Standard Deviation Of Estimation Error Research Articles

PPG-based blood pressure estimation can benefit from scalable multi-scale fusion neural networks and multi-task learning

The continuous measurement of blood pressure (BP) plays an important role in preventing cardiovascular diseases. However, common cuff-based devices with cumbersome operations are difficult to realize continuous BP monitoring. We propose a continuous BP estimation method based on the end-to-end multi-scale fusion and multi-task learning neural network (MSF-MTLNet). It can use the 8-second PPG segment and its derivatives as input and automatically learn their multi-scale features to improve BP accuracy. The proposed method implements feature extraction by adaptively fusing multiple convolution kernels with different sizes through the attention mechanism. Simultaneously, multi-task learning was introduced to discover task-relevant features. A total of 277,600 segments from 1825 patients in the University of California, Irvine database are used for experiments. They are divided into the independent training set, validation set, and test set according to the ratio of 8:1:1 in an inter-subject manner. The mean and standard deviation of estimation error for systolic blood pressure and diastolic blood pressure are 0.97 ± 8.87 mmHg and 0.55 ± 4.23 mmHg, respectively, which outperforms the current cutting-edge method. Our approach almost meets the Association for the Advancement of Medical Instrumentation standard. Considering the British Hypertension Society standards, it achieves an 'A' grade for DBP estimation and a 'B' grade for SBP estimation. Experimental results show that MSF-MTLNet can obtain promising precision in cuffless and continuous BP estimation.

A clinical set-up for noninvasive blood pressure monitoring using two photoplethysmograms and based on convolutional neural networks.

Blood pressure is a reliable indicator of many cardiac arrhythmias and rheological problems. This study proposes a clinical set-up using conventional monitoring systems to estimate systolic and diastolic blood pressures continuously based on two photoplethysmogram signals (PPG) taken from the earlobe and toe. Several amendments were applied to conventional clinical monitoring devices to construct our project plan. We used two monitors to acquire two PPGs, one ECG, and invasive blood pressure as the reference to evaluate the estimation accuracy. One of the most critical requirements was the synchronization of the acquired signals that was accomplished by using ECG as the time reference. Following data acquisition and preparation procedures, the performance of each PPG signal alone and together was investigated using deep convolutional neural networks. The proposed architecture was evaluated on 32 records acquired from 14 patients after cardiovascular surgery. The results showed a better performance for toe PPG in comparison with earlobe PPG. Moreover, they indicated the algorithm accuracy improves if both signals are applied together to the network. According to the British Hypertension Society standards, the results achieved grade A for both blood pressure measurements. The mean and standard deviation of estimation errors were +0.3±4.9 and +0.1±3.2mmHg for systolic and diastolic BPs, respectively. Since the method is based on conventional monitoring equipment and provides a high estimation consistency, it can be considered as a possible alternative for inconvenient invasive BP monitoring in clinical environments.

Application of information fusion techniques and satellite products in the optimal redesign of rain gauge networks

Rain gauge networks are usually redesigned to improve the accuracy of spatial and temporal estimates and reduce the monitoring costs. In addition to the rain-gauge data, satellite-based data can be used for the optimal redesign of rainfall monitoring networks. Despite high spatial and temporal resolutions of products of meteorological satellites, they must be calibrated using ground-based data. In this paper, a new methodology is presented for an optimal redesign of rain-gauge networks. In this methodology, after the bias correction of some satellite-based rainfall products (i.e., PERSIANN-CCS, TRMM3B42RTV7, and CMORPH), they are combined using a Bayesian information fusion technique. The spatiotemporal rainfall maps, which are developed using the fusion model, are used in an optimization model. The optimization model provides the optimal locations of the rain-gauge stations, considering the objectives of minimizing both the monitoring cost and the average standard deviation of estimation errors. To illustrate the applicability and efficiency of the proposed methodology, it is applied to the Khorasan Razavi Province in Iran. The results show that by using the satellite data and the Bayesian information fusion technique, the summation of standard deviations of estimation errors is significantly reduced from 18,787.9 to 778.28 mm.

Format-transparent phase estimation based on KL divergence in coherent optical systems

We propose a novel format-transparent phase estimation method in coherent optical systems by minimizing the Kullback-Leibler (KL) divergence between the signal constellation and the samples for estimation. The proposed metric exhibits the same standard deviation of estimation errors as that in conventional blind phase searching (BPS) with an infinite resolution, while eliminating the pre-decisions in BPS so that phase estimation can be realized using a recursive algorithm. The complexity and the performance of the proposed KL method are compared with previously reported 2-stage BPS, Kalman filtering, principal component analysis (PCA), and the PCA + BPS hybrid method. It is shown that this method is particularly suitable for probabilistically shaped (PS) formats in which the PCA method does not work properly. It exhibits better performance than Kalman filtering and the PCA + BPS hybrid method and has lower complexity than 2-stage BPS. It is also shown that the proposed KL method has a relaxed cycle-slip problem and is less sensitive to the noise due to a smaller number of samples compared to the 2-stage BPS and the PCA + BPS hybrid method. Therefore, the proposed method can be a very promising solution for format-transparent phase estimation in coherent optical systems, particularly using the PS formats.

Channel frequency response estimation method based on pilot’s filtration and extrapolation

Introduction. Mobility is one of the main requirements for modern communication system. For OFDM systems it means spreading the wideband signals thru the multipath channel with variable in time parameters. Receiver should estimate channel parameters for demodulation the received signal. Problem statement. The pilots from current and previous received OFDM symbols are used for channel estimation. Development of channel frequency response estimation method that use only pilots from current received symbol is the task. Method development. This paper proposes a channel frequency response estimation method based on pilot’s filtration and extrapolation. Method consists of two stages. At first stage performs pilot’s filtration in forward and backward directions by Kalman filter and combining the results in each point. It allows increase the accuracy of channel estimation. At second stage performs extrapolation the channel frequency response between pilots in forward and backward directions and combining the results. Experimental results. Performed analysis of developed method by statistical modeling on example of communication system with channel frequency response described as second order autoregressive model. The standard deviation of estimation error for developed algorithm and Kalman algorithm was calculated. Mean square error of channel estimation for developed method and method of least square was compared. Conclusions. Developed algorithm allows decrease the standard deviation of channel frequency response estimation error in comparing with Kalman algorithm. Mean square error of channel frequency response estimation for developed method is lower than for method of least square. Key words: OFDM, digital communication system, wireless channel, channel frequency response, estimation, autoregressive model, Kalman filter.

An Advanced Radiative Transfer and Neural Network Scheme and Evaluation for Estimating Water Vapor Content from MODIS Data

This work made an improvement upon and a further evaluation of previous work for estimating water vapor content from near-infrared around 1 μm from MODIS data. The accuracy of RM-NN is determined by the complicated relationship of the geophysical parameters. An advanced scheme is proposed for building different training databases for different seasons in different regions to reduce the complexity. The training database includes three parts. The first part is a simulation database by MODTRAN for different weather conditions, which is made as a basic database; the second part is reliable field measurement data in observation stations; and the third part is the MYD05_L2 product on clear days, which is produced by the standard product algorithm for water vapor content. The comparative analyses based on simulation data indicate that maximum accuracy of single condition could be improved by about 34% relative to the “all conditions” results. Two study regions in China and America are selected as test areas, and the evaluation shows that the mean and the standard deviation of estimation error are about 0.08 g cm−2 and 0.09 g cm−2, respectively. All the analysis indicates that the advanced scheme can improve the retrieval accuracy of water vapor content, which can make full use of the advantages of previous methods.

Retrospective prediction of intraurban spatiotemporal distribution of PM2.5 in Taipei

Numerous studies have shown that fine airborne particulate matter particles (PM2.5) are more dangerous to human health than coarse particles, e.g. PM10. The assessment of the impacts to human health or ecological effects by long-term PM2.5 exposure is often limited by lack of PM2.5 measurements. In Taipei, PM2.5 was not systematically observed until August, 2005. Taipei is the largest metropolitan area in Taiwan, where a variety of industrial and traffic emissions are continuously generated and distributed across space and time. PM-related data, i.e., PM10 and Total Suspended Particles (TSP) are independently systematically collected by different central and local government institutes. In this study, the retrospective prediction of spatiotemporal distribution of monthly PM2.5 over Taipei will be performed by using Bayesian Maximum Entropy method (BME) to integrate (a) the spatiotemporal dependence among PM measurements (i.e. PM10, TSP, and PM2.5), (b) the site-specific information of PM measurements which can be certain or uncertain information, and (c) empirical evidence about the PM2.5/PM10 and PM10/TSP ratios. The performance assessment of the retrospective prediction for the spatiotemporal distribution of PM2.5 was performed over space and time during 2003–2004 by comparing the posterior pdf of PM2.5 with the observations. Results show that the incorporation of PM10 and TSP observations by BME method can effectively improve the spatiotemporal PM2.5 estimation in the sense of lower mean and standard deviation of estimation errors. Moreover, the spatiotemporal retrospective prediction with PM2.5/PM10 and PM2.5/TSP ratios can provide good estimations of the range of PM2.5 levels over space and time during 2003–2004 in Taipei.

Estimation of water vapor content in near-infrared bands around 1 μm from MODIS data by using RM–NN

An algorithm based on the radiance transfer model (RM) and a dynamic learning neural network (NN) for estimating water vapor content from moderate resolution imaging spectrometer (MODIS) 1B data is developed in this paper. The MODTRAN4 is used to simulate the sun-surface-sensor process with different conditions. The dynamic learning neural network is used to estimate water vapor content. Analysis of the simulation data indicates that the mean and standard deviation of estimation error are under 0.06 gcm(-2 )and 0.08 gcm(-2). The comparison analysis indicates that the estimation result by RM-NN is comparable to that of a MODIS water vapor content product (MYD05_L2). Finally, validation with ground measurement data shows that RM-NN can be used to accurately estimate the water vapor content from MODIS 1B data, and the mean and standard deviation of the estimation error are about 0.12 gcm(-2 )and 0.18 gcm(-2).

Comparison of interpolation methods for depth to groundwater and its temporal and spatial variations in the Minqin oasis of northwest China

Severe water shortages and dramatic declines in groundwater levels have resulted in environmental deterioration in the Minqin oasis, an arid region of northwest China. Understanding temporal and spatial variations in the depth to groundwater in the region is important for developing management strategies. Depth to groundwater records for 48 observation wells in the Minqin oasis were available for 22 years from 1981 to 2003, allowing us to compare three different interpolation methods based on three selected years (1981, 1990, 2002) as starting points. The three methods were inverse distance weighting (IDW), radial basis function (RBF), and kriging (including ordinary kriging (OK), simple kriging (SK), and universal kriging (UK)). Cross-validation was applied to evaluate the accuracy of the various methods, and two indices – the correlation coefficient ( R 2) and the root mean squared error ( RMSE) – were used to compare the interpolation methods. Another two indices – deviation of estimation errors ( σ) and 95% prediction interval (95 PPI) – were used to assess prediction errors. Comparison of interpolated values with observed values indicates that simple kriging is the optimal method for interpolating depth to groundwater in this region: it had the lowest standard deviation of estimation errors and smallest 95% prediction interval (95 PPI). By using the simple kriging method and an autoregressive model for depth to groundwater based on the data from 1981 to 2003, this work revealed systematic temporal and spatial variations in the depth to groundwater in the Minqin oasis. The water table has declined rapidly over the past 22 years, with the average depth to groundwater increasing from 4.95 m in 1981 to 14.07 m in 2002. We attribute the decline in the water table to excessive extraction and to decreases in irrigation channel leakage.

A spiking network model for learning reward timing in cortex

Event Abstract Back to Event A spiking network model for learning reward timing in cortex The ability to represent time is an essential component of cognition but its neural basis is unknown. Although extensively studied both behaviorally and electrophysiologically, a general theoretical framework describing the elementary neural mechanisms used by the brain to learn temporal representations is lacking. It is commonly believed that the underlying cellular mechanisms reside in high order cortical regions but recent studies show sustained neural activity in primary sensory cortices that can represent the timing of expected reward. In particular, a recent study by Shuler and Bear (2006) has shown learned, reward timing dependent cortical activity in primary visual cortex. We postulate that a network of laterally connected cortical neurons is sufficient for generating the timing dependent neuronal dynamics, that the timing information can be stored within synaptic efficacies, and that this cortical activity can be learned through a novel variant of reinforcement learning. One of the advantages of the theory proposed here is that it does not require specialized processes such as tagged delay lines of phase locked oscillators, as assumed explicitly or implicitly in previous theories of timing. We mathematically formulate the neuronal dynamics and the learning rule, and implement our model computationally both in a rate based implementation and in a model of conductance based spiking neurons. We show that this theory can account for various aspects of the experimental data, but also explore the limitations of this model. We further analyze the spiking neural model using a quasi-steady state mean field theory (e.g: Renart et al, 2003). This analysis reduces the dynamics of the network to a single non-linear dynamical equation. We show that the results of the mean field theory are in close agreement with the simulation results. Our theoretical model can account for existing experimental results, and can also produce novel predictions. We show several such predictions which include change in pair wise correlations as a result of learning, and an increase in spontaneous and evoked activity after learning. Using the original data from the Shuler and Bear (2006) paper we show that the experimental data is consistent with these predictions and that both evoked activity and spontaneous activity are significantly increased by 74% and 40% respectively as a result of training. One prominent experimental feature of temporal interval estimation is the scalar rule (Webber law), which states that the standard deviation of estimation errors increase linearly with the estimated interval. Using a simple population decoding scheme based on the activity of the trained network of spiking neurons we show that this model produces estimation errors that increase approximately linearly with the estimated interval. We explore the origin of these results, and how they compare to experimental findings. Here we present a theory to account for the specific results of Shuler and Bear (2006) which can also form the basis for a general theory of timing estimation in the cortex. We computationally implement and mathematically analyze the theory, and propose experimental tests. We also show here experimental confirmation of some of our theoretical predictions. Conference: Computational and systems neuroscience 2009, Salt Lake City, UT, United States, 26 Feb - 3 Mar, 2009. Presentation Type: Poster Presentation Topic: Poster Presentations Citation: (2009). A spiking network model for learning reward timing in cortex. Front. Syst. Neurosci. Conference Abstract: Computational and systems neuroscience 2009. doi: 10.3389/conf.neuro.06.2009.03.313 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 04 Feb 2009; Published Online: 04 Feb 2009. 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A phoneme duration model considering speaking‐rate and linguistic features for speech recognition

In this paper, we proposed a method of phoneme duration modeling for speech recognition. A phoneme with extremely short or long duration often causes a decline of performance of speech recognition. In order to improve performance of recognition, an estimation of phoneme duration determined by various parameters is required. However, there was no usual method of duration modeling for speech recognition considering the influence of both speaking‐rate and linguistic feature (phoneme location in sentence, part‐of‐speech, et al.), which influence phoneme duration strongly. Therefore, we modeled influence of speaking‐rate by two‐dimensional normal distribution of phoneme duration and local average of vowel duration. Each normal distribution is determined by tree‐based clustering with various questions, which include linguistic feature. With an experiment of estimation of phoneme duration by this model, we acquired 20.8% reduction of standard deviation of estimation error. We also used the proposed duration model for rescoring of N‐best hypothesis of speech recognition. With an experiment of rescoring of recognition results for spontaneous speech, we acquired significant reduction of 4.7% in phoneme error rate.

Estimation of Areal Frequency and Mean Trace Length of Discontinuities Observed in Non-Planar Surfaces

Mauldon (1998) suggested end-point estimators of areal frequency and mean trace length for a planar sampling window which were recently proved to be unbiased maximum likelihood estimators by Lyman (2003). The present paper is to expand the concept and applicability of the end-point estimators to those for a general non-planar sampling window. The generalized end-point estimators are verified and its applicability for variable discontinuity orientation is checked by Monte Carlo simulation. Standard deviation of estimation error and estimation efficiency of areal frequency and mean trace length are also considered.

Optimal design of a groundwater monitoring network in Daqing, China

In the Daqing region of China there are 34 groundwater well fields with a groundwater withdrawal of 81.9×104 m3/d. Due to over-abstraction of the groundwater resources from the 1960s to present, a cone of depression up to 4,000 km2 has formed in the area. To monitor the change in the groundwater environment, it is necessary to design an effective groundwater-monitoring network. The sites for monitoring groundwater level were selected by applying the finite-element method coupled with Kalman filtering to the area in which the groundwater resources have been extensively exploited. The criterion is a threshold value of the standard deviation of estimation error. This threshold value is determined by the tradeoff between maximum information and minimum cost, in which the maximum information is characterized by the standard deviation and the minimum cost is equivalent to the number of observation wells. The groundwater flow model was calibrated by an optimal algorithm coupled the finite-element method with Kalman filtering by using the data from 16 observation wells from 1986 to 1993. A simulation algorithm coupled with the finite-element method with Kalman filtering analyzed the location data obtained from the existing 38 observation wells in the same region. The spatial distribution of standard deviation of estimation error is computed and the locations that have the maximum standard deviation are selected as additional sites for augmenting the existing observational well network at a given threshold value of the standard deviation surface. Based on the proposed method for selecting a groundwater level monitoring network, an optimal monitoring network with 88 observation wells with the measurement frequency of 12 times per year is selected in the Daqing region of China.

Air-sea interacting effects to the sea surface temperature observation by NOAA/AVHRR

Abstract Abstract. By combining the brightness temperatures by NOAA-9/AVHRR and the sea surface temperature by Mutsu Bay automatic marine monitoring buoy system, the total number of 390 match-ups was set up. The temporal and spatial coincidence in each match-up is within 30 minutes and one pixel resolution. Following to the split-window method, a regression function for the sea surface temperature estimation was calculated and its standard deviation of estimation errors was 0-59°C. The residues were carefully examined with respect to the sensor calibration data and the meteorological data at match-up collections. Then it was found that large errors appeared when differences between the air temperature and the buoy temperature were large. Those were estimated to be caused by the air-sea interacting effects. By removing the match-ups with larger errors, a selected data set with 334 match-ups was prepared and the SST estimation function was recalculated. The standard deviation of errors reduced to 0-34 °C.

Estimation Errors of Component Spectra Estimated by Means of the Concentration-Spectrum Correlation: Part I

It is shown by theoretical analysis and computer simulations that statistical errors accompany the estimates of component spectra of complex mixtures calculated by the concentration-spectrum correlation method. It is revealed that the estimation errors consist of a superposition of other component spectra, each multiplied by a weighting factor. The weighting factor contains three statistical parameters of the sample: two sample standard deviations of both the objective and the interfering components, and the sample correlation coefficient between these two component concentrations. The probability density function of the weighting factor, as well as its ensemble average and standard deviation, is derived. It is shown that the ensemble standard deviation of estimation errors, which is a good measure for the accuracy of the estimated spectrum, can be estimated by the nonparametric method called a bootstrap. The behavior of the estimation errors and the effectiveness of the bootstrap method are demonstrated by computer simulations.