Refined instrumental variable estimation: maximum likelihood optimization of a unified Box–Jenkins model

For many years, various methods for the identification and estimation of parameters in linear, discretetime transfer functions have been available and implemented in widely available Toolboxes for MatlabTM. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The estimation is based on the formulation of a pseudo-linear regression relationship involving optimal prefilters that is derived from an appropriately unified Box–Jenkins transfer function model. The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box–Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms

Learning Transfer Operators by Kernel Density Estimation

Inference of transfer operators from data is often formulated as a classical problem that hinges on the Ulam method. The usual description, which we will call the Ulam-Galerkin method, is in terms of projection onto basis functions that are characteristic functions supported over a fine grid of rectangles. In these terms, the usual Ulam-Galerkin approach can be understood as density estimation by the histogram method. Here we show that the problem can be recast in statistical density estimation formalism. This recasting of the classical problem, is a perspective that allows for an explicit and rigorous analysis of bias and variance, and therefore toward a discussion of the mean square error. Keywords: Transfer Operators; Frobenius-Perron operator; probability density estimation; Ulam-Galerkin method;Kernel Density Estimation

Identifiability and parameter estimation of the single particle lithium-ion battery model

This paper investigates the identifiability and estimation of the parameters of the single particle model (SPM) for lithium-ion battery simulation. Identifiability is addressed both in principle and in practice. The approach begins by grouping parameters and partially non-dimensionalising the SPM to determine the maximum expected degrees of freedom in the problem. We discover that, excluding open circuit voltage, there are only six independent parameters. We then examine the structural identifiability by considering whether the transfer function of the linearised SPM is unique. It is found that the model is unique provided that the electrode open circuit voltage functions have a known non-zero gradient, the parameters are ordered, and the electrode kinetics are lumped into a single charge transfer resistance parameter. We then demonstrate the practical estimation of model parameters from measured frequency-domain experimental electrochemical impedance spectroscopy (EIS) data, and show additionally that the parametrised model provides good predictive capabilities in the time domain, exhibiting a maximum voltage error of 20 mV between model and experiment over a 10 minute dynamic discharge.Comment: 16 pages, 9 figures, pre-print submitted to the IEEE Transactions on Control Systems Technolog

Deconvolution from Wavefront Sensing Using Optimal Wavefront Estimators

A cost effective method to improve the space surveillance mission performance of United States Air Force (USAF) ground-based telescopes is investigated and improved. A minimum variance wavefront estimation technique is used to improve Deconvolution from Wavefront Sensing (DWFS), a method to mitigate the effects of atmospheric turbulence on imaging systems that does not require expensive adaptive optics. Both least-squares and minimum variance wavefront phase estimation techniques are investigated, using both Gaussian and Zernike polynomial elementary functions. Imaging simulations and established performance metrics are used to evaluate these wavefront estimation techniques for a one-meter optical telescope. Performance metrics include the average pupil-averaged mean square phase error of the residual wavefront, the average system transfer function, the signal-to-noise ratio (SNR) of the system transfer function, and the optical transfer function correlation. Results show that the minimum variance estimation technique that employs Zernike polynomial elementary functions offers improvements over all other estimation techniques in each of the performance metrics. Extended object simulations are also conducted which demonstrate the improvements in image quality and resolution that result from the modifications to the DWFS method. Implementation of the DWFS method into USAF space surveillance telescopes is investigated

A study of parameter identification

A set of definitions for deterministic parameter identification ability were proposed. Deterministic parameter identificability properties are presented based on four system characteristics: direct parameter recoverability, properties of the system transfer function, properties of output distinguishability, and uniqueness properties of a quadratic cost functional. Stochastic parameter identifiability was defined in terms of the existence of an estimation sequence for the unknown parameters which is consistent in probability. Stochastic parameter identifiability properties are presented based on the following characteristics: convergence properties of the maximum likelihood estimate, properties of the joint probability density functions of the observations, and properties of the information matrix

Efficient transfer entropy analysis of non-stationary neural time series

Information theory allows us to investigate information processing in neural systems in terms of information transfer, storage and modification. Especially the measure of information transfer, transfer entropy, has seen a dramatic surge of interest in neuroscience. Estimating transfer entropy from two processes requires the observation of multiple realizations of these processes to estimate associated probability density functions. To obtain these observations, available estimators assume stationarity of processes to allow pooling of observations over time. This assumption however, is a major obstacle to the application of these estimators in neuroscience as observed processes are often non-stationary. As a solution, Gomez-Herrero and colleagues theoretically showed that the stationarity assumption may be avoided by estimating transfer entropy from an ensemble of realizations. Such an ensemble is often readily available in neuroscience experiments in the form of experimental trials. Thus, in this work we combine the ensemble method with a recently proposed transfer entropy estimator to make transfer entropy estimation applicable to non-stationary time series. We present an efficient implementation of the approach that deals with the increased computational demand of the ensemble method's practical application. In particular, we use a massively parallel implementation for a graphics processing unit to handle the computationally most heavy aspects of the ensemble method. We test the performance and robustness of our implementation on data from simulated stochastic processes and demonstrate the method's applicability to magnetoencephalographic data. While we mainly evaluate the proposed method for neuroscientific data, we expect it to be applicable in a variety of fields that are concerned with the analysis of information transfer in complex biological, social, and artificial systems.Comment: 27 pages, 7 figures, submitted to PLOS ON