Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic fu...Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic function-like objective functions.Specifically,a series of generalized new SAF algorithms are proposed by introducing the q-deformed hyperbolic function as the cost function,named SAF-qDHSI,SAF-qDHCO,SAFqDHTA&SAF-qDHSE algorithms,respectively.Then,the proposed algorithm is theoretically demonstrated with detailed mean convergence and computational complexity analysis;secondly,the effect of different q values on the performance of the new algorithm is verified through data simulation;the new algorithm still has better performance under the interference of Gaussian noise and non-Gaussian noise even when facing the system mutation;finally,the new algorithm is verified through the measured engineering data,and the results show that the new algorithm has better convergence and robustness compared with the existing algorithm.In conclusion,the generalized algorithm based on the new cost function proposed in this paper is more effective in nonlinear system identification.展开更多
This study creates a three-dimensional surface spline(3DSS)model of China's Mainland based on surface and CHAMP satellite observations.Through this model,the magnetic field analyses of domestic plateau(Qinghai-Tib...This study creates a three-dimensional surface spline(3DSS)model of China's Mainland based on surface and CHAMP satellite observations.Through this model,the magnetic field analyses of domestic plateau(Qinghai-Tibet Plateau 28°N-38°N,78°E-102°E),plain(middle and lower reaches of Yangtze River Plain 27°N-34°N,111°E-122°E),and marine(parts of the East and South China Seas 16°N-30°N,123°E-136°E)areas have been investigated.Single models of plateau and plain have also been created.To compare and verify results,the corresponding two-dimensional(2DTY)and three-dimensional(3DTY)Taylor polynomial models have been derived.Issues such as the removal of disturbing geomagnetic fields,the data gap between surface and satellite level,and boundary effect are all seriously considered.With an aim to evaluate the resulting model,some randomly selected points are not join the modeling,by which we thereby inspected the results in terms of residuals,change rate absolutes,and Root Mean Square Error(RMSE).Results show that except component Y,the change rate absolutes of other components are less than 1%both in domestic and single models,which means that the modeling result of 3DSS is better than the other two models.Plateau and plain 3DSS models reflect the fine distribution of the magnetic field after comparison with domestic distribution.The 3DSS model fits the plateau best,followed by the plain,while the worst fit is in the marine area.This means that the modeling precision depends mainly on the number and distribution of measuring points.展开更多
In this work, we seek the relationship between the order of the polynomial model and the number of knots and intervals that we need to fit the splines regression model. Regression models (polynomial and spline regress...In this work, we seek the relationship between the order of the polynomial model and the number of knots and intervals that we need to fit the splines regression model. Regression models (polynomial and spline regression models) are presented and discussed in detail in order to discover the relation. Intrinsically, both models are dependent on the linear regression model. Spline is designed to draw curves to balance the goodness of fit and minimize the mean square error of the regression model. In the splines model, the curve at any point depends only on the observations at that point and some specified neighboring points. Using the boundaries of the intervals of the splines, we fit a smooth cubic interpolation function that goes through (n + 1) data points. On the other hand, polynomial regression is a useful technique when the pattern of the data indicates a nonlinear relationship between the dependent and independent variables. Moreover, higher-degree polynomials can capture more intricate patterns, but it can also lead to overfitting. A simulation study is implemented to illustrate the performance of splines and spline segments based on the degree of the polynomial model. For each model, we compute the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to compare the optimal polynomial order for fitting the data with the number of knots and intervals for the splines model. Both AIC and BIC can help to identify the model that best balances fit and complexity, aiming to prevent overfitting by penalizing the use of excessive parameters. We compare the results that we got from applying the polynomial regression model with the splines model results in terms of point estimates, the mean sum of squared errors, and the fitted regression line. We can say that order five of the polynomial model may be used to estimate splines with five segments.展开更多
In this paper, a new spline adaptive filter using a convex combination of exponential hyperbolic sinusoidal is presented. the algorithm convexly combines an exponential hyperbolic sinusoidal Hammerstein spline adaptiv...In this paper, a new spline adaptive filter using a convex combination of exponential hyperbolic sinusoidal is presented. the algorithm convexly combines an exponential hyperbolic sinusoidal Hammerstein spline adaptive filter and a Wiener-type spline adaptive filter to maintain the robustness in non-Gaussian noise environments when dealing with both the Hammerstein nonlinear system and the Wiener nonlinear system. The convergence analyses and simulation experiments are carried out on the proposed algorithm. The experimental results show the superiority of the proposed algorithm to other algorithms.展开更多
基金financially supported by the National Natural Science Foundation of China (8225041038)the Sichuan Science and Technology Program (23NSFSC2916)the Fundamental Research Funds for the Central Universities, Southwest Minzu University (ZYN2024077)
文摘Based on the superiority of adaptive filtering algorithms designed with hyperbolic function-like objective functions,this paper proposes generalized spline adaptive filtering(SAF)algorithms designed with hyperbolic function-like objective functions.Specifically,a series of generalized new SAF algorithms are proposed by introducing the q-deformed hyperbolic function as the cost function,named SAF-qDHSI,SAF-qDHCO,SAFqDHTA&SAF-qDHSE algorithms,respectively.Then,the proposed algorithm is theoretically demonstrated with detailed mean convergence and computational complexity analysis;secondly,the effect of different q values on the performance of the new algorithm is verified through data simulation;the new algorithm still has better performance under the interference of Gaussian noise and non-Gaussian noise even when facing the system mutation;finally,the new algorithm is verified through the measured engineering data,and the results show that the new algorithm has better convergence and robustness compared with the existing algorithm.In conclusion,the generalized algorithm based on the new cost function proposed in this paper is more effective in nonlinear system identification.
基金supported by the National Natural Science Foundation of China(Nos.42030203,41974073,and 41404053)。
文摘This study creates a three-dimensional surface spline(3DSS)model of China's Mainland based on surface and CHAMP satellite observations.Through this model,the magnetic field analyses of domestic plateau(Qinghai-Tibet Plateau 28°N-38°N,78°E-102°E),plain(middle and lower reaches of Yangtze River Plain 27°N-34°N,111°E-122°E),and marine(parts of the East and South China Seas 16°N-30°N,123°E-136°E)areas have been investigated.Single models of plateau and plain have also been created.To compare and verify results,the corresponding two-dimensional(2DTY)and three-dimensional(3DTY)Taylor polynomial models have been derived.Issues such as the removal of disturbing geomagnetic fields,the data gap between surface and satellite level,and boundary effect are all seriously considered.With an aim to evaluate the resulting model,some randomly selected points are not join the modeling,by which we thereby inspected the results in terms of residuals,change rate absolutes,and Root Mean Square Error(RMSE).Results show that except component Y,the change rate absolutes of other components are less than 1%both in domestic and single models,which means that the modeling result of 3DSS is better than the other two models.Plateau and plain 3DSS models reflect the fine distribution of the magnetic field after comparison with domestic distribution.The 3DSS model fits the plateau best,followed by the plain,while the worst fit is in the marine area.This means that the modeling precision depends mainly on the number and distribution of measuring points.
文摘In this work, we seek the relationship between the order of the polynomial model and the number of knots and intervals that we need to fit the splines regression model. Regression models (polynomial and spline regression models) are presented and discussed in detail in order to discover the relation. Intrinsically, both models are dependent on the linear regression model. Spline is designed to draw curves to balance the goodness of fit and minimize the mean square error of the regression model. In the splines model, the curve at any point depends only on the observations at that point and some specified neighboring points. Using the boundaries of the intervals of the splines, we fit a smooth cubic interpolation function that goes through (n + 1) data points. On the other hand, polynomial regression is a useful technique when the pattern of the data indicates a nonlinear relationship between the dependent and independent variables. Moreover, higher-degree polynomials can capture more intricate patterns, but it can also lead to overfitting. A simulation study is implemented to illustrate the performance of splines and spline segments based on the degree of the polynomial model. For each model, we compute the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to compare the optimal polynomial order for fitting the data with the number of knots and intervals for the splines model. Both AIC and BIC can help to identify the model that best balances fit and complexity, aiming to prevent overfitting by penalizing the use of excessive parameters. We compare the results that we got from applying the polynomial regression model with the splines model results in terms of point estimates, the mean sum of squared errors, and the fitted regression line. We can say that order five of the polynomial model may be used to estimate splines with five segments.
基金supported by the National Natural Science Foundation of China (Grant No. 62371242, Grant No. 61871230)。
文摘In this paper, a new spline adaptive filter using a convex combination of exponential hyperbolic sinusoidal is presented. the algorithm convexly combines an exponential hyperbolic sinusoidal Hammerstein spline adaptive filter and a Wiener-type spline adaptive filter to maintain the robustness in non-Gaussian noise environments when dealing with both the Hammerstein nonlinear system and the Wiener nonlinear system. The convergence analyses and simulation experiments are carried out on the proposed algorithm. The experimental results show the superiority of the proposed algorithm to other algorithms.
