Abstract
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.
Highlights
It is well known that discrete-time dynamical systems can be described as first-order difference equations relating internal variables called states [1]
There are a variety of applications that use state estimation, such as control [4,5,6,7], parameter identification [8,9,10], power systems [11,12], fault detection [13,14,15,16,17], prognosis [18,19], cyber–physical systems [20], hydrologic and geophysical data assimilation [21,22], maritime tracking [23], consensusbased state estimation using wireless sensor networks [24,25,26], navigation systems [27], and transportation and highway traffic management [28,29,30], to mention a few
The quantization process is a nonlinear map that results in a significant loss of information on the system dynamics, which produces a biased state estimation and incorrect characterization of the filtering and smoothing probability density functions (PDFs)
Summary
It is well known that discrete-time dynamical systems can be described as first-order difference equations relating internal variables called states [1]. The quantization process is a nonlinear map that results in a significant loss of information on the system dynamics, which produces a biased state estimation and incorrect characterization of the filtering and smoothing probability density functions (PDFs) In this context, several suboptimal filtering and smoothing algorithms for state-space systems with quantized data have been developed, for instance, standard- [49,54], unscented- [55], and extended- [36] Kalman filters for quantized data, in which some structural elements of the state-space models and the quantizer are exploited.
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