Browsing by Author "Godoy, Boris I."

Filtering and smoothing algorithms are key tools to develop decision-making strategies and parameter identification techniques in different areas of research, such as economics, financial data analysis, communications, and control systems. These algorithms are used to obtain an estimation of the system state based on the sequentially available noisy measurements of the system output. In a real-world system, the noisy measurements can suffer a significant loss of information due to (among others): (i) a reduced resolution of cost-effective sensors typically used in practice or (ii) a digitalization process for storing or transmitting the measurements through a communication channel using a minimum amount of resources. Thus, obtaining suitable state estimates in this context is essential. In this paper, Gaussian sum filtering and smoothing algorithms are developed in order to deal with noisy measurements that are also subject to quantization. In this approach, the probability mass function of the quantized output given the state is characterized by an integral equation. This integral was approximated by using a Gauss–Legendre quadrature; hence, a model with a Gaussian mixture structure was obtained. This model was used to develop filtering and smoothing algorithms. The benefits of this proposal, in terms of accuracy of the estimation and computational cost, are illustrated via numerical simulations.

In this paper, we explore the identification of sparse FIR systems having quantized output data. Our approach is based on the use of regularization. We explore several aspects concerning the implementation of the Expectation-Maximization (EM) algorithm, including: i) a general framework, based on mean-variance Gaussian mixtures, for incorporating a regularization term that forces sparsity, ii) utilization of Markov Chain Monte Carlo techniques (namely a Gibbs sampler) and scenarios to implement the EM algorithm for multiple input multiple output systems. We show that for single input single output systems, it is possible to obtain closed form expressions for solving the EM algorithm.

In this paper we address the joint estimation of the channel impulse response in orthogonal frequency division multiplexing systems with phase distortion, namely phase noise and carrier frequency offset, phase noise bandwidth and the additive noise variance. The estimation algorithm is based on an implementation of the Extended Kalman Filter within the general framework of the Expectation-Maximization algorithm. We focus on the partial training case, where the transmitted signal is not fully known. To tackle this problem, we utilize a Rao-Blackwellized Extended Kalman Filter. We also compare our results with another nonlinear filtering technique, namely Rao-Blackwellized Particle Filtering, applied to this joint estimation problem. The performance of the two filtering techniques considered in this paper is evaluated in terms of the mean square error of the channel estimates and the numerical complexity introduced by each of these techniques.

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.

The problem of state estimation of a linear, dynamical state-space system where the output is subject to quantization is challenging and important in different areas of research, such as control systems, communications, and power systems. There are a number of methods and algorithms to deal with this state estimation problem. However, there is no consensus in the control and estimation community on (1) which methods are more suitable for a particular application and why, and (2) how these methods compare in terms of accuracy, computational cost, and user friendliness. In this paper, we provide a comprehensive overview of the state-of-the-art algorithms to deal with state estimation subject to quantized measurements, and an exhaustive comparison among them. The comparison analysis is performed in terms of the accuracy of the state estimation, dimensionality issues, hyperparameter selection, user friendliness, and computational cost. We consider classical approaches and a new development in the literature to obtain the filtering and smoothing distributions of the state conditioned to quantized data. The classical approaches include the extended Kalman filter/smoother, the quantized Kalman filter/smoother, the unscented Kalman filter/smoother, and the sequential Monte Carlo sampling method, also called particle filter/smoother, with its most relevant variants. We also consider a new approach based on the Gaussian sum filter/smoother. Extensive numerical simulations—including a practical application—are presented in order to analyze the accuracy of the state estimation and the computational cost.