On Filtering and Smoothing Algorithms for Linear State-Space Models Having Quantized Output Data

Angel L. Cedeño (), Rodrigo A. González, Boris I. Godoy, Rodrigo Carvajal and Juan C. Agüero
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Angel L. Cedeño: Electronics Engineering Department, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 2390123, Chile
Rodrigo A. González: Department of Mechanical Engineering, Eindhoven University of Technology, 5612 AZ Eindhoven, The Netherlands
Boris I. Godoy: Department of Automatic Control, Lund University, 221 00 Lund, Sweden
Rodrigo Carvajal: School of Electrical Engineering, Pontificia Universidad Católica de Valparaíso, Av. Brasil 2147, Valparaíso 2374631, Chile
Juan C. Agüero: Electronics Engineering Department, Universidad Técnica Federico Santa María, Av. España 1680, Valparaíso 2390123, Chile

Mathematics, 2023, vol. 11, issue 6, 1-25

Abstract: 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.

Keywords: extended Kalman filter/smoother; unscented Kalman filter/smoother; Gaussian sum filter/smoother; particle filter/smoother; state estimation; quantized data (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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