Browsing by Author "Orellana, Rafael"

In this paper, we develop a filtering algorithm for Wiener systems written in state-space form which considers correlated noise sources. The output non-linearity is approximated by using a piece-wise linear function. The probability function of the output signal conditioned to the system state is written as a Gaussian mixture distribution. A Gaussian sum filter algorithm to obtain the a posteriori probability density function of the state given the current and past output is developed. The associated statistics of the system state are obtained. The benefits of our proposal are illustrated via numerical simulations.

We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is motivated by the MM algorithm, combined with the systematic and iterative structure of the Expectation-Maximization algorithm. The resulting algorithm can deal with hidden variables in Maximum Likelihood and Maximum a Posteriori estimation problems, Instrumental Variables, Regularized Optimization and Constrained Optimization problems. The key advantage of the proposed algorithm is to provide a systematic procedure to build surrogate functions for a class of problems where hidden variables are usually involved. Numerical examples show the benefits of the proposed approach.

This paper presents a novel identification method for stochastic continuous-time systems applied to Adaptive Optics. We consider a discrete-time sampled-data model of a linear combination of continuous-time second-order systems for modelling disturbances. The Maximum Likelihood framework is used in time and frequency domain to develop an estimation algorithm with sampled-data. We propose an estimation algorithm where we write the likelihood function in the frequency domain in terms of the discrete-time output spectrum (Whittle's log-likelihood function). An approximation for the discrete-time spectrum is used in order to reduce the computational load. A comparative analysis of the proposed method and some available methods is illustrated via numerical simulations.

In this paper we address the problem of identifying a static errors-in-variables system. Our proposal is based on the Expectation-Maximization algorithm, in which we consider that the distribution of the noise-free input is approximated by a finite Gaussian mixture. This approach allows us to estimate the static system parameters, the input and output noise variances, and the Gaussian mixture parameters. We show the benefits of our proposal via numerical simulations.

In this paper a Maximum likelihood estimation algorithm for Finite Impulse Response Errors-in-Variables systems is developed. We consider that the noise-free input signal is Gaussian-mixture distributed. We propose an Expectation-Maximization-based algorithm to estimate the system model parameters, the input and output noise variances, and the Gaussian mixture noise-free input parameters. The benefits of our proposal are illustrated via numerical simulations.

In this paper, we have proposed a new paradigm for modeling of SAG mills. Typically, important parameters found in the modeling of such processes are described as state-space system model rather than unknown parameters. Here, we propose to estimate the system model using the maximum likelihood approach. Additionally, we propose using a new measurement that has not been considered in other modeling approaches. The benefits of our proposal are illustrated via numerical simulations. The results demonstrate that incorporating this new measurement within the framework of maximum likelihood estimation improves the accuracy of estimating the unknown parameters.

In this paper we develop a Maximum Likelihood estimation algorithm for the estimation of infinite mixture distributions. We assume a known conditional distribution, whilst the weighting distribution is assumed unknown and it is approximated by a finite Gaussian mixture. Our approach allows for the correct estimation of the Gaussian mixture parameters. We illustrate the estimation performance of our proposal with numerical simulations.

In this paper a Maximum Likelihood estimation algorithm for error-model modelling using a stochastic embedding approach is developed. The error-model distribution is approximated by a finite Gaussian mixture. An Expectation-Maximization based algorithm is proposed to estimate the nominal model and the distribution of the parameters of the error-model by using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

In this paper a Maximum Likelihood estimation algorithm for model error modelling in a continuous-time system is developed utilising sampled data and a Stochastic Embedding approach. Orthonormal basis functions are used to model both the continuous-time nominal model and the error-model. The stochastic properties of the error-model distribution are defined by using a Gaussian mixture model. For the estimation of the nominal model and the error-model distribution we develop a technique based on the Expectation-Maximization algorithm using sampled data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.