TY - JOUR

T1 - A two-filter approach for state estimation utilizing quantized output data

AU - Cedeño, Angel L.

AU - Albornoz, Ricardo

AU - Carvajal, Rodrigo

AU - Godoy, Boris I.

AU - Agüero, Juan C.

N1 - Funding Information:
PIIC program of DGP at Universidad T?cnica Federico Santa Mar?a No. 062/2018 and 035/2021. Grants ANID-Fondecyt 1211630 and 11201187, ANID-Basal Project FB0008 (AC3E). Chilean National Agency for Research and Development (ANID) Scholarship Program/Doctorado Nacional/2020-21202410.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/11/1

Y1 - 2021/11/1

N2 - 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.

AB - 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.

KW - Gaussian sum filtering

KW - Gaussian sum smoothing

KW - Gauss–Legendre quadrature

KW - Quantized data

KW - State estimation

UR - http://www.scopus.com/inward/record.url?scp=85119090981&partnerID=8YFLogxK

U2 - 10.3390/s21227675

DO - 10.3390/s21227675

M3 - Article

C2 - 34833748

AN - SCOPUS:85119090981

VL - 21

JO - Sensors (Switzerland)

JF - Sensors (Switzerland)

SN - 1424-8220

IS - 22

M1 - 7675

ER -