scholarly journals Research on Robustness of Geometric Algebra Based Adaptive Filtering Algorithms In Non-Gaussian Environment

2021 ◽  
Author(s):  
Rui Wang ◽  
Yi Wang ◽  
Yanping Li ◽  
Wenming Cao
Keyword(s):  
Mean Square Error ◽  
Adaptive Filtering ◽  
Geometric Algebra ◽  
Mean Square ◽  
Robust Algorithms ◽  
Filtering Algorithms ◽  
Minimum Error ◽  
The Mean ◽  
Non Gaussian ◽  
Stable Noise

Abstract In this paper, two new geometric algebra (GA) based adaptive filtering algorithms in non-Gaussian environment are proposed, which are deduced from the robust algorithms based on the minimum error entropy (MEE) criterion and the joint criterion of the MEE and the mean square error (MSE) with the help of GA theory. Some experiments validate the effectiveness and superiority of the GA-MEE and GA-MSEMEE algorithms in α-stable noise environment. At the same time, the GA-MSEMEE algorithm has faster convergence speed compared with the GA-MEE.

scholarly journals Diffusion Generalized MCC with a Variable Center Algorithm for Robust Distributed Estimation

Electronics ◽  
2021 ◽  
Vol 10 (22) ◽  
pp. 2807
Author(s):  
Wentao Ma ◽  
Panfei Cai ◽  
Fengyuan Sun ◽  
Xiao Kou ◽  
Xiaofei Wang ◽  
...  
Keyword(s):  
Adaptive Filtering ◽  
Gaussian Noise ◽  
Distributed Estimation ◽  
Filtering Algorithms ◽  
Combine Strategy ◽  
Stable Performance ◽  
The Mean ◽  
Maximum Correntropy Criterion ◽  
Non Gaussian ◽  
Variable Center

Classical adaptive filtering algorithms with a diffusion strategy under the mean square error (MSE) criterion can face difficulties in distributed estimation (DE) over networks in a complex noise environment, such as non-zero mean non-Gaussian noise, with the object of ensuring a robust performance. In order to overcome such limitations, this paper proposes a novel robust diffusion adaptive filtering algorithm, which is developed by using a variable center generalized maximum Correntropy criterion (GMCC-VC). Generalized Correntropy with a variable center is first defined by introducing a non-zero center to the original generalized Correntropy, which can be used as robust cost function, called GMCC-VC, for adaptive filtering algorithms. In order to improve the robustness of the traditional MSE-based DE algorithms, the GMCC-VC is used in a diffusion adaptive filter to design a novel robust DE method with the adapt-then-combine strategy. This can achieve outstanding steady-state performance under non-Gaussian noise environments because the GMCC-VC can match the distribution of the noise with that of non-zero mean non-Gaussian noise. The simulation results for distributed estimation under non-zero mean non-Gaussian noise cases demonstrate that the proposed diffusion GMCC-VC approach produces a more robustness and stable performance than some other comparable DE methods.

The Bordeaux Automatic Meridian Circle

1978 ◽  
Vol 48 ◽  
pp. 227-228
Author(s):  
Y. Requième
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Meridian Circle ◽  
The Mean ◽  
Full Automation

In spite of important delays in the initial planning, the full automation of the Bordeaux meridian circle is progressing well and will be ready for regular observations by the middle of the next year. It is expected that the mean square error for one observation will be about ±0.”10 in the two coordinates for declinations up to 87°.

Limit tolerances for sums of measurement errors

2018 ◽  
Vol 934 (4) ◽  
pp. 59-62
Author(s):  
V.I. Salnikov
Keyword(s):  
Normal Distribution ◽  
Mean Square Error ◽  
Gaussian Distribution ◽  
Measurement Errors ◽  
Theory And Practice ◽  
Mean Square ◽  
The Mean ◽  
Limiting Values ◽  
Limiting Value

The question of calculating the limiting values of residuals in geodesic constructions is considered in the case when the limiting value for measurement errors is assumed equal to 3m, ie ∆рred = 3m, where m is the mean square error of the measurement. Larger errors are rejected. At present, the limiting value for the residual is calculated by the formula 3m√n, where n is the number of measurements. The article draws attention to two contradictions between theory and practice arising from the use of this formula. First, the formula is derived from the classical law of the normal Gaussian distribution, and it is applied to the truncated law of the normal distribution. And, secondly, as shown in [1], when ∆рred = 2m, the sums of errors naturally take the value equal to ?pred, after which the number of errors in the sum starts anew. This article establishes its validity for ∆рred = 3m. A table of comparative values of the tolerances valid and recommended for more stringent ones is given. The article gives a graph of applied and recommended tolerances for ∆рred = 3m.

scholarly journals Reconstruction of Diffusion Coefficients and Power Exponents from Single Lagrangian Trajectories

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 111
Author(s):  
Leonid M. Ivanov ◽  
Collins A. Collins ◽  
Tetyana Margolina
Keyword(s):  
Black Sea ◽  
Diffusion Coefficients ◽  
Current System ◽  
Mean Square Displacement ◽  
California Current ◽  
The Black Sea ◽  
Mean Square ◽  
California Current System ◽  
The Mean ◽  
Non Gaussian

Using discrete wavelets, a novel technique is developed to estimate turbulent diffusion coefficients and power exponents from single Lagrangian particle trajectories. The technique differs from the classical approach (Davis (1991)’s technique) because averaging over a statistical ensemble of the mean square displacement (<X2>) is replaced by averaging along a single Lagrangian trajectory X(t) = {X(t), Y(t)}. Metzler et al. (2014) have demonstrated that for an ergodic (for example, normal diffusion) flow, the mean square displacement is <X2> = limT→∞τX2(T,s), where τX2 (T, s) = 1/(T − s) ∫0T−s(X(t+Δt) − X(t))2 dt, T and s are observational and lag times but for weak non-ergodic (such as super-diffusion and sub-diffusion) flows <X2> = limT→∞≪τX2(T,s)≫, where ≪…≫ is some additional averaging. Numerical calculations for surface drifters in the Black Sea and isobaric RAFOS floats deployed at mid depths in the California Current system demonstrated that the reconstructed diffusion coefficients were smaller than those calculated by Davis (1991)’s technique. This difference is caused by the choice of the Lagrangian mean. The technique proposed here is applied to the analysis of Lagrangian motions in the Black Sea (horizontal diffusion coefficients varied from 105 to 106 cm2/s) and for the sub-diffusion of two RAFOS floats in the California Current system where power exponents varied from 0.65 to 0.72. RAFOS float motions were found to be strongly non-ergodic and non-Gaussian.

scholarly journals IndoorPlant: A Model for Intelligent Services in Indoor Agriculture Based on Context Histories

Sensors ◽  
2021 ◽  
Vol 21 (5) ◽  
pp. 1631
Author(s):  
Bruno Guilherme Martini ◽  
Gilson Augusto Helfer ◽  
Jorge Luis Victória Barbosa ◽  
Regina Célia Espinosa Modolo ◽  
Marcio Rosa da Silva ◽  
...  
Keyword(s):  
Technology Acceptance ◽  
Mean Square Error ◽  
Ease Of Use ◽  
Coefficient Of Determination ◽  
Square Root ◽  
Mean Square ◽  
Use Context ◽  
The Mean ◽  
Acceptance Model ◽  
The Internet Of Things

The application of ubiquitous computing has increased in recent years, especially due to the development of technologies such as mobile computing, more accurate sensors, and specific protocols for the Internet of Things (IoT). One of the trends in this area of research is the use of context awareness. In agriculture, the context involves the environment, for example, the conditions found inside a greenhouse. Recently, a series of studies have proposed the use of sensors to monitor production and/or the use of cameras to obtain information about cultivation, providing data, reminders, and alerts to farmers. This article proposes a computational model for indoor agriculture called IndoorPlant. The model uses the analysis of context histories to provide intelligent generic services, such as predicting productivity, indicating problems that cultivation may suffer, and giving suggestions for improvements in greenhouse parameters. IndoorPlant was tested in three scenarios of the daily life of farmers with hydroponic production data that were obtained during seven months of cultivation of radicchio, lettuce, and arugula. Finally, the article presents the results obtained through intelligent services that use context histories. The scenarios used services to recommend improvements in cultivation, profiles and, finally, prediction of the cultivation time of radicchio, lettuce, and arugula using the partial least squares (PLS) regression technique. The prediction results were relevant since the following values were obtained: 0.96 (R2, coefficient of determination), 1.06 (RMSEC, square root of the mean square error of calibration), and 1.94 (RMSECV, square root of the mean square error of cross validation) for radicchio; 0.95 (R2), 1.37 (RMSEC), and 3.31 (RMSECV) for lettuce; 0.93 (R2), 1.10 (RMSEC), and 1.89 (RMSECV) for arugula. Eight farmers with different functions on the farm filled out a survey based on the technology acceptance model (TAM). The results showed 92% acceptance regarding utility and 98% acceptance for ease of use.

Burst Erasures and the Mean-Square Error for Cyclic Parseval Frames

2011 ◽  
Vol 57 (7) ◽  
pp. 4622-4635 ◽  
Author(s):  
Bernhard G. Bodmann ◽  
Pankaj K. Singh
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Parseval Frames ◽  
The Mean

A MODIFIED RATIO TYPE ESTIMATOR OF FINITE POPULATION MEAN UNDER STRATIFIED RANDOM SAMPLING SCHEME

2021 ◽  
pp. 58-60
Author(s):  
Naziru Fadisanku Haruna ◽  
Ran Vijay Kumar Singh ◽  
Samsudeen Dahiru
Keyword(s):  
Mean Square Error ◽  
Random Sampling ◽  
Minimum Mean Square Error ◽  
Real Life ◽  
Population Data ◽  
Auxiliary Variable ◽  
Mean Square ◽  
Data Set ◽  
Population Mean ◽  
The Mean

In This paper a modied ratio-type estimator for nite population mean under stratied random sampling using single auxiliary variable has been proposed. The expression for mean square error and bias of the proposed estimator are derived up to the rst order of approximation. The expression for minimum mean square error of proposed estimator is also obtained. The mean square error the proposed estimator is compared with other existing estimators theoretically and condition are obtained under which proposed estimator performed better. A real life population data set has been considered to compare the efciency of the proposed estimator numerically.

Adaptive and augmented nonlinear filters : theory and applications

2018 ◽  
Author(s):  
◽  
Tao Sun
Keyword(s):  
Kalman Filter ◽  
Mean Square Error ◽  
Gaussian Approximation ◽  
Adaptive Strategy ◽  
Nonlinear Filters ◽  
Nonlinear Transformation ◽  
Mean Square ◽  
Gaussian Filters ◽  
Non Gaussian ◽  
Gaussian Estimation

[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] Nonlinear estimation and filtering have been intensively studied for decades since it has been widely used in engineering and science such as navigation, radar signal processing and target tracking systems. Because the posterior density function is not a Gaussian distribution, then the optimal solution is intractable. The nonlinear/non-Gaussian estimation problem is more challenging than the linear/Gaussian case, which has an optimal closed form solution, i.e. the celebrated Kalman filter. Many nonlinear filters including the extended Kalman filter, the unscented Kalman filter and the Gaussian-approximation filters, have been proposed to address nonlinear/non-Gaussian estimation problems in the past decades. Although the estimate yield by Gaussian-approximation filters such as cubature Kalman filters and Gaussian-Hermite quadrature filters is satisfied in many applications, there are two obvious drawbacks embedded in the use of Gaussian filters. On the one hand, with the increase of the quadrature points, much computational effort is devoted to approximate Gaussian integrals, which is not worthy sometimes. On the other hand, by the use of the update rule, the estimate constrains to be a linear function of the observation. In this dissertation, we aim to address this two shortcoming associated with the conventional nonlinear filters. We propose two nonlinear filters in the dissertation. Based on an adaptive strategy, the first one tries to reduce the computation cost during filtering without sacrificing much accuracy, because when the system is close to be linear, the lower level Gaussian quadrature filter is sufficient to provide accurate estimate. The adaptive strategy is used to evaluate the nonlinearity of the system at current time first and then utilize different quadrature rule for filtering. Another filter aims to modify the conventional update rule, i.e. the linear minimum mean square error (LMMSE) rule, to involve a nonlinear transformation of the observation, which is proven to be an efficient way to exploit more information from the original observation. According to the orthogonal property, we propose a novel approach to construct the nonlinear transformation systematically. The augmented nonlinear filter outperforms Gaussian filters and other conventional augmented filters in terms of the root mean square error and onsistency. Furthermore, we also extend the work to the more general case. The higher order moments can be utilized to construct the nonlinear transformation and in turn, the measurement space can be expand efficiently. Without the Gaussian assumption, the construction of the nonlinear transformation only demand the existence of a finite number of moments. Finally, the simulation results validate and demonstrate the superiority of the adaptive and augmented nonlinear filters.

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