Carlos H. Muravchik

Posterior Cramer-Rao bounds for discrete-time nonlinear filtering

A mean-square error lower bound for the discrete-time nonlinear filtering problem is derived based on the van Trees (1968) (posterior) version of the Cramer-Rao inequality. This lower bound is applicable to multidimensional nonlinear, possibly non-Gaussian, dynamical systems and is more general than the previous bounds in the literature. The case of singular conditional distribution of the one-step-ahead state vector given the present state is considered. The bound is evaluated for three important examples: the recursive estimation of slowly varying parameters of an autoregressive process, tracking a slowly varying frequency of a single cisoid in noise, and tracking parameters of a sinusoidal frequency with sinusoidal phase modulation.

Estimating brain conductivities and dipole source signals with EEG arrays

Techniques based on electroencephalography (EEG) measure the electric potentials on the scalp and process them to infer the location, distribution, and intensity of underlying neural activity. Accuracy in estimating these parameters is highly sensitive to uncertainty in the conductivities of the head tissues. Furthermore, dissimilarities among individuals are ignored when standardized values are used. In this paper, we apply the maximum-likelihood and maximum a posteriori (MAP) techniques to simultaneously estimate the layer conductivity ratios and source signal using EEG data. We use the classical 4-sphere model to approximate the head geometry, and assume a known dipole source position. The accuracy of our estimates is evaluated by comparing their standard deviations with the Crame/spl acute/r-Rao bound (CRB). The applicability of these techniques is illustrated with numerical examples on simulated EEG data. Our results show that the estimates have low bias and attain the CRB for sufficiently large number of experiments. We also present numerical examples evaluating the sensitivity to imprecise assumptions on the source position and skull thickness. Finally, we propose extensions to the case of unknown source position and present examples for real data.

Cortical deficits of emotional face processing in adults with ADHD: Its relation to social cognition and executive function

Although it has been shown that adults with attention-deficit hyperactivity disorder (ADHD) have impaired social cognition, no previous study has reported the brain correlates of face valence processing. This study looked for behavioral, neuropsychological, and electrophysiological markers of emotion processing for faces (N170) in adult ADHD compared to controls matched by age, gender, educational level, and handedness. We designed an event-related potential (ERP) study based on a dual valence task (DVT), in which faces and words were presented to test the effects of stimulus type (faces, words, or face-word stimuli) and valence (positive versus negative). Individual signatures of cognitive functioning in participants with ADHD and controls were assessed with a comprehensive neuropsychological evaluation, including executive functioning (EF) and theory of mind (ToM). Compared to controls, the adult ADHD group showed deficits in N170 emotion modulation for facial stimuli. These N170 impairments were observed in the absence of any deficit in facial structural processing, suggesting a specific ADHD impairment in early facial emotion modulation. The cortical current density mapping of N170 yielded a main neural source of N170 at posterior section of fusiform gyrus (maximum at left hemisphere for words and right hemisphere for faces and simultaneous stimuli). Neural generators of N170 (fusiform gyrus) were reduced in ADHD. In those patients, N170 emotion processing was associated with performance on an emotional inference ToM task, and N170 from simultaneous stimuli was associated with EF, especially working memory. This is the first report to reveal an adult ADHD-specific impairment in the cortical modulation of emotion for faces and an association between N170 cortical measures and ToM and EF.

EEG/MEC error bounds for a static dipole source with a realistic head model

We derive Cramer-Rao bounds (CRBs) on the errors of estimating the parameters (location and moment) of a static current dipole source using data from electro-encephalography (EEG), magneto-encephalography (MEG), or the combined EEG/MEG modality. We use a realistic head model based on knowledge of surfaces separating tissues of different conductivities obtained from magnetic resonance (MR) or computer tomography (CT) imaging systems. The electric potentials and magnetic field components at the respective sensors are functions of the source parameters through integral equations. These potentials and field are formulated for solving them by the boundary or the finite element method (BEM or FEM) with a weighted residuals technique. We present a unified framework for the measurements computed by these methods that enables the derivation of the bounds. The resulting bounds may be used, for instance, to choose the best configuration of the sensors for a given patient and region of expected source location. Numerical results are used to demonstrate an application for showing expected accuracies in estimating the source parameters as a function of its position in the brain, based on real EEG/MEG system and MR or CT images.

Approximate average head models for EEG source imaging

We examine the performance of approximate models (AM) of the head in solving the EEG inverse problem. The AM are needed when the individuals MRI is not available. We simulate the electric potential distribution generated by cortical sources for a large sample of 305 subjects, and solve the inverse problem with AM. Statistical comparisons are carried out with the distribution of the localization errors. We propose several new AM. These are the average of many individual realistic MRI-based models, such as surface-based models or lead fields. We demonstrate that the lead fields of the AM should be calculated considering source moments not constrained to be normal to the cortex. We also show that the imperfect anatomical correspondence between all cortices is the most important cause of localization errors. Our average models perform better than a random individual model or the usual average model in the MNI space. We also show that a classification based on race and gender or head size before averaging does not significantly improve the results. Our average models are slightly better than an existing AM with shape guided by measured individual electrode positions, and have the advantage of not requiring such measurements. Among the studied models, the Average Lead Field seems the most convenient tool in large and systematical clinical and research studies demanding EEG source localization, when MRI are unavailable. This AM does not need a strict alignment between head models, and can therefore be easily achieved for any type of head modeling approach.

A nonlinear reduced order observer for permanent magnet synchronous motors

This paper introduces a nonlinear reduced order observer for speed and rotor position estimation in permanent magnet synchronous motors (PMSM). The observer is based on the model of the motor represented in the stationary two-axes coordinates. The theoretical principles of the proposed observer are discussed. Sufficient conditions for convergence as well as convergence speed are established. The observer is designed and tested by simulation. The results show that the observer gives a good estimation of speed and rotor position. In addition, it has low sensitivity to torque disturbances and perturbations of the mechanical parameters.<<ETX>>

Effects of geometric head model perturbations on the EEG forward and inverse problems

We study the effect of geometric head model perturbations on the electroencephalography (EEG) forward and inverse problems. Small magnitude perturbations of the shape of the head could represent uncertainties in the head model due to errors on images or techniques used to construct the model. They could also represent small scale details of the shape of the surfaces not described in a deterministic model, such as the sulci and fissures of the cortical layer. We perform a first-order perturbation analysis, using a meshless method for computing the sensitivity of the solution of the forward problem to the geometry of the head model. The effect on the forward problem solution is treated as noise in the EEG measurements and the Crame/spl acute/r-Rao bound is computed to quantify the effect on the inverse problem performance. Our results show that, for a dipolar source, the effect of the perturbations on the inverse problem performance is under the level of the uncertainties due to the spontaneous brain activity. Thus, the results suggest that an extremely detailed model of the head may be unnecessary when solving the EEG inverse problem.

Nonlinear control of a permanent magnet synchronous motor with disturbance torque estimation

This paper introduces a sensorless nonlinear control scheme for controlling the speed of a permanent magnet synchronous motor (PMSM) driving an unknown load torque. The states of the motor and disturbance torque are estimated via an extended nonlinear observer avoiding the use of mechanical sensors. The control strategy is an exact feedback linearization law, with trajectory tracking evaluated on estimated values of the PMSM states and the disturbance torque. The system performance is evaluated by simulations.

A meshless method for solving the EEG forward problem

We present a numerical method to solve the quasi-static Maxwell equations and compute the electroencephalography (EEG) forward problem solution. More generally, we develop a computationally efficient method to obtain the electric potential distribution generated by a source of electric activity inside a three-dimensional body of arbitrary shape and layers of different electric conductivities. The method needs only a set of nodes on the surface and inside the head, but not a mesh connecting the nodes. This represents an advantage over traditional methods like boundary elements or finite elements since the generation of the mesh is typically computationally intensive. The performance of the proposed method is compared with the boundary element method (BEM) by numerically solving some EEG forward problems examples. For a large number of nodes and the same precision, our method has lower computational load than BEM due to a faster convergence rate and to the sparsity of the linear system to be solved.

GPS Digital Tracking Loops Design for High Dynamic Launching Vehicles

This paper describes the design of digital tracking loops for GPS receivers in a high dynamics environment, without external aiding. We adopted the loop structure of a frequency-locked loop (FLL)-assisted phase-locked loop (PLL) and design it to track accelerations steps, as those occurring in launching vehicles. We used a completely digital model of the loop where the FLL and PLL parts are jointly designed, as opposed to the classical discretized analog model with separately designed FLL and PLL. The new approach does not increase the computational burden. We performed simulations and real RF signal experiments of a fixed-point implementation of the loop, showing that reliable tracking of steps up to 40 g can be achieved