Estimation in the partially observed stochastic Morris-Lecar neuronal model with particle filter and stochastic approximation methods

Parameter estimation in multidimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. In neuroscience, the membrane potential evolution in single neurons can be measured at high frequency, but biophysical realistic models have to include the unobserved dynamics of ion channels. One such model is the stochastic Morris-Lecar model, defined by a nonlinear two-dimensional stochastic differential equation. The coordinates are coupled, that is, the unobserved coordinate is nonautonomous, the model exhibits oscillations to mimic the spiking behavior, which means it is not of gradient-type, and the measurement noise from intracellular recordings is typically negligible. Therefore, the hidden Markov model framework is degenerate, and available methods break down. The main contributions of this paper are an approach to estimate in this ill-posed situation and nonasymptotic convergence results for the method. Specifically, we propose a sequential Monte Carlo particle filter algorithm to impute the unobserved coordinate, and then estimate parameters maximizing a pseudo-likelihood through a stochastic version of the Expectation-Maximization algorithm. It turns out that even the rate scaling parameter governing the opening and closing of ion channels of the unobserved coordinate can be reasonably estimated. An experimental data set of intracellular recordings of the membrane potential of a spinal motoneuron of a red-eared turtle is analyzed, and the performance is further evaluated in a simulation study.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS729 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Simulation of Multi-element Antenna Systems for Navigation Applications

The application of user terminals with multiple antenna inputs for use with the global satellite navigation systems like GPS and Galileo becomes more and more attraction in last years. Multiple antennas may be spread over the user platform and provide signals required for the platform attitude estimation or may be arranged in an antenna array to be used together with array processing algorithms for improving signal reception, e.g. for multipath and interference mitigation. In order to generate signals for testing of receivers with multiple antenna inputs and corresponding receiver algorithms in a laboratory environment a unique HW signal simulation tool for wavefront simulation has been developed. The signals for a number of antenna elements in a flexible user defined geometry are first generated as digital signals in baseband and then mixed up to individual RF-outputs. The paper describes the principle function of the system and addresses some calibration issues. Measurement set-ups and results of data processing with simulated signals for different applications are shown and discussed

Tracking system study

A digital computer program was generated which mathematically describes an optimal estimator-controller technique as applied to the control of antenna tracking systems used by NASA. Simulation studies utilizing this program were conducted using the IBM 360/91 computer. The basic ideas of applying optimal estimator-controller techniques to antenna tracking systems are discussed. A survey of existing tracking methods is given along with shortcomings and inherent errors. It is explained how these errors can be considerably reduced if optimal estimation and control are used. The modified programs generated in this project are described and the simulation results are summarized. The new algorithms for direct synthesis and stabilization of the systems including nonlinearities, are presented