Non-Gaussian probabilistic MEG source localisation based on kernel density estimation

A Robust Hierarchical Estimation Scheme for Vehicle State Based on Maximum Correntropy Square-Root Cubature Kalman Filter

Accurate acquisition of vehicle dynamics state information is essential for vehicle active safety control systems. However, these states cannot be easily measured, and the measurement is expensive. Conventional Kalman filters perform well for vehicle state estimation in Gaussian environments but exhibit low accuracy and robustness under practical non-Gaussian noise. Vehicle model parameter ingestion, inaccurate tire force calculation, and non-Gaussian noise from on-board sensors cause great challenges to the estimation of vehicle driving states. Therefore, this paper presents a robust hierarchical estimation scheme for vehicle driving state based on the maximum correntropy square-root cubature Kalman filter (MCSCKF) using easily measurable on-board sensor information. First, the vehicle mass is dynamically updated based on the recursive least squares (FRLS) method with a forgetting factor. Then, an adaptive sliding mode observer (ASMO) is designed to estimate the longitudinal and lateral tire forces. Ultimately, the vehicle states are estimated based on the MCSCKF under non-Gaussian noise. Two typical operating situations are carried out to verify the validity of the proposed estimation scheme. The results prove that the proposed estimation scheme can estimate the vehicle's driving state accurately compared to other common methods. And the MCSCKF algorithm has better accuracy and robustness than the traditional Kalman filters for vehicle state estimation in non-Gaussian situations.

Enhanced Data Covariance Estimation Using Weighted Combination of Multiple Gaussian Kernels for Improved M/EEG Source Localization

In the recent past, estimating brain activity with magneto/electroencephalography (M/EEG) has been increasingly employed as a noninvasive technique for understanding the brain functions and neural dynamics. However, one of the main open problems when dealing with M/EEG data is its non-Gaussian and nonstationary structure. In this paper, we introduce a methodology for enhancing the data covariance estimation using a weighted combination of multiple Gaussian kernels, termed WM-MK, that relies on the Kullback-Leibler divergence for associating each kernel weight to its relevance. From the obtained results of validation on nonstationary and non-Gaussian brain activity (simulated and real-world EEG data), WM-MK proves that the accuracy of the source estimation raises by more effectively exploiting the measured nonlinear structures with high time and space complexity.

Passive Acoustic Mapping Using Data-Adaptive Beamforming Based on Higher Order Statistics

Sources of nonlinear acoustic emissions, particularly those associated with cavitation activity, play a key role in the safety and efficacy of current and emerging therapeutic ultrasound applications, such as oncological drug delivery, blood-brain barrier opening, and histotripsy. Passive acoustic mapping (PAM) is the first technique to enable real-time and non-invasive imaging of cavitation activity during therapeutic ultrasound exposure, through the recording and passive beamforming of broadband acoustic emissions using an array of ultrasound detectors. Initial limitations in PAM spatial resolution led to the adoption of optimal data-adaptive beamforming algorithms, such as the robust capon beamformer (RCB), that provide improved interference suppression and calibration error mitigation compared to non-adaptive beamformers. However, such approaches are restricted by the assumption that the recorded signals have a Gaussian distribution. To overcome this limitation and further improve the source resolvability of PAM, we propose a new beamforming approach termed robust beamforming by linear programming (RLPB). Along with the variance, this optimization-based method uses higher-order-statistics of the recorded signals, making no prior assumption on the statistical distribution of the acoustic signals. The RLPB is found via numerical simulations to improve resolvability over time exposure acoustics and RCB. In vitro experimentation yielded improved resolvability with respect to the source-to-array distance on the order of 22% axially and 13% transversely relative to RCB, whilst successfully accounting for array calibration errors. The improved resolution and decreased dependence on accurate calibration of RLPB is expected to facilitate the clinical translation of PAM for diagnostic, including super-resolution, and therapeutic ultrasound applications.

A Nonlinear Framework of Delayed Particle Smoothing Method for Vehicle Localization under Non-Gaussian Environment

In this paper, a novel nonlinear framework of smoothing method, non-Gaussian delayed particle smoother (nGDPS), is proposed, which enables vehicle state estimation (VSE) with high accuracy taking into account the non-Gaussianity of the measurement and process noises. Within the proposed method, the multivariate Student's t-distribution is adopted in order to compute the probability distribution function (PDF) related to the process and measurement noises, which are assumed to be non-Gaussian distributed. A computation approach based on Ensemble Kalman Filter (EnKF) is designed to cope with the mean and the covariance matrix of the proposal non-Gaussian distribution. A delayed Gibbs sampling algorithm, which incorporates smoothing of the sampled trajectories over a fixed-delay, is proposed to deal with the sample degeneracy of particles. The performance is investigated based on the real-world data, which is collected by low-cost on-board vehicle sensors. The comparison study based on the real-world experiments and the statistical analysis demonstrates that the proposed nGDPS has significant improvement on the vehicle state accuracy and outperforms the existing filtering and smoothing methods.

Multi-Dimensional Dynamics of Human Electromagnetic Brain Activity

Magnetoencephalography (MEG) and electroencephalography (EEG) are invaluable neuroscientific tools for unveiling human neural dynamics in three dimensions (space, time, and frequency), which are associated with a wide variety of perceptions, cognition, and actions. MEG/EEG also provides different categories of neuronal indices including activity magnitude, connectivity, and network properties along the three dimensions. In the last 20 years, interest has increased in inter-regional connectivity and complex network properties assessed by various sophisticated scientific analyses. We herein review the definition, computation, short history, and pros and cons of connectivity and complex network (graph-theory) analyses applied to MEG/EEG signals. We briefly describe recent developments in source reconstruction algorithms essential for source-space connectivity and network analyses. Furthermore, we discuss a relatively novel approach used in MEG/EEG studies to examine the complex dynamics represented by human brain activity. The correct and effective use of these neuronal metrics provides a new insight into the multi-dimensional dynamics of the neural representations of various functions in the complex human brain.

Spatially Sparse, Temporally Smooth MEG Via Vector ℓ0

In this paper, we describe a new method for solving the magnetoencephalography inverse problem: temporal vector ℓ0-penalized least squares (TV-L0LS). The method calculates maximally sparse current dipole magnitudes and directions via spatial ℓ0 regularization on a cortically-distributed source grid, while constraining the solution to be smooth with respect to time. We demonstrate the utility of this method on real and simulated data by comparison to existing methods.

Optimising beamformer regions of interest analysis

Beamforming is a spatial filtering based source reconstruction method for EEG and MEG that allows the estimation of neuronal activity at a particular location within the brain. The computation of the location specific filter depends solely on an estimate of the data covariance matrix and on the forward model. Increasing the number of M/EEG sensors, increases the quantity of data required for accurate covariance matrix estimation. Often however we have a prior hypothesis about the site of, or the signal of interest. Here we show how this prior specification, in combination with optimal estimations of data dimensionality, can give enhanced beamformer performance for relatively short data segments. Specifically we show how temporal (Bayesian Principal Component Analysis) and spatial (lead field projection) methods can be combined to produce improvements in source estimation over and above employing the approaches individually.

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This paper concerns optimising beamformer analysis for anatomical ROIs.

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Channel reduction is performed using an ROI projection and Bayesian PCA.

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This improves covariance matrix estimation for a given data length.

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The proposed approach results in improvements in source estimation.