Boris I. Godoy

On identification of FIR systems having quantized output data

In this paper, we present a novel algorithm for estimating the parameters of a linear system when the observed output signal is quantized. This question has relevance to many areas including sensor networks and telecommunications. The algorithms described here have closed form solutions for the SISO case. However, for the MIMO case, a set of pre-computed scenarios is used to reduce the computational complexity of EM type algorithms that are typically deployed for this kind of problem. Comparisons are made with other algorithms that have been previously described in the literature as well as with the implementation of algorithms based on the Quasi-Newton method.

EM-Based Maximum-Likelihood Channel Estimation in Multicarrier Systems With Phase Distortion

In this paper, we address channel-impulse response (CIR) estimation in multicarrier systems with phase distortion, namely, phase noise (PHN) and carrier frequency offset (CFO). The estimation problem also considers the joint estimation of the channel noise variance, CFO, and PHN bandwidth. We develop a general state-space model for multicarrier systems, separating the complex signals into their real and imaginary parts. This provides a valid framework for any modulation scheme (proper or improper). We use the expectation-maximization (EM) algorithm to solve the maximum-likelihood (ML) estimation problem. Our approach exploits the linear and Gaussian structure associated with the transmitted signal. Due to the nonlinear nature of the PHN, sequential Monte Carlo (MC) techniques are considered. Our analysis includes general expressions under different training scenarios. We show, via simulation, the impact of PHN bandwidth estimation on overall parameter estimation, and we study the impact of different training levels. In addition, we consider the accuracy of the parameter estimates, providing expressions for the Fisher information matrix (FIM) and focusing on the estimation accuracy of the PHN bandwidth.

Identification of sparse FIR systems using a general quantisation scheme

This paper presents an identification scheme for sparse FIR systems with quantised data. We consider a general quantisation scheme, which includes the commonly deployed static quantiser as a special case. To tackle the sparsity issue, we utilise a Bayesian approach, where an ℓ1 a priori distribution for the parameters is used as a mechanism to promote sparsity. The general framework used to solve the problem is maximum likelihood (ML). The ML problem is solved by using a generalised expectation maximisation algorithm.

An EM-based identification algorithm for a class of hybrid systems with application to power electronics

In this paper we present an identification algorithm for a class of continuous-time hybrid systems. In such systems, both continuous-time and discrete-time dynamics are involved. We apply the expectation-maximisation algorithm to obtain the maximum likelihood estimate of the parameters of a discrete-time model expressed in incremental form. The main advantage of this approach is that the continuous-time parameters can directly be recovered. The technique is particularly well suited to fast-sampling rates. As an application, we focus on a standard identification problem in power electronics. In this field, our proposed algorithm is of importance since accurate modelling of power converters is required in high- performance applications and for fault diagnosis. As an illustrative example, and to verify the performance of our proposed algorithm, we apply our results to a flying capacitor multicell converter.

A map approach for ℓ q -norm regularized sparse parameter estimation using the EM algorithm

In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty term in the cost function of the estimation problem through the use of an appropriate prior distribution, we show how the EM algorithm can be used to efficiently solve the corresponding optimization problem. To this end, we rely on variance-mean Gaussian mixtures (VMGM) to describe the prior distribution, while we incorporate many nice features of these mixtures to our estimation problem. The corresponding MAP estimation problem is completely expressed in terms of the EM algorithm, which allows for handling nonlinearities and hidden variables that cannot be easily handled with traditional methods. For comparison purposes, we also develop a Coordinate Descent algorithm for the ℓq-norm penalized problem and present the performance results via simulations.

A scenario-based approach to parameter estimation in state-space models having quantized output data

In this paper we describe an algorithm for estimating the parameters of a linear, discrete-time system, in state-space form, having quantized measurements. The estimation is carried out using the maximum likelihood criterion. The solution is found using the expectation maximization (EM) algorithm. A technical difficulty in applying this algorithm for this problem is that the a posteriori probability density function, found in the EM algorithm, is non-Gaussian. To deal with this issue, we sequentially approximate it using scenarios, i.e., a weighted sum of impulses which are deterministically computed. Numerical experiments show that the proposed approach leads to a significantly more accurate estimation than the one obtained by ignoring the presence of the quantizer and applying standard estimation methods.

Scenario-based EM identification for FIR systems having quantized output data

Abstract In this paper we describe a novel algorithm for estimating the parameters of a linear system when the observed output signal is quantized. This question has relevance to many areas including sensor networks and telecommunications. The algorithm utilizes a set of pre-computed scenarios to reduce the computational complexity of EM type algorithms that are typically deployed for this kind of problem. More generally, the idea of utilizing scenarios seems to have widespread potential in system identification.

A Simulation Study on Model Predictive Control and Extremum Seeking Control for Heap Bioleaching Processes

Abstract Heap bioleaching processes are of increasing interest in the mining industry to recover metals from secondary ores. Recently, it has been proposed to use feedback control to improve the rate of mineral extraction. In this paper we compare two feedback approaches, namely Model Predictive Control (MPC) and Extremum Seeking Control (ESC), to improve copper extraction in a heap bioleaching process. Simplified linear models obtained in previous work are used to design an MPC strategy incorporating input constraints. ESC is tuned to maximise copper extraction rate using aeration rate. Simulation results run on a high complexity model of the process show that similar copper extraction rates can be obtained using either strategy. While better control efforts are obtained with MPC, ESC achieves similar results and shows potential for this intrinsically complex process, requiring little knowledge about the plant.

Identification of Continuous-Time Transfer Function Models from Non-Uniformly Sampled Data in Presence of Colored Noise

This paper considers the problem of continuous-time model identification from non-uniformly sampled input-output data, having the measured output corrupted by colored noise. We concentrate on the continuous-time transfer function model identification. A Box-Jenkins model structure is used to describe the system, thus providing independent parameterizations for the plant and the noise. Monte Carlo simulation analysis is also used to illustrate the properties of the proposed estimation method.

On the accuracy of phase noise bandwidth estimation in OFDM systems

Phase noise is of importance in OFDM systems, since it generates intercarrier interference and general system performance degradation. In this paper we analyse the accuracy of maximum likelihood estimation of the phase noise bandwidth for OFDM systems. We utilize the auxiliary functions used in the EM algorithm to obtain an expression for the Fisher information matrix. Our key conclusion is that it is difficult to obtain accurate estimates of the phase noise bandwidth for practical cases when the number of subcarriers is limited.