Associate Professor James Welsh

The Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) is one of the most popular direct methods for linear continuous-time system identification. Only recently, some optimal asymptotic properties of this method have been proven. Here we provide a comprehensive analysis of the convergence of the SRIVC method for over-parameterized models. The results we derive are used to discuss practical aspects of the method and to analyze the behavior of the normalized error variance norm, which is a central part in Young's Information Criterion for model order selection. The theoretical findings are validated through simulation examples.

For many years, the Simplified Refined Instrumental Variable method for Continuous-time systems (SRIVC) has been widely used for identification. The intersample behaviour of the input plays an important role in this method, and it has been shown recently that the SRIVC estimator is not consistent if an incorrect assumption on the intersample behaviour is considered. In this paper, we present an extension of the SRIVC algorithm that is able to deal with continuous-time multisine signals, which cannot be interpolated exactly through hold reconstructions. The proposed estimator is generically consistent for any input reconstructed through zero or first-order-hold devices, and we show that it is generically consistent for continuous-time multisine inputs as well. The statistical performance of the proposed estimator is compared to the standard SRIVC estimator through extensive simulations.

In this article, an upper bound is established for the estimation error of a standard least squares (LS) algorithm used to identify a continuous-time model from filtered, sampled input-output data. It is found that the error has three constituent components due to the initial conditions, observation noise, and sample period. In particular, the initial condition bias is bounded by O(1/[N\Delta t]), which requires sufficiently large [N¿ t] for accurate LS estimation. The theoretical results obtained are confirmed by simulation.

In nonlinear system identification, Volterra kernel estimation based on regularized least squares can be performed by taking a Bayesian approach. In this framework, covariance structures which describe the Gaussian kernels are represented by a set of hyperparameters. The hyperparameters are traditionally tuned through a global optimization which maximizes their marginal likelihood with respect to the measured data. The global optimization is computationally intensive for high-order estimates, as the number of hyperparameters increases quadratically with the Volterra series order. In this letter, we propose a new method of hyperparameter tuning based on expectation-maximization (EM). The technique allows the global optimization to be split into smaller components such that the search space of any given optimization problem is not prohibitively large. The main advantage of the proposed EM method is improved computation time scaling with respect to Volterra series order. The computation time benefits of the EM-based method are demonstrated through a numerical example for the case where the maximum nonlinear order is known.

An accurate transformer model is an important tool for use in the study of power transformers. However, a manufacturer's proprietary restrictions will generally make access to the detailed design specifications of a transformer difficult. Therefore, in order to construct a physically representative transformer model, it is often necessary to estimate the model parameters. One approach is to fit the model to data obtained from tests, such as frequency-response analysis. However, during the process of fitting a model to a data set, it is critical that the estimated parameters appropriately represent the transformer under test. An estimator that is not constrained can converge on a parameter set which may satisfy the objective function but is not physically representative of the transformer. It is therefore important to constrain the model parameters. The aim of this paper is to formulate a methodology to obtain initial estimates and constraints for several fundamental transformer parameters. To demonstrate applicability, the initial parameter estimates and constraints are applied to a range of distribution transformers of varying age and manufacture, ranging in size from 200 kVA to 18 MVA. © 1986-2012 IEEE.

The aim of this paper is to develop a method to estimate high order FIR and ARX models using least squares with re-weighted nuclear norm regularization. Typically, the choice of the tuning parameter in the reweighting scheme is computationally expensive, hence we propose the use of the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) framework to overcome this problem. Furthermore, we suggest the use of the prediction error criterion (PEC) to select the tuning parameter in the SPARSEVA algorithm. Numerical examples demonstrate the veracity of this method which has close ties with the traditional technique of cross validation, but using much less computations.

The aim of this paper is to propose a new method to select the model order in continuous time system identification, instrumental variable methods. The idea is to over-parameterize the model and utilize regularization based on the l1 norm to obtain a sparse estimate. The model order of the identified system is then determined by the rank of the Hankel matrix of the estimated parameter. Simulation results show that the proposed method works very effectively. For low signal to noise ratio (SNR), it offers a significant improvement to existing model order selection methods with the performance at high SNR comparable to the existing methods.

In this paper we utilise magnetoresistive sensors and an Unscented Kalman Filter to develop a finger tracking system for physical therapy and human-machine interaction. The aim of this finger tracking system is to provide a light weight apparatus with a prolonged operational period. The finger tracking algorithm utilises two-dimensional measurements of each joint relative to a magnetic field reference point to obtain an accurate model of the finger position as opposed to other light weight systems that provide information in only one dimension. The nonlinear interaction between joint movements and sensor measurement requires a nonlinear filtering technique, as such, a Kalman filter that utilises an unscented transformation was utilised.

We study identification of stochastic Wiener dynamic systems using so-called indirect inference. The main idea is to first fit an auxiliary model to the observed data and then in a second step, often by simulation, fit a more structured model to the estimated auxiliary model. This two-step procedure can be used when the direct maximum-likelihood estimate is dificult or intractable to compute. One such example is the identification of stochastic Wiener systems, i.e., linear dynamic systems with process noise where the output is measured using a nonlinear sensor with additive measurement noise. It is in principle possible to evaluate the loglikelihood cost function using numerical integration, but the corresponding optimization problem can be quite intricate. This motivates studying consistent, but sub-optimal, identification methods for stochastic Wiener systems. We will consider indirect inference using the best linear approximation as an auxiliary model.We show that the key to obtain a reliable estimate is to use uncertainty weighting when fitting the stochastic Wiener model to the auxiliary model estimate. The main technical contribution of this paper is the corresponding asymptotic variance analysis. A numerical evaluation is presented based on a first-order finite impulse response system with a cubic non-linearity, for which certain illustrative analytic properties are derived.

© 2014 IEEE.The aim of this paper is to develop constraints to ensure stability of the model in the continuous time, simplified refined instrumental variable system identification algorithm (SRIVC) for over-parameterized models. Specifically, a convex stability domain in the space of polynomial coefficients will be generated and the system parameters will be estimated within this domain. It is found that the model fit obtained using the proposed method offers an improvement to the typical SRIVC method. A Monte Carlo simulation is presented to illustrate the performance of the proposed approach.

A well known difficulty in system identification over a large bandwidth is the ill-conditioning of the normal matrix. This typically manifests itself as poor or erroneous estimates. Several methods have been proposed in the literature for addressing this issue. However, none appear to give an entirely satisfactory solution. Here we present a novel technique, utilising particular basis functions, aimed specifically at improving the numerical properties of the least squares normal matrix in transfer function estimation over a wide bandwidth. We show that, under some mild assumptions, the achieved condition number is actually independent of the frequency range. Several examples are presented showing the superior performance of the proposed method when applied to wide-band estimation problems.