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Improving the quality of pulse rate variability derived from wearable devices using adaptive, spectrum and nonlinear filtering

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BIOMEDICAL SIGNAL PROCESSING AND CONTROL 2025年 102卷

作者： Prucnal, Monika A. Polak, Adam G. Kazienko, Przemyslaw Wroclaw Univ Sci & Technol Wroclaw Tech Dept Elect & Photon Metrol Wroclaw Poland Wroclaw Univ Sci & Technol Wroclaw Tech Dept Artificial Intelligence Wroclaw Poland

The popularity of wearable devices that record the photoplethysmographic (PPG) signal is increasing their use as monitors of circulatory and nervous systems function, including the extraction of pulse rate variability (PRV). Unfortunately, PPG is susceptible to interferences, including motion artifacts, which introduce errors into PRV. The aim of this study was to analyze the effectiveness of different approaches to filtering PPG (however, without recent deep learning methods) using an accelerometer (ACC) signal, in order to improve the accuracy of PRV extraction. This research concerns single and combined methods: adaptive filtering (AF) using the normalized least mean squares, spectrum filtering (SF) and nonlinear filtering (NF) using empirical mode decomposition. filtering was complemented by postprocessing (PP): improving the accuracy of peak determination in PPG, correction of non-physiological values in PRV and its autoregressive modeling. The corrected PRVs were compared with reference heart rate variabilities (HRVs) extracted from the simultaneously recorded ECG by calculating the relative root mean square error (RRMSE). The results for different filtering sequences schemes indicate that filtering PPG signals with SF reduced the PRV error the most and NF the least. In various laboratory experiments, SF + PP, as well as SF + AF + NF + PP, resulted in the overall lower RRMSE, while in conditions similar to everyday life, the sequence of SF + AF + NF + PP proved to be the best sequence of methods (BS). The work shows that the use of the proposed BS of methods allows for improving the accuracy of PRV signal, increasing its similarity to the reference HRV for all types of analyzed experiments.

关键词： Photoplethysmography (PPG) Pulse rate variability (PRV) Heart rate variability (HRV) Adaptive filtering Spectrum filtering nonlinear filtering Signal postprocessing

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Consensus-Based Distributed nonlinear filtering With Kernel Mean Embedding

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2025年第2期61卷 4973-4987页

作者： Guo, Liping Wang, Jimin Zhao, Yanlong Zhang, Ji-Feng Chinese Acad Sci Inst Syst Sci Acad Math & Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China Univ Sci & Technol Beijing Sch Automat & Elect Engn Beijing Peoples R China Minist Educ Key Lab Knowledge Automat Ind Proc Beijing 100083 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100049 Peoples R China Zhongyuan Univ Technol Sch Automat & Elect Engn Zhengzhou 450007 Peoples R China

This article proposes a consensus-based distributed nonlinear filter with kernel mean embedding (KME) to fill the gap of kernel-based filters for distributed sensor networks. Specifically, to approximate the posterior distribution, the system state is embedded into a higher dimensional reproducing kernel Hilbert space (RKHS), and then the nonlinear measurement function is linearly represented. As a result, an update rule for the KME of posterior distribution is established in the RKHS. To demonstrate that the proposed distributed filter can achieve centralized estimation accuracy, a centralized filter is first developed by extending the standard Kalman filter in the state space to the RKHS. Then, the proposed distributed filter is proved to be equivalent to the centralized one. Two examples highlight the effectiveness of the developed filters in target tracking scenarios, including a nearly constantly moving target and a turning target, respectively, with range, bearing, and range-rate measurements.

关键词： Filters Kernel Vectors Kalman filters Density functional theory Accuracy nonlinear filters Estimation Target tracking Posterior probability Consensus algorithm distributed sensor network kernel mean embedding (KME) nonlinear filtering posterior approximation

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Large deviation estimates for nonlinear filtering with discontinuity and small noise☆

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2025年 187卷

作者： Qian, Hongjiang Cao, Yanzhao Yin, George Auburn Univ Dept Math & Stat Auburn AL 36849 USA Univ Connecticut Dept Math Storrs CT USA

This paper develops large deviation estimates for nonlinear filtering with discontinuity in the drift of the signal and small noise intensities in both the signal and the observations. A variational approach related to Mortensen's optimization problem is utilized in our analysis. The discontinuity of the drift in the signal naturally arises in many applications, including modeling communication channels with a "hard limiter". Our results extend the work of Reddy et al. (2022), in which smooth functions were used. To address the discontinuous in the drift of the signal, relaxed controls are used to study the asymptotic fraction of time the controlled signals spend in each half-space divided by the discontinuity hyperplane. Large deviation estimates are established by the weak convergence method using the stochastic control representation for positive functionals of Brownian motions and Laplace asymptotics of the Kallianpur-Striebel formula.

关键词： nonlinear filtering Small noise Large deviations Discontinuity

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AN IMPROVED EXTENDED KALMAN FILTER BASED ON PIECEWISE SELF-ADJUSTING WEIGHTED nonlinear PREDICTIVE filtering ALGORITHM FOR MOBILE ROBOT POSITIONING AND NAVIGATION

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INTERNATIONAL JOURNAL OF ROBOTICS & AUTOMATION 2025年第1期40卷 56-64页

作者： Fan, Qiyuan Yen, Kin Sam Univ Sains Malaysia Sch Mech Engn Engn Campus Nibong Tebal 14300 Penang Malaysia

This paper introduces piecewise self-adjusting weighted nonlinear predictive filtering (PSAWNPF) algorithm, an enhanced extended Kalman filter (EKF) approach tailored for optimal mobile robot positioning and navigation. The algorithm uniquely incorporates quaternion-based attitude representation and a self-adjusting weighting mechanism into a conventional EKF framework. The quaternion-based attitude representation facilitates linear matrix operations, while the self-adjusting weighting mechanism dynamically adapts based on real-time error estimation, enhancing both computational efficiency and position estimation accuracy. Experimental validation on a mobile robot equipped with LiDAR and gyroscope demonstrates the superior performance of PSAWNPFEKF, recording a 3.1% uncertainty interval for position estimation, compared to 5.3% for the unscented Kalman filter (UKF) and 6.5% for traditional EKF algorithms. The PSAWNPF-EKF algorithm also achieves a substantial 24% reduction in the average operation time for predefined routes, surpassing other algorithms. The findings affirm PSAWNPF-EKF as the most accurate and efficient option among the three algorithms for mobile robot positioning and navigation. Looking forward, future research can explore the adaptability and applicability of PSAWNPF-EKF in diverse scenarios, such as autonomous vehicle navigation and aerial drone mapping, further expanding its impact in the realm of robotics and autonomous systems.

关键词： Kalman filter SLAM mobile robot localisation and navigation nonlinear filtering

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nonlinear filtering using the wavelet transform

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SIGNAL PROCESSING 2000年第3期80卷 441-450页

作者： Chun, J Chun, J Korea Adv Inst Sci & Technol Dept Elect Engn Yusong Gu Taejon 305701 South Korea

We present a fast nonlinear filtering algorithm that propagates the entire underlying conditional probability density functions recursively in a computationally efficient manner using the discrete wavelet transform. With the multiresolution analysis capability offered by the wavelet transform, we can speed up the computation by ignoring the high-frequency details of the probability density function up to a certain level. The level of the wavelet decomposition can be determined at each time step adaptively. According to our simulation, the proposed algorithm appears to be potentially more accurate than the widely used extended Kalman filter. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： wavelet transform nonlinear filtering probability density function

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nonlinear filtering and control of a switching diffusion with small observation noise

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SIAM JOURNAL ON CONTROL AND OPTIMIZATION 1998年第5期36卷 1638-1668页

作者： Zhang, Q Univ Georgia Dept Math Athens GA 30602 USA

This paper is concerned with nonlinear filtering and control of a switching diffusion coupled by an unknown Markov chain. Two statistical estimation methods are used to track the unknown Markov chain. Computable approximate filters are obtained based on these methods. The filters are then used to construct controls for the partially observed system. These controls are shown to be asymptotically optimal as the observation noise tends to zero. Finally an example is considered and numerical experiments are reported.

关键词： nonlinear filtering hybrid system interacting multiple model small observation noise nearly optimal control

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nonlinear filtering IN OBJECT AND FOURIER SPACE IN A JOINT TRANSFORM OPTICAL CORRELATOR - COMPARISON AND EXPERIMENTAL REALIZATION

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APPLIED OPTICS 1995年第20期34卷 3942-3949页

作者： VALLMITJANA, S CARNICER, A MARTINBADOSA, E JUVELLS, I The authors are with the Laboratori d’Optica Departament de Física Aplicada i Electrònica Universitat de Barcelona Diagonal 647 Barcelona E-08028 Spain.

The use of different kinds of nonlinear filtering in a joint transform correlator are studied and compared. The study is divided into two parts, one corresponding to object space and the second to the Fourier domain of the joint power spectrum. In the first part, phase and inverse filters are computed;their inverse Fourier transforms are also computed, thereby becoming the reference in the object space. In the Fourier space, the binarization of the power spectrum is realized and compared with a new procedure for removing the spatial envelope. Ail cases are simulated and experimentally implemented by a compact joint transform correlator.

关键词： JOINT TRANSFORM CORRELATOR PATTERN RECOGNITION nonlinear filtering

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nonlinear filtering of an optical pulse train using dissipative Kerr solitons

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OPTICA 2019年第11期6卷 1386-1393页

作者： Brasch, Victor Obrzud, Ewelina Lecomte, Steve Herr, Tobias Swiss Ctr Elect & Microtechnol CSEM Time & Freque Rue Observ 58 CH-2000 Neuchatel Switzerland Univ Geneva Dept Astron Chemin Maillettes 51 CH-1290 Versoix Switzerland

The capability to store light for extended periods of time enables optical cavities to act as narrowband optical filters, whose linewidth corresponds to the cavity's inverse energy storage time. Here, we report on nonlinear filtering of an optical pulse train based on temporal dissipative Kerr solitons in microresonators. Our experimental results in combination with analytical and numerical modeling show that soliton dynamics enables information storage about the system's physical state longer than the cavity's energy storage time, thereby giving rise to a filter width that can be more than an order of magnitude below the cavity's intrinsic linewidth. Such nonlinear optical filtering can find immediate applications in optical metrology, and low-timing jitter ultrashort optical pulse generation and potentially opens new avenues for microwave photonics. (c) 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

关键词： nonlinear filtering Optical signals Phase modulation Pulse generation Signal processing Ultrashort pulses

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nonlinear filtering of statistically connected video sequences based on hidden Markov chains

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JOURNAL OF COMMUNICATIONS TECHNOLOGY AND ELECTRONICS 2010年第3期55卷 307-315页

作者： Petrov, E. P. Medvedeva, E. V.

A method for the synthesis of algorithms for nonlinear filtering of statistically connected (correlated) video sequences of digital halftone images distorted by a white Gaussian noise is proposed. The method is based on the use of hidden Markov chains as a mathematical model for video sequences of digital halftone images, which, in limited observation intervals, can be represented by multidimensional Markov chains.

关键词： nonlinear filtering

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nonlinear filtering of backpropagated fields

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 1999年第7期16卷 1799-1805页

作者： Sanchez-de-la-Llave, JD Morales-Porras, A Testorf, M McGahan, RV Fiddy, MA Univ Lowell Dept Elect & Comp Engn Lowell MA 01854 USA USAF Res Lab Bedford MA 01731 USA

As a result of interest in imaging strongly scattering targets, the Air Force Research Laboratory is making available to the community sets of data from various targets;We describe a nonlinear filtering technique, namely, homomorphic filtering, which we have applied to recover an image of the target from the backpropagated field calculated from the scattering data. We show new results for targets that other methods, especially linearized methods, are unable to image. While we obtain good images with real data, convolutional effects arising from limited data can sometimes degrade performance. (C) 1999 Optical Society of America [S0740-3232(99)01907-9].

关键词： Forward scattering In field scattering Inverse scattering Multiple scattering nonlinear filtering Scattering

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