Frequency estimation of narrow band signals in Gaussian noise via Unscented Kalman Filter

Corbetta, Stefano; Dardanelli, Andrea; Boniolo, Ivo; Savaresi, Sergio M.; Bittanti, Sergio

doi:10.1109/cdc.2010.5716955

Cited by 2 publications

(3 citation statements)

References 14 publications

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“…Q and R are the state and measurement noise covariances, respectively. The respiratory frequency (rate) of breathing signal in (2) is time-varying and can be called as instantaneous frequency [65] and rewritten as,…”

Section: B State-space Formulationmentioning

confidence: 99%

“…The respiratory frequency (rate) of breathing signal in (2) is time-varying and can be called as instantaneous frequency [65] and rewritten as, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}\begin{equation*} x_{1,k}= A \sin (\Phi _{k}+\phi). \tag{5}\end{equation*} \end{document} where third–order state space representation of the signal is given as a rotating vector in Cartesian plane and projections of this rotating vector is given as the states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$x_{1,k}$ \end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$x_{2,k}$ \end{document} , and its angular velocity equals to the instantaneous frequency \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} }{}$x_{3,k}=\Omega _{k}$ \end{document} .…”

Section: System Model and Data Processingmentioning

confidence: 99%

“…1 , the first critical issue for the system performance is the considered signal model. We utilize the third-order state-space model for signal representation and this model is also considered for frequency tracking in previous studies [64] , [65] . The proposed system uses the amplitude of the received unmodulated carrier wave (CW) signals captured by low-cost software defined radio (SDR) modules.…”

Section: Introductionmentioning

confidence: 99%

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Non-Contact Respiratory Rate Estimation in Real-Time With Modified Joint Unscented Kalman Filter

2020

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It can be life-saving to monitor the respiratory rate (RR) even for healthy people in real-time. It is reported that the infected people with coronavirus disease 2019 (COVID-19), generally develop mild respiratory symptoms in the early stage. It will be more important to continuously monitor the RR of people in nursing homes and houses with a non-contact method. Conventional, contact-based, methods are not suitable for long-term health monitoring especially in-home care services. The potentials of wireless radio signals for health care applications, such as fall detection, etc., are examined in literature. In this paper, we focus on a device-free real-time RR monitoring system using wireless signals. In our recent study, we proposed a non-contact RR monitoring system with a batch processing (delayed) estimation method. In this paper, for real-time monitoring, we modify the standard joint unscented Kalman filter (JUKF) method for this new and time-critical problem. Due to the nonlinear structure of the RR estimation problem with respect to the measurements, a novel modification is proposed to transform measurement errors into parameter errors by using the hyperbolic tangent function. It is shown in the experiments conducted with the real measurements taken using healthy volunteers that the proposed modified joint unscented Kalman filter (ModJUKF) method achieves the highest accuracy according to the windowing-based methods in the timevarying RR scenario. It is also shown that the ModJUKF not only reduces the computational complexity approximately 8.54% but also improves the accuracy 36.7% with respect to the standard JUKF method. INDEX TERMS Unscented Kalman filter, joint unscented Kalman filter, respiratory rate tracking, devicefree, vital signs, health monitoring, radio signals.

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Section: B State-space Formulationmentioning

confidence: 99%

Section: System Model and Data Processingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-Contact Respiratory Rate Estimation in Real-Time With Modified Joint Unscented Kalman Filter

2020

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A multi‐tone central divided difference frequency tracker with adaptive process noise covariance tuning

Brumana

Piroddi

2020

Adaptive Control & Signal

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SummaryThe problem of real‐time frequency estimation of nonstationary multi‐harmonic signals is important in many applications. In this paper, we propose a novel multi‐frequency tracker based on a state‐space representation of the signal with Cartesian filters and the second‐order central divided difference filter (CDDF), which improves the performance of the extended Kalman filter (EKF) by using Stirling's interpolation method to approximate the mean and covariance of the state vector. A crucial element of the method is the adaptive scaling of the process noise covariance matrix appearing in the filter equations, as a function of the innovation sequence, which tunes the accuracy‐reactivity trade‐off of the filter. The proposed solution is evaluated against two approaches from the literature, namely the factorized adaptive notch filter (FANF) and the extended Kalman filter frequency tracker (EKFFT). Several experiments emphasize the estimation accuracy of the proposed method as well as the improved robustness with respect to initial errors and input signal complexity. The presented method appears to be particularly efficient with rapidly varying frequencies, thanks to the update mechanism that adjusts the filter parameters based on the amplitude of the estimation error.

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Frequency estimation of narrow band signals in Gaussian noise via Unscented Kalman Filter

Cited by 2 publications

References 14 publications

Non-Contact Respiratory Rate Estimation in Real-Time With Modified Joint Unscented Kalman Filter

Non-Contact Respiratory Rate Estimation in Real-Time With Modified Joint Unscented Kalman Filter

A multi‐tone central divided difference frequency tracker with adaptive process noise covariance tuning

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