required. These protocols consist of computing and updating the probability distribution of the magnetic field based on measurement outcomes and of determining optimized acquisition settings for the next measurement. However, the computational steps feeding into the measurement settings of the next iteration must be performed quickly enough to allow real-time updates. This article addresses the issue of computational speed by implementing an approximate Bayesian estimation technique, where probability distributions are approximated by a finite sum of Gaussian functions. Given that only three parameters are required to fully describe a Gaussian density, we find that in many cases, the magnetic field probability distribution can be described by fewer than ten parameters, achieving a reduction in computation time by factor 10 compared to existing approaches. ForT2*=1μs, only a small decrease in computation time is achieved. However, in these regimes, the proposed Gaussian protocol outperforms the existing one in tracking accuracy.

A novel adaptive resampling for sequential Bayesian filtering to improve frequency estimation of time-varying signals

This paper presents a new algorithm for adaptive resampling, called percentile-based resampling (PBR) in a sequential Bayesian filtering, i.e., particle filter (PF) in particular, to improve tracking quality of the frequency trajectories under noisy environments. Since the conventional resampling scheme used in the PF suffers from computational burden, resulting in less efficiency in terms of computation time and complexity as well as the real time applications of the PF. The strategy to remedy this issue is proposed in this work. After state updating, important high particle weights are used to formulate the pre-set percentile in each sequential iteration to create a new set of high quality particles for the next filtering stage. The number of particles after PBR remains the same as the original. To verify the effectiveness of the proposed method, we first evaluated the performance of the method via numerical examples to a complex and highly nonlinear benchmark system. Then, the proposed method was implemented for frequency estimation for two time-varying signals. From the experimental results, via three measurement metrics, our approach delivered better performance than the others. Frequency estimates obtained by our method were excellent as compared to the conventional resampling method when number of particles were identical. In addition, the computation time of the proposed work was faster than those recent adaptive resampling schemes in literature, emphasizing the superior performance to the existing ones.

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.

A Comprehensive Case Study of Data-Driven Methods for Robust Aircraft Sensor Fault Isolation

Recent catastrophic events in aviation have shown that current fault diagnosis schemes may not be enough to ensure a reliable and prompt sensor fault diagnosis. This paper describes a comparative analysis of consolidated data-driven sensor Fault Isolation (FI) and Fault Estimation (FE) techniques using flight data. Linear regression models, identified from data, are derived to build primary and transformed residuals. These residuals are then implemented to develop fault isolation schemes for 14 sensors of a semi-autonomous aircraft. Specifically, directional Mahalanobis distance-based and fault reconstruction-based techniques are compared in terms of their FI and FE performance. Then, a bank of Bayesian filters is proposed to compute, in flight, the fault belief for each sensor. Both the training and the validation of the schemes are performed using data from multiple flights. Artificial faults are injected into the fault-free sensor measurements to reproduce the occurrence of failures. A detailed evaluation of the techniques in terms of FI and FE performance is presented for failures on the air-data sensors, with special emphasis on the True Air Speed (TAS), Angle of Attack (AoA), and Angle of Sideslip (AoS) sensors.

Application of Machine Learning Models for Tracking Participant Skills in Cognitive Training

A key need in cognitive training interventions is to personalize task difficulty to each user and to adapt this difficulty to continually apply appropriate challenges as users improve their skill to perform the tasks. Here we examine how Bayesian filtering approaches, such as hidden Markov models and Kalman filters, and deep-learning approaches, such as the long short-term memory (LSTM) model, may be useful methods to estimate user skill level and predict appropriate task challenges. A possible advantage of these models over commonly used adaptive methods, such as staircases or blockwise adjustment methods that are based only upon recent performance, is that Bayesian filtering and deep learning approaches can model the trajectory of user performance across multiple sessions and incorporate data from multiple users to optimize local estimates. As a proof of concept, we fit data from two large cohorts of undergraduate students performing WM training using an N-back task. Results show that all three models predict appropriate challenges for different users. However, the hidden Markov models were most accurate in predicting participants' performances as a function of provided challenges, and thus, they placed participants at appropriate future challenges. These data provide good support for the potential of machine learning approaches as appropriate methods to personalize task performance to users in tasks that require adaptively determined challenges.

Iterated posterior linearization filters and smoothers with cross-correlated noises

In the article, several concise and efficient iterated posterior linearization filtering and smoothing methodologies are proposed for nonlinear systems with cross-correlated noises. Based on the Gaussian approximation (GA), the presented methods are derived via performing statistical linear regressions (SLRs) of the nonlinear state-space models w.r.t the current posterior distribution in an iterated way. Various posterior linearization methods can be developed by employing different approximation computation approaches for the Gaussian-weighted integrals encountered in SLRs. These new estimation methods enjoy not only the accuracy and robustness of the GA filter but also the lower computational complexity. Estimation performances of the designed methods are illustrated and compared with conventional estimation schemes by two common numerical examples.

Automated Neuron Reconstruction from 3D Fluorescence Microscopy Images Using Sequential Monte Carlo Estimation

Microscopic images of neuronal cells provide essential structural information about the key constituents of the brain and form the basis of many neuroscientific studies. Computational analyses of the morphological properties of the captured neurons require first converting the structural information into digital tree-like reconstructions. Many dedicated computational methods and corresponding software tools have been and are continuously being developed with the aim to automate this step while achieving human-comparable reconstruction accuracy. This pursuit is hampered by the immense diversity and intricacy of neuronal morphologies as well as the often low quality and ambiguity of the images. Here we present a novel method we developed in an effort to improve the robustness of digital reconstruction against these complicating factors. The method is based on probabilistic filtering by sequential Monte Carlo estimation and uses prediction and update models designed specifically for tracing neuronal branches in microscopic image stacks. Moreover, it uses multiple probabilistic traces to arrive at a more robust, ensemble reconstruction. The proposed method was evaluated on fluorescence microscopy image stacks of single neurons and dense neuronal networks with expert manual annotations serving as the gold standard, as well as on synthetic images with known ground truth. The results indicate that our method performs well under varying experimental conditions and compares favorably to state-of-the-art alternative methods.

A Bayesian Filtering Approach for Error Mitigation in Ultra-Wideband Ranging

Ultra-wideband (UWB) sensors have been widely used in multi-robot systems for cooperative tracking and positioning purposes due to their advantages such as high ranging accuracy and good real-time performance. In order to reduce the influence of non-line-of-sight (NLOS) UWB communication caused by the presence of obstacles on ranging accuracy in indoor environments, the paper proposes a novel Bayesian filtering approach for UWB ranging error mitigation. Nonparametric UWB sensor models, namely received signal strength (RSS) model and time of arrival (TOA) model, are constructed to capture the probabilistic noise characteristics under the influence of different obstruction conditions and materials within a typical indoor environment. The proposed Bayesian filtering approach can be used either as a standalone error mitigation approach for peer-to-peer (P2P) ranging, or as a part of a higher level Bayesian state estimation framework. Experiments were conducted to validate and evaluate the proposed approach in two configurations, i.e., inter-robot ranging, and mobile robot tracking in a wireless sensor network. The experimental results show that the proposed method can accurately identify the line-of-sight (LOS) and NLOS scenarios with wood and metal obstacles in a probabilistic representation and effectively improve the ranging/tracking accuracy. In addition, the low computational overhead of the approach makes it attractive in real-time systems.

Time-Matching Random Finite Set-Based Filter for Radar Multi-Target Tracking

The random finite set (RFS) approach provides an elegant Bayesian formulation of the multi-target tracking (MTT) problem without the requirement of explicit data association. In order to improve the performance of the RFS-based filter in radar MTT applications, this paper proposes a time-matching Bayesian filtering framework to deal with the problem caused by the diversity of target sampling times. Based on this framework, we develop a time-matching joint generalized labeled multi-Bernoulli filter and a time-matching probability hypothesis density filter. Simulations are performed by their Gaussian mixture implementations. The results show that the proposed approach can improve the accuracy of target state estimation, as well as the robustness.

Real-Time Tracking of Selective Auditory Attention From M/EEG: A Bayesian Filtering Approach

Humans are able to identify and track a target speaker amid a cacophony of acoustic interference, an ability which is often referred to as the cocktail party phenomenon. Results from several decades of studying this phenomenon have culminated in recent years in various promising attempts to decode the attentional state of a listener in a competing-speaker environment from non-invasive neuroimaging recordings such as magnetoencephalography (MEG) and electroencephalography (EEG). To this end, most existing approaches compute correlation-based measures by either regressing the features of each speech stream to the M/EEG channels (the decoding approach) or vice versa (the encoding approach). To produce robust results, these procedures require multiple trials for training purposes. Also, their decoding accuracy drops significantly when operating at high temporal resolutions. Thus, they are not well-suited for emerging real-time applications such as smart hearing aid devices or brain-computer interface systems, where training data might be limited and high temporal resolutions are desired. In this paper, we close this gap by developing an algorithmic pipeline for real-time decoding of the attentional state. Our proposed framework consists of three main modules: (1) Real-time and robust estimation of encoding or decoding coefficients, achieved by sparse adaptive filtering, (2) Extracting reliable markers of the attentional state, and thereby generalizing the widely-used correlation-based measures thereof, and (3) Devising a near real-time state-space estimator that translates the noisy and variable attention markers to robust and statistically interpretable estimates of the attentional state with minimal delay. Our proposed algorithms integrate various techniques including forgetting factor-based adaptive filtering, ℓ₁-regularization, forward-backward splitting algorithms, fixed-lag smoothing, and Expectation Maximization. We validate the performance of our proposed framework using comprehensive simulations as well as application to experimentally acquired M/EEG data. Our results reveal that the proposed real-time algorithms perform nearly as accurately as the existing state-of-the-art offline techniques, while providing a significant degree of adaptivity, statistical robustness, and computational savings.